Chapter 5: Modeling and Analysis Chapter Resources & Downloads

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5.1 Opening Vignette: Dupont Simulates Rail Transportation System and Avoids Costly Expense
5.2 Modeling For MSS - Forecasting
5.5 Influence Diagrams (Including Software)
5.6 MSS Modeling With Spreadsheets
5.7 Decision Analysis of a Few Alternatives (Decision  Tables And Decision Trees) (Including Decision Analysis Software)
5.8 Optimization Via Mathematical Programming - Linear Programming Example and General Description of Modeling
5.10 Simulation
5.11 Multidimensional Modeling---OLAP
5.12 Visual Interactive Modeling and Visual Interactive Simulation
5.13 Quantitative Software Packages----OLAP
Exercises
Internet Exercises
Case Applications

Additional Web Material

WEB CASE APPLICATION W5.1: Visual Simulation for a Hospital Recovery Room
Additional Exercise
Group Exercise
Major Group Term DSS Project 3 (Long Description)

Web Appendices

Appendix W5-A: A Spreadsheet-based Economic Order Quantity Simulation Model
Appendix W5-B: The Analytic Hierarchy Process (AHP) Using Expert Choice
Appendix W5-C: Waiting Line Modeling (Queueing) in a Spreadsheet
Appendix W5-D: Visual IFPS/PLUS
Appendix W5-E: Visual IFPS/Plus and Spreadsheet Simulation Models

5.1 Opening Vignette: Dupont Simulates Rail Transportation System and Avoids Costly Expense

· Refers to ProModel Corporation, Orem, UT Web site (www.promodel.com) (p. 166).

5.2 Modeling For MSS

· Forecasting

Recall that decision making involves choosing an alternative course of action by evaluating the possible consequences of the alternatives. Although the choice is made today, the possible consequences often occur sometime in the future. Therefore, the quality of the decision largely depends on the quality of the forecast (see DeLurgio and Bhame, 1991; and Jain, 1996).

Forecasting models are an integral part of many MSS. One can build a forecasting model or one may use preprogrammed software packages such as Autobox (Automatic Forecasting Systems, Warminster, PA), and ForecastMaster (Scientific Systems Inc., Woburn, MA), ForecastPlus (Stat Pac Inc., Edina, MN), FUTURCAST (Futurion Inc., Ridgewood, NJ) and SmartForecast (Smart Software Inc., Belmont, MA). Also, many MSS development tools (e.g., financial planning languages and spreadsheets) have some built-in forecasting capabilities.

The Uses of Forecasts

The major use of forecasting, as it relates to modeling, is to predict the value of the model variables (often demand), as well as the logical relationships of the model, at some time in the future. The future time of interest depends on "when" we want to evaluate the results (Broadie and Glasserman, 1996). For example, in an investment decision we may be interested in prices and income a year from today, while in a capital investment decision we may be interested in projected prices and income during the next five years. Generally speaking, we distinguish between three types of forecasts: (a) short run (up to one year), where the forecast is used mainly in deterministic (certainty) models, b) intermediate term (1-3 years); and (c) long run (beyond three years), where the forecast is used in both deterministic and probabilistic models.

Forecasting Models and Methods

What happens in the future usually depends on a multiplicity of factors, most of which are uncontrollable. Furthermore, data availability, accuracy, cost, and the time required to make the forecast also play an important role. Because of this, several successful forecasting methods have been developed.

Forecasting methods can be grouped in several ways. One classification scheme distinguishes between formally recognized forecasting techniques and informal approaches such as intuition, spur-of-the-moment guesses, and seat-of-the-pants predictions. Our attention in this section is directed to formal methods, which can be divided into four categories: judgment methods, counting methods, time-series methods, and association or causal methods. Each category is briefly discussed below. For a more detailed discussion, see Turban and Meredith (1994).

Judgment Method. Judgment methods are those based on subjective estimates and expert opinion, rather than on hard data. They are often used for long-range forecasts, especially where external factors (e.g., technological or political developments) may play a significant role. They also are used where historical data are very limited or nonexistent, such as in new product/service introductions. For example, the best scheduling of a new television show on a network requires the expert opinion of the program director (Reddy, Aronson and Stam, 1998). Expert systems may be developed and used. Decision aids like Expert Choice may assist a manager in formulating forecasts.

Counting Methods. Counting methods involve some kind of experimentations or surveys of a sample data with an attempt to generalize about the entire market. These methods are primarily used for forecasting demand for products/services, a part of marketing research. This type of forecasting is quantitative, based on hard data and thus generally considered more objective than the previous types. Again, consider the example of television scheduling. Market sampling is performed to determine the markets to which certain shows or show types appeal. If "Monday Night Football" (which has a strong middle-aged male audience) is being aired on one network, a competing network might choose to air a show that appeals to women in the age range of 18-45. See Reddy, Aronson and Stam (1998) for details.

Time-series Analysis. A time series is a set of values of some business or economic variable, measured at successive (usually equal) intervals of time. For example, quarterly sales of a firm make up a time series, as does the population in a city (e.g., counted annually), the weekly demand for hospital beds, and so on. We undertake time-series analysis in decision making because we believe that knowledge of past behavior of the time series might help our understanding of (and therefore our ability to predict) the behavior of the series in the future. In some instances, such as the stock market, this assumption may be unjustified. See Figure W5.1A for an Excel spreadsheet example of exponential smoothing.

Figure W5.1A Excel Spreadsheet Model of an Exponential Smoothing Forecasting.
(Click on the image to enlarge.)
Click here to Save/Open the actual worksheet Figw5_1.xls.
 
 
 

Figure W5.1B Chart of the Excel Spreadsheet Model of an Exponential Smoothing Forecasting.
(Click on the image to enlarge.)

Association or Causal Methods. Association or causal methods include data analysis for finding data associations and, if possible, cause-effect relationships. They are more powerful than the time-series methods, but they are also more complex. Their complexity comes from two sources: First, they include more variables, some of which are external to the situation. Second, they use sophisticated statistical techniques for segregating the various types of variables. Causal approaches are most appropriate for intermediate term forecasting.

Generally speaking, judgment methods, which are subjective in nature, are used in those cases where quantitative methods are inappropriate. Time pressure, lack of data, or lack of money may prevent the use of quantitative models. Complexity of historical data (due to interactions or fluctuations, for example) may also inhibit the use of historical data.

Keep the following in mind:

• Most models require some forecasting, but no one is a perfect forecaster.
• Neural network-based forecasting methods are becoming increasingly more important.

The latest development in improved forecasting techniques is the use of neural networks (see Chapters 16 and 17), and examples of methods and applications in Hill et al. (1996).

There is an excellent handbook on forecasting (Armstrong, 2001) available. It includes a set of forecasting principles (in Section 20), and a software review (in Section 19). Though expensive it would be a worthwhile purchase by someone who forecasts for a living.

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Forecasting Questions for Discussion

1. Describe judgmental forecasting methods.

2. What is time-series analysis?

3. What are causal forecasting models?

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Forecasting Exercise

1. Explain how to perform forecasting in a spreadsheet.

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Sample List of Forecasting Packages
 
 

Software	Company
Autocast II	Delphus, Inc. Morristown, NJ
Crystal Ball 2000	Decisioneering, Inc. Denver, CO
Forecast Pro for Windows	Business Forecast Systems, Inc.  Belmont, MA
SmartForecast	Smart Software, Inc.  Belmont, MA
Solo Statistical Software	BMDP Statistical Software, Inc.  Los Angeles, CA

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Forecasting References

Armstrong, J.S. (ed.). (2001). Principles of Forecasting: A Handbook for Researchers and Practitioners. Boston: Kluwer Academic Publishers. Also see the companion Web site (www.forecastingprinciples.com).

Broadie, M. and P. Glasserman. (1996, February). "Estimating Security Price Derivatives using Simulation." Management Science. Vol. 42. No. 2. 269-285.

DeLurgio, S. and C. Bhame. (1991). Forecasting Systems for Management. Homewood, IL: Business One Irwin.

Hill, T., M. O’Connor and W. Remus. (1996, July). "Neural Network Models for Time Series Forecasts. Management Science. Vol. 42. No. 7. 1082-1092.

Jain, C. L. (1996, Summer). "Monthly Corporate Forecast Meeting." Journal of Business Forecasting Methods & Systems. Vol. 15. No. 2. p. 2, 28.

Lim, J. S. and M. O’Connor. (1996). "Judgmental Forecasting with Interactive Forecasting Support Systems. Decision Support Systems. Vol. 16. 339-357.

Reddy, S., J. E. Aronson and A. Stam. (1998). "SPOT - Scheduling Programs Optimally for Television." Management Science. Vol. 44. No. 1. January. 83-102.

Turban, E. and J. Meredith. (1994). Fundamentals of Management Science, 6th ed. Homewood, IL: Irwin.

5.5 Influence Diagrams

· Software (pp. 173-175)
 

Software Name	Company Name	Web Site
Analytica	Lumina Decision Systems, Los Altos, CA	www.lumina.com
DecisionPro	Vanguard Software Corporation, Cary, NC	www.vanguardsw.com
DATA Decision Analysis Software	TreeAge Software Inc., Williamstown, MA	www.treeage.com
Decide Decision Analysis Tool	DecisiveTools, L.L.C., Denver, CO	www.decisivetools.com
Precision Tree	Palisade Corporation, Newfield, NY	www.palisade.com

5.6 MSS Modeling With Spreadsheets

· Click to Save/Open the Excel file for Figure 5.3: Excel Spreadsheet Static Model Example of a Simple Loan (p. 177 of the text).

· Click to Save/Open the Excel file for Figure 5.4: Excel Spreadsheet Dynamic Model Example of a Simple Loan (p. 178 of the text).

5.7 Decision Analysis of a Few Alternatives (Decision Tables And Decision Trees)

· Decision Trees (p. 180).

Refers to TreeAge Software Inc., Williamstown, MA, Web site (www.treeage.com) and Palisade Corporation, Newfield, NY, Web site (www.palisade.com).

Decision Analysis and Multicriteria Decision-making Software Packages

Company Name	Web site
Vanguard Software Corporation	www.vanguardsw.com
Expert Choice Inc.	www.expertchoice.com
Systems Analysis Laboratory,  Helsinki University of Technology	www.hipre.hut.fi
Logical Decisions Group	www.logicaldecisions.com

o DSS In Action 5.1: Solving Multicriteria Problems, refers to Web site www.expertchoice.com and on this book’s Web site alternative software packages for handling multicriteria problems.
 
 

Analytical Hierarchy Process (AHP) Software Packages

Package	Company	Web Site
AliahTHINK!	Aliah, Inc.	www.aliah.com (not available)
Criterium Decision Plus	Infoharvest, Inc.	www.infoharvest.com
Expert Choice	Expert Choice Inc.	www.expertchoice.com
Logical Decisions	Logical Decisions	www.logicaldecisions.com
Web Hipre	DECISIONARIUM Systems Analysis Laboratory Helsinki University of Technology	www.decisionarium.hut.fi

For more Decision Analysis Software vendors, see OR/MS Today's Decision Analysis Software Survey at www.lionhrtpub.com/orms/surveys/das/vendors.html.

For further details, see Buede (1996), and Greenfield (1996).

Buede, D.  (1996, August)."Decision Analysis Software Survey: Aiding Insight III," OR/MS Today. 73-79.

Greenfield, L. (1996, November 17). "Decision Analysis Tools," The Data Warehousing Information Center Web page: pwp.starnetinc.com/larryg/decision.html).

5.8 Optimization Via Mathematical Programming

· Linear programming (p. 184)
We refer often to two excellent products from Lindo Systems Inc., Chicago, IL (www.lindo.com). Lindo is a linear programming system that lets you state the problem pretty much the same way as the formal mathematical expression. Lindo allows for integer variables. Lingo is a modeling language. Lingo lets you define sets and work with them using functions such as SUM, etc. It also can interface with database systems directly, allowing you to develop a data management system easily around the model. Lingo can be used to model and solve nonlinear and integer problems as well. We also refer to the "Blending Problem," a classical example of linear programming, which follows:

Linear Programming: The Blending Problem (Minimization)

In Chapter 2, we presented a simple product-mix problem and formulated it as an LP. Here, we introduce another classical LP problem called the blending problem.

In preparing Sungold paint, it is required that the paint have a brilliance rating of at least 300 degrees and a hue level of at least 250 degrees. Brilliance and hue levels are determined by two ingredients, Alpha and Beta. Both Alpha and Beta contribute equally to the brilliance rating; one ounce (dry weight) of either produces one degree of brilliance in one drum of paint. However, the hue is controlled entirely by the amount of Alpha; one ounce of it producing three degrees of hue in one drum of paint. The cost of Alpha is 45 cents per ounce, and the cost of Beta is 12 cents per ounce. Assuming that the objective is to minimize the cost of the resources, then the problem is to find the quantity of Alpha and Beta to be included in the preparation of each drum of paint.

Formulation of the Blending Problem. The decision variables are:

x₁ = Quantity of Alpha to be included, in ounces, in each drum of paint
x₂ = Quantity of Beta to be included, in ounces, in each drum of paint

The objective is to minimize the total cost of the ingredients required for one drum of paint. Since the cost of Alpha is 45 cents per ounce, and since x₁ ounces are going to be used in each drum, then the cost per drum is 45 x₁. Similarly, for Beta the cost is 12 x₂. The total cost is, therefore, 45 x₁ + 12 x₂, and, as our objective function, it is to be minimized, subject to the constraints (relationships among the variables) of the following specifications:

1. To provide a brilliance rating of at least 300 degrees in each drum. Since each ounce of Alpha or Beta increases the brightness by one degree, the following relationship exists:

Supplied by Alpha Supplied by Beta Demand

1 x₁ + 1 x₂ > 300

2. To provide a hue level of at least 250 degrees, the effect of Alpha (alone) on hue can similarly be written as:

Supplied by Alpha Supplied by Beta Demand

3 x₁ + 0 x₂ > 250

3. Negative quantities of Alpha and Beta are not allowed (one cannot remove nonexistent chemicals from a drum of paint), so, we have nonnegativity constraints that are written as:

x₁ > 0
x₂ > 0

In summary, the blending problem is formulated as follows: Find x₁ and x₂ that

Minimize z = 45 x₁ + 12 x₂
subject to

1 x₁ + 1 x₂ > 300 (brightness specification)
3 x₁ + 0 x₂ > 250 (hue specification)
   x₁ ,     x₂> 0 (nonnegativity)

Solution.

The model is shown in the Excel Worksheet in Figure W5.2 and its solution using the Solver Tool is shown in Figure W5.3. The optimum found by Solver in Excel and Lindo is
                                      x₁ = 83.333
                                      x₂ = 216.667
                                    Total cost = $63.50

Note: The solution that is good for one drum will be correct for many drums as long as capacity or other constraints are not being violated. Optimization models are frequently included in decision support implementations as is shown in DSS In Action 5.2 and 5.3.

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Figure W5.2 Excel Spreadsheet: Initial Model of the Linear Programming Blending Problem.
(Click on the image to enlarge.)

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.
 
 
 

Figure W5.3 Excel Spreadsheet: Solver Solution Run for the Linear Programming Blending Problem.
(Click on the image to enlarge)

Click here to Open/Save the Excel File Blend.xls .

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File Blend.tak Contents:

MIN .45 x1 + .12 x2
SUBJECT TO
DEMAND1)   x1 + x2 >= 300
DEMAND2) 3 x1      >= 250
END
LEAVE

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File Blend.out Contents:
Here are the Results of a Run of Lindo in Solving the Blending Problem.

  MIN     0.45 X1 + 0.12 X2
  SUBJECT TO
   DEMAND1)   X1 + X2 >=   300
   DEMAND2)   3 X1 >=   250
  END

 LP OPTIMUM FOUND AT STEP      2

        OBJECTIVE FUNCTION VALUE

        1)      63.50000

  VARIABLE        VALUE          REDUCED COST
        X1        83.333336          0.000000
        X2       216.666672          0.000000
 

       ROW   SLACK OR SURPLUS     DUAL PRICES
  DEMAND1)         0.000000         -0.120000
  DEMAND2)         0.000000         -0.110000

 NO. ITERATIONS=       2

 RANGES IN WHICH THE BASIS IS UNCHANGED:

                           OBJ COEFFICIENT RANGES
 VARIABLE         CURRENT        ALLOWABLE        ALLOWABLE
                   COEF          INCREASE         DECREASE
       X1        0.450000         INFINITY         0.330000
       X2        0.120000         0.330000         0.120000

                           RIGHTHAND SIDE RANGES
      ROW         CURRENT        ALLOWABLE        ALLOWABLE
                    RHS          INCREASE         DECREASE
  DEMAND1      300.000000         INFINITY       216.666672
  DEMAND2      250.000000       650.000000       250.000000
 
 

Figure W5.4 Lindo Run: Linear Programming Model of the Blending Problem (TAKE File) and Output (DIVERT File).

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General LP Formulation and Terminology

Let us now generalize the formulation. Every LP problem is composed of:

Decision Variables. The variables whose values are unknown and are searched for. Usually they are designated by x₁,..., x₂ , and so on.

Objective Function. This is a mathematical expression, given as a linear function, that shows the relationship between the decision variables and a single goal (or objective) under consideration. The objective function is a measure of goal attainment. Examples of such goals are total profit, total cost, share of the market, and the like.

If the managerial problem involves multiple goals, one can use the following two-step approach:

1. Select a primary goal whose level is to be maximized or minimized.
2. Transform the other goals into constraints indicating acceptable lower and upper limits, which must only be satisfied. For example, one may attempt to maximize profit (the primary goal) subject to a growth rate of at least 12 percent per year (a secondary goal). There are many alternative approaches to multiple-objective optimization. One is to weight the goals based on importance into a single objective function. Another seeks to obtain the decision maker’s economic utility functions for each goal. This is beyond the scope of this material.

Optimization. Linear programming attempts to either maximize or minimize the value of the objective function, depending upon the model’s goal.

Coefficients of the Objective Function. The coefficients of the variables in the objective function (e.g., 45 and 12 in the blending problem) are called the profit (or cost) coefficients. They express the rate at which the value of the objective function increases or decreases by including in the solution one unit of each of a corresponding decision variable.

Constraints. The maximization (or minimization) is performed subject to a set of constraints. Therefore, linear programming can be defined as a constrained optimization problem. These constraints are expressed in the form of linear inequalities (or sometimes equalities). They reflect the fact that resources are limited, or the constraints specify some requirements; and that the variables are related strictly through constants multiplied by variables.

Input-Output (Technology) Coefficients. The coefficients of the constraints' variables are called the input-output coefficients. They indicate the rate at which a given resource is depleted or utilized. They appear on the left-hand side of the constraints.

Capacities. The capacities (or availability) of the various resources, usually expressed as some upper or lower limit, are given on the right-hand side of the constraints. The right-hand side also expresses minimum requirements.

Example. These major components of a linear programming model are illustrated for the blending problem:

Find x₁ and x₂ (decision variables) that minimize the value of the linear objective function z:
                                     z = 45 x₁ + 12 x₂
                                (cost coefficients are 45 and 12
                               decision variables are x₁ and x₂ )

subject to the linear constraints:
                                     1 x₁ + 1 x₂ > 300
                                     3 x₁ + 0 x₂ > 250
                              (input-output coefficients are 1,1; 2,0
                            capacities or requirements are 300 and 250)

Optimization functions are available in many DSS tools. However, optimization packages are available as add-ins for Excel and other DSS tools. Also, it is relatively easy to interface other optimization software with Excel, database management systems, and similar tools.

5.10 Simulation

· Object-oriented Simulation (p. 192) refers to CACI Products Company Web site (www.caciasl.com).

· Risk analysis in spreadsheets: The economic order quantity simulation model referred to on p. 177 and p. 193 appears below in a Web Appendix.

· The spreadsheet simulation model for evaluating a simple cash-flow problem (p. 193) is a simple risk model. Click on the file name to get it: Simcashflow.xls.

5.11 Multidimensional Modeling---OLAP

· Refers to Cognos Inc. Web site (www.cognos.com) and Cognos (2000) (P194)
· Vendors of OLAP Systems (p. 197) are listed in the table below:

5.12 Visual Interactive Modeling and Visual Interactive Simulation

· Visual Interactive Simulation

Refers to Orca Computer Inc., Web site www.orcacomputer.com (p. 199).

· Visual Interactive Models And DSS

o For examples of Operations Management Examples of VIM in DSS - see the various simulation software vendor Web sites - especially ProModel and GPSS (p. 200).

o Refers to the IMAGE Society Inc. Web site www.public.asu.edu, which is not available; see the Society for Imaging Science and Technology Web site www.imaging.org instead, and Computer Simulation International Web site www.scs.org (p. 201).

5.13 Quantitative Software Packages----OLAP

• Refers to OR/MS Today (1999) - see their Web site at www.lionhrtpub.com/ORMS.shtml (p. 201)

• Sample of Statistical Packages (p. 202)

 

Company Name	Web Site
SPSS Inc., Chicago, IL	www.spss.com
Minitab Inc., State College, PA	www.minitab.com
SAS Institute Inc., Cary, NC	www.sas.com
TSP International, Palo Alto CA	www.tspintl.com
StatPac Inc.	www.statpac.com

• Management Science (Analytical Modeling) Packages (p. 202)

 

Company Name	Web Site
INFORMS Online	www.informs.org
Lionheart Publishing Inc.	www.lionhrtpub.com
Computer Simulation International	www.scs.org

• Other Specific DSS Applications
 

Company Name	Software	Web Site
Lindo Systems Inc.,Chicago, IL	Lindo, Lingo	www.lindo.com
Frontline Systems Inc., Incline Village, NV	Solver	www.frontsys.com
Palisade Corporation, Newfield, NY	@Risk, Evolver	www.palisade.com
Promised Land Technologies Inc., New Haven, CT	BrainCel	www.promland.com

• Examples of Neural Network Software that produce c++ code (p. 203)
 

Company	Product	Web Site
California Scientific Software	Brainmaker	www.calsci.com
NeuralWare	NeuralWorks	www.neuralware.com
Trajan Software Ltd.	Trajan 6.0 Professional	www.trajan-software.demon.co.uk
Ward Systems Group, Inc.	NeuroShell	www.wardsystems.com

Most of these packages also include very flexible interfaces (Excel, databases, etc.)

 
 
• Representative Ready-made Specific DSS

 

Name of Package	Vendor	Description
AutoMod, AutoSched	AutoSimulations Bountiful, UT www.autosim.com	3 D true-scale walk-through animations for manufacturing and material handling; Short interval manufacturing scheduling and capacity analysis
Budgeting & Reporting	Helmsman Group, Inc. Plainsboro, NJ www.helmsmangroup.com	Financial data warehousing
FACTOR/AIM PACKAGING	Frontstep, Inc, Columbus, OH www.frontstep.com (was Pritsker Corp. Indianapolis, IN www.pritsker.com)	Manufacturing simulator with costing capabilities, High speed/high volume food and beverage industry simulator
MedModel, ServiceModel	ProModel Corp. Orem, UT www.promodel.com	Healthcare simulation software, Service industry simulation software
OIS	Olsen & Associates Ltd. Zürich, Switzerland www.olsen.ch	Directional forecasts, trading models, risk management
OptiPlan Professional, OptiCaps, OptiCalc	Advanced Planning Systems, Inc. Alpharetta, GA	Supply chain planning
FlexSim (was Taylor II)	Flexsim Software Products, Corp. Orem, UT www.flexsim.com	Manufacturing and material handling simulation environment
PLANNING WORKBENCH	Prescient Systems, Inc. West Chester, PA www.prescientsystems.com	Graphics-based planning system for the process industry
PROVISA	The Lanner Group (AT&T) Solon, OH	Finite capacity scheduling for manufacturing
Solver, Scheduler, Planner	ILOG Mountain View, CA	Constraint-based reasoning engine for budget resource allocation
StatPac Gold	Stat Pac Inc. Edina, MN www.statpac.com	Survey analysis package
TRAPEZE	Trapeze Software Group Mississauga, ON www.trapsoft.com	Planning, scheduling and operations for fixed route, demand-responsive and flexible route operations
TruckStops, OptiSite, BUSTOPS	MicroAnalytics, Inc. Arlington, VA	Distribution management and transportation

Virtual Reality Sources (As Related to VIS/VIM)

Software	Organization	Description
Consulting VR	Space/Management Programs Inc. www.space-chi.com	Virtual Reality and Visual Simulation Design Firm
RealiView RealiMation Space-Time Editor	DataPath Limited Derby, England www.datapath.co.uk	Computer Animation Visual Models
	ZFX Animation Kingsport, TN	Animation, Visual Simulation

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Exercises

5.c. Refers to Palisade Corporation Web site www.palisade.com (p. 208).

13. Refers to Web-Hipre Web site www.hipre.hut.fi (p. 211).

14. Lindo is available from Lindo Systems Inc.'s Web site www.lindo.com (p. 211).

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Internet Exercises

 6. Refers to SAS Institute Inc. Web site www.sas.com, SPSS Inc. Web site www.spss.com , CACI Products Company Web site www.caciasl.com, Lindo Systems Inc. Web site www.lindo.com (p. 213).

Case Application 5.2

Refers to Expert Choice Inc., Pittsburgh, PA Web site www.expertchoice.com (p. 217). Click on the three file names to obtain the Expert Choice model files: Scott.def, Scott.ec1, and Scott.lst.

The Lingo Modeling Language And The Access Database Integration refers to the Lindo Systems Inc. Web site www.lindo.com (p. 222).

Web Case Application W5.1: Visual Simulation for a Hospital Recovery Room

An often crowded recovery room led to a study of the main operating theatre suite in a large British general hospital which consists of six operating theatres together with a common postoperative recovery unit. Management was concerned about the level of throughput of the system. Senior medical staff felt that insufficient recovery spaces had been provided when the suite of theaters had been built which, if correct, was a physical constraint requiring considerable financial investment to remedy. They also thought that shortage of porters (to get the patients from the wards to theatre and back) and recovery nurses were current operational problems.

The study was undertaken to identify delays and restrictions in the system (due to resource imbalances) by using a visual interactive simulation (VIS) model to explore the relationship between various throughput levels and resource allocations. In particular, the VIS model was used to investigate extreme loadings of the system because of the very high capital cost that would be required if additional recovery spaces were to be provided. In addition, and indeed before being able to consider the "hard" aspects of such a system, the researchers had to understand the relationships among the various groups of health-service staff who constituted the "soft" part of the system.

While there was no evidence of delays due to the shortage of recovery spaces there were occasions when all recovery spaces were in use, i.e., when the system was at its limit. Any increase in throughput was therefore likely to lead to delays due to the nonavailability of recovery spaces. To investigate the effects of throughput increases, a VIS model of the system was constructed.

A major benefit of using visual interactive simulation in hospitals is that it enables the medical, administrative, and nursing staff to understand suggested changes to the system being modeled more easily. This proved to be the case in this study also.

Visual interactive simulation has two prime advantages: first it enables those who work in the system being modeled to validate the model, i.e., to become convinced that the model is a reasonable and accurate representation of reality; second, it provides a convenient means for the decision makers to consider different ways of running the system. Simulation cannot provide an answer to "What is the best feasible solution?" A process of trial and error or intelligent guesswork has to be used to get an understanding of the inter-relationships and then some fine tuning can follow to obtain better solutions. Simulation allows experimentation in a safe environment for testing new scenarios before deciding which changes, if any, should be implemented. The model turned out to be a complicated scheduling problem involving theatres, surgical teams, anesthetists, recovery nurses, and porters.

An advantage of VIS is that those with an intimate knowledge of the actual system can provide some measure of validation by checking how well what is happening on screen captures reality. The model was a reasonable representation of reality as was justified in that there were no major differences between the observations and the outputs from the model.

Several scenarios of the model were run to check the effect of varying the number of porters and scheduling more sessions (operations) per week. An increase of the number of scheduled sessions by 28 percent, from 47 to 60 per week, resulted in one scenario in an increase in patients by 22 per cent. This extra workload was capable of being dealt with by an 11 percent increase in nursing recovery hours with a similar level of service as measured by the average wait of patients due to the unavailability of nurses. There was very little evidence of delays due to unavailability of recovery spaces, but there was a proportional increase in the number of occasions when all spaces were in use.

Given that in general it was found that the available recovery spaces were sufficient to service the six theatres when all were scheduled and the very large capital cost represented by a modern six-suite theatre block, it would seem worth further investigation as to whether or not more of the necessary support staff should be recruited by the hospital management to make full use of it.

A worst case scenario in the recovery unit was modeled and tested. To eliminate the porters as a constraint, six were allocated in the model. Various combinations of the numbers of spaces and recovery nursing hours were tried and a typical equilibrium result required 14 spaces and 485 recovery nursing hours.

In theory, very large increases in throughput can be accommodated with quite modest increases in the number of recovery spaces. Recovery spas, including building work and equipment, are very expensive to provide, and this very unlikely worst case scenario demonstrates that the maximum number of any new spaces should be limited to five, which was seven less than originally believed to be necessary.

The major benefit of this study was that it resulted in a much greater understanding of the interconnected complexity of the overall system on the part of the various groups of staff involved. There is no simple answer to the original problem of increasing throughput.

The model yields useful information for such decisions in terms of the likely impact on the flow of patients of one less or one more porter and of similar changes in recovery nursing staff. The worst case scenario also helps management to put an upper limit on any proposed increase in recovery spaces. Essentially, the VIS model was used to focus on the issues and discover that no increase in facility size was necessary -- just better scheduling.

(Condensed from W. E. McAleer, J. A. Turner, D. Lismore and I. A. Naqvi, "Simulation of a Hospital’s Theatre Suite," Journal of Management in Medicine, Vol. 9, No. 5, 1995, 14-26.)

Case W5.1 Questions

1. Why is this scheduling problem so complex?

2. What are the real issues in this case? At the start of the study, did the stakeholders really understand what options were feasible? Why or why not?

3. How did the visual interactive simulation model help the hospital’s management focus on the issues?

4. How did the visual interactive simulation model get the various stakeholders to buy into its results?

5. How could the VIS developers modify their model to describe emergency room operations or the cafeteria operations?

Additional Exercise

W5.1. The Maximum Diversity Problem and a Heuristic. A new optimization model, called the Maximum Diversity Problem, describes the situation of selecting a group of m items (people, etc.) from a total set of n, while trying to maximize the interaction or differences among the items selected. By way of a fictional illustrative example, the mayor of the city of Athens, GA, Gwen, wants to form a diverse committee to investigate an important matter and provide advice. She has selected 7 potential members and wants to choose 3 of the 7 (usually problems like this are much larger and involve selecting on the order of 10 people from a group of 100 or more). Her expert staff has looked into a number of factors that can contribute to diversity. They might be income level, gender, race, political party, membership, age, job function, location of home, rent vs. own home, education area, education level, etc. (these are not meant to be discriminatory -- items like these contribute to diversity). From these individual items for each person, her staff has scaled and combined the results in a weighted fashion to develop a measure of diversity (or dissimilarity), d_ij = the ‘interaction’ between person i and person j. All the measures are compiled into the diversity matrix below:
 
 

So, if say we choose people 1, 3, and 6, 1 interacts with 3 at a ‘value’ of 3, 1 interacts with 6 at a value of 6, and 3 interacts with 6 at a value of 3 for a total interaction of 3 + 6 + 3 = 12. Although Mayor Gwen’s talented staff can develop the measures, they cannot solve the problem directly, because this is actually one of those large-scale combinatorial problems (many possible solutions to explore).

a. Fortunately, heuristics can be applied to obtain relatively close to optimal solutions. Identify a high quality solution by selecting 3 out of the 7 potential candidates. How did you make the selection? Describe the ‘heuristic’ you developed and used. What heuristic methods did not work well?

b. Write a computer program to evaluate all possible solutions (and store the best solution found at every iteration). Let it run for about 15 minutes. (Figure this out by solving 100 solutions, and then determine how many you need to get to 15 minutes.) Did it evaluate all the possibilities? How close is its best solution to yours? Try a larger problem, say choose 5 out of 20 people (use random data).

c. Write a computer program to execute your heuristic. Compare it’s results to those from the program developed in part b. Can you improve upon it?
 

Group Exercise

Visit a local business that inventories something (such as a store, manufacturing company, auto repair shop, or fast food restaurant). Interview the owner or manager about the inventory policies (and models if any) that they use. Do they match the standard assumptions of the EOQ model? If not, what is different? Who developed their policy? Why is it being used? Is it accurate? Do they use the EOQ model to make estimates of the order quantities? If so, explain how. See whether you can estimate (with the owner or manager) the values of the parameters used in the models above. Try the parameters in the model and compare the results to the real system. How closely do they match? If they do not use the EOQ model, why not? Or could they? Do they have a demand forecasting method in operation (see Section W5.1 above)? Write up your results in a report.

Major Group Term DSS Project 3 (Long Description)

Part 1: Learn about the Model

The transportation problem is a classical linear programming specialization that has had major impact in commodity distribution since it was first solved in 1941. The model essentially indicates what to ship where at a minimum cost. There are supplies, demands, and known unit costs of shipping. For example, the Swissvale Soup Company may be shipping crates full of soup from two factories or supplies (Pittsburgh and San Francisco - cities numbered 1 and 2) to two regional warehouses or demands (Dallas and Boston - cities numbered 3 and 4). The raw data describing this problem on a weekly basis can be stated in the following table:
 
 

Pittsburgh has 130 crates of soup available per week, while San Francisco has 210. Dallas requires 200 crates, while Boston requires 140. The per unit shipping costs are $15 from Pittsburgh to Dallas, etc.

The problem may be represented on a graph and is one of the best-known network programming problems:

The linear programming model of this problem may be defined as:

Let x_ij = the amount shipped from supply i (i = 1,2) to demand j (j = 3, 4); c_ij = the unit shipping cost from supply i to demand j (see the table); s_i = available supply of crates of soup at supply i, and d_j = soup crates required at demand j.

There is a variable for every potential pair of cities for which ‘flow’ may occur. There is a constraint for every supply and every demand point (node). The supply constraints ensure that each supply provides its available resource to the system, while the demand constraints ensure that each demand point draws its needed requirements from the system. The objective is to minimize the total cost of shipping.

Minimize Total Cost = 15 x₁₃ + 12 x₁₄ + 18 x₂₃ + 23 x₂₄

Subject to

Supply 1: x₁₃ + x₁₄ = 130

Supply 2: x₂₃ + x₂₄ = 210

Demand 3: x₁₃ + x₂₃ = 200

Demand 4: x₁₄ + x₂₄ = 140

and the nonnegativity constraints are:

x_ij ³ 0, for i = 1, 2; j = 3, 4.

a. Model and solve this problem in Excel. First set this up and use trial and error to try to establish a solution. Then, use the Solver Tool. Also solve this in a dedicated Linear Programming (such as Lindo or QSB 2+) or network programming (or transportation problem solver) (such as QSB 2+ or NETFLO) Package.

b. Note that the total supply must equal the total demand. If there is too much supply, we add a dummy demand city (with a demand equal to the excess supply). The excess supply would simply not be produced and shipped. If it ‘must’ be, then, let the model decide the most efficient way to cut back the factories’ production. Similarly, if there is too much demand, we add a dummy supply with a capacity to provide the missing soup. Conceptually, that means that there will be customers going without their soup when supplied from the fictional warehouse. (It is possible to identify alternative sources that could supply the product and use the actual cost of shipping plus whatever additional costs are incurred - the penalty - for using it.)

Suppose both Pittsburgh and San Francisco each have 200 crates of soup available per week for shipping. Model and solve this problem (don’t forget the dummy demand). Then, examine the effect of lowering the available supplies of Pittsburgh and San Francisco by equal amounts (to 170 each) - solve this problem, and compare the results to the solution to the original problem. What happened?

c. Since this is only one week of Swissvale Soup’s shipping operations, one should consider developing a dynamic model. One way to handle this is to develop a larger transportation problem framework. For example, suppose we allow inventory and backordering. Inventory costs $2 per unit per week in Pittsburgh, and $2.30 per unit per week in San Francisco; while backordering costs $3.50 and $4.10 in the supplies, respectively. This will allow Swissvale Soup to smooth production of soup and technically meet demand over time. Suppose the soup demands over the next 4 weeks are
 

Supplies remain fixed at 130 and 210 per week for Pittsburgh and San Francisco, respectively.

One extension of the model is relatively simple (see Aronson, 1989; and Bowman, 1956). Repeat each supply in every time period for a total of 8. Repeat each demand as well. If the total supply does not equal the total demand, add a dummy supply or demand as needed. Then, a variable that represents shipping from a supply to a demand in the future indicates that a period of inventory is invoked for every period forward you go. For example, let i = 1, 2, 3, 4, ..., 8 represent the supplies, j = 9, 10, 11, 12, ..., 16. Supply 3 is actually supply 1 in period 2. Demand 14 is actually demand 4 (Boston) in period 3. So, the inventory for two weeks must be charged (in Pittsburgh), and c_3,14 = 15 + 2 + 2 = 19. When shipping from "now" to meet demand in the "past," backordering charges are likewise invoked.

Model this problem and solve it as you did in part a.

d. Advanced part - check some references and develop a transshipment model version of the part c situation. Model and solve it. (Hint, see Aronson, 1989).

Part 2: Develop a Working Prototype of a Complete DSS

One of the major problems in DSS development is that the components do not necessarily glue together readily. Another major problem is that many optimization packages require specific types of variable names (x1, x2, etc.) while more meaningful descriptions are required for decision makers ("Crates of soup shipped from Pittsburgh to Boston", etc.). Though, we have not yet covered the details of the user interface component of DSS in detail (see Chapter 7), it is time to learn about developing a DSS based on two real-world DSS projects similar to one in which one author was involved. This project involves building a model-based DSS using generator tools to ease up on the efforts. The real difficult part will be in providing the cement among the three components: the DBMS, the MBMS and the user interface. The problem to be implemented is that of a transshipment problem (see Part 1) (if desired, the transshipment problem mentioned in Part 1d, or a pure linear programming model may be substituted).

Develop a PC-based DSS, in a PC database package, say Microsoft Access, to manage the input data to a network optimization system, independent of the database. Basically, the DBMS should handle all the data definitions, data storage and data manipulation, and data validation and verification (basically, the model structure and managerially meaningful names for the locations and shipping links). The DBMS also should handle the user interface. Then, determine how to interface the data from the DBMS with an optimization package (like QSB 2+, Lindo, or Excel Solver). Once the data are verified as OK, the DBMS will produce an input file for the optimizer (so you must determine the input file format required), run the optimizer (in DOS, you can pipe commands directly into software by putting them in a file and use the < symbol as in

QSB <optcmd.cmd - the DBMS may need to create this file as well), and retrieve data from its output file into another database. Windows-based systems are more seamlessly integrated. From this database of results, the DBMS must match up the variables from the optimizer with managerially meaningful terms and produce a screen and report that is usable. You may also want to define reports with a special report database.

DSS Operational Summary

• The DBMS provides a user interface.
• The DBMS stores the shipping data and allows the user to edit it, and verify its integrity.
• The DBMS produces a model input file and a command file that the optimizer can read.
• The DBMS invokes the optimizer that automatically solves the problem.
• The DBMS reads the output file from the optimizer into a result database.
• The DBMS synthesizes usable reports from the result database. These may be queried online or printed.

References for Major Group Term DSS Project 3

Aronson, J. E. (1989). "A Survey of Dynamic Network Flows." Annals of Operations Research, Vol. 20. pp. 1-66.

Bowman, E. H. (1956). "Production Scheduling by the Transportation Method of Linear Programming." Operations Research. Vol. 4. No. 2. pp. 100-103.
 

Appendix W5-A: A Spreadsheet-based Economic Order Quantity Simulation Model

We show the development of an example of a simulation model in a spreadsheet. We use the well-known Economic Order Quantity (EOQ) model (see Turban and Meredith, 1994; or Hillier and Lieberman, 1995). In the basic EOQ inventory model (see Chapter 1), we assume constant annual demand (continuous demand over time) (D = 1,200 boxes of widgets or whatever), a fixed ordering cost (K = $5.00), a holding cost (H = $1.20) (usually a percentage of the unit cost). All costs and the demand are constant (total certainty) and independent. Since this decision is made once, this is a static model. The decision variable Q represents the quantity ordered. The total inventory cost (TC) is the sum of annual ordering costs (T_O) and inventory carrying costs (T_H). (Note: on average, there are Q/2 boxes in stock - but you need enough space to store Q items.)

TC = T_O + T_H = KD / Q + H (Q / 2) = $5(1200) / Q + $1.20 (Q / 2) = $6000 / Q + $.60 Q

To find the minimum of the total cost TC, we can take three different approaches.

1. We can plot values for TC as a function of Q and visually identify the minimum of TC (see Exercise 1).

where SQRT means square root.

Because the annual demand is 1,200, an order is placed 1200/100 = 12 times per year or once per month.

The total inventory cost is:

TC = $6000 / 100 + $.60 (100) = 60 + $60 = $120

These formulas are implemented in the small, deterministic (under assumed certainty) DSS spreadsheet model shown in Figure W5.6.
 
 

The Simulation Model

Suppose now that the demand is considered under risk. Based on the EOQ computation above, we plan to order once per month, but demand follows a normal probability distribution with a mean of 100 boxes and a standard deviation of 10 boxes per month. Now we must develop a dynamic risk model to determine the best (or at least a very good) order quantity. In addition to the other costs, there is a cost of running out of boxes - there is a fixed stockout cost of $10 (paid only once in a month and only if we stock out) and a per unit stockout cost of $0.25 (because of the lost customer goodwill).

Clearly, if we adopt a policy of ordering the EOQ = 100, there is a 50 percent chance of a stockout in any month (why?). This is the case of no buffer stock. Thus, we should consider having some buffer stock by ordering more than 100 boxes. By ordering more, we then lessen the likelihood of a stockout, saving money, but we invoke additional inventory costs. We can evaluate this situation in the Excel-based simulation model, shown in Figure W5.7a,b,c. The results are shown for 5 years, broken down by each of the 60 months for a buffer stock of 0.
 
 

The cell formulas and explanations are given in the table below for cells that do not clearly indicate what they are (simple numbers or labels).
 

At the top of the worksheet are the standard EOQ calculations. The next section summarizes the results of the 60-month run: the average Total Monthly Cost is $16.13 translating to a one-year expense of $193.55. There were 28 stockouts (quite excessive) over the 60 months. The next section shows all the results for the 60-month run.

We performed a what-if analysis with the model by changing the decision variable, the order quantity in cell E47, to 110 and 120. We ran 10 runs each for Q = 100, Q = 110, and Q = 120. The results along with the average are summarized at the bottom. They are $189.639, $152.735, and $158.497 for Q = 100, 110, and 120 respectively (we copied the value of cell H60 to these cells). You can see the effect of the buffer stock. As Q increases, the total cost decreases initially because of lower stockout costs, but as we approach Q = 120, this decrease is offset by the increase in inventory costs.

Stockouts can be dangerous if the model is describing a production process. They may stop production and create idle workers and equipment. For a store, or a firm delivering service to customers, it can be devastating; plus there is the lost goodwill of the customers.
 

Software

Though the model was developed directly in Excel, we recommend using @Risk (Palisade Corp., www.palisade.com) to develop a full simulation model that automatically gathers the results for statistical analysis. A functional demo version is available from the Palisade Corp. Web site.
 

Appendix W5-A References

Hillier F. S. and G. Lieberman. (1995). Introduction to Operations Research, 6th. ed. New York: Irwin.

Turban, E. and J. Meredith (1994). Fundamentals of Management Science. 6th ed. Homewood, IL: Irwin.
 

Appendix W5-A Exercises

1. Implement the deterministic EOQ model in Excel as shown in Figure W5.6.

a. Use the EOQ formula to determine the EOQ directly.

3. Do a simulation study evaluating the number of stockouts and stockout cost for the Q values used in Exercise 2. When is the stockout cost insignificant in terms of the decision to be made?

4. Try Q=100 in the simulation model. Did you stock out half of the months? Why do you expect to stock out, on average, in one-half of the months?

Appendix W5-B: The Analytic Hierarchy Process (AHP) Using Expert Choice
(Note: in the textbook there is material on AHP/Expert Choice as well.)

The Analytic Hierarchy Process (AHP) developed by Saaty (1990, 1995, 1996) helps a decision maker arrive at the best decision in a case of multiple conflicting objectives (criteria). The AHP makes it possible to deal with both tangible and intangible factors. With it, one organizes thought and intuition in a logical fashion using a hierarchy and enters judgments according to understanding and experience. This approach tolerates uncertainty and allows for revision so that individuals and groups can grapple with all their concerns. The AHP is implemented in the Expert Choice software package. (Windows-based versions of the software are available from Expert Choice Inc., Pittsburgh, PA, www.expertchoice.com . Demo versions along with a tutorial are available directly over the Web.)

The answers can be tested for sensitivity to changes in judgment. Problems are broken down into smaller constituent parts so the decision maker makes only simple pairwise (two at a time) comparison judgments throughout the hierarchy to arrive at overall priorities for the alternatives of action. The decision problem may involve social, political, and technical factors; several parties; and many objectives, criteria, and alternatives; and may require negotiation. The process can be used for applications such as:

• Predict likely outcomes
• Allocate resources
• Plan projected and desired futures
• Exercise control over changes in the decision-making system
• Evaluate employees and allocate wage increases
• Facilitate group decision-making processes
• Select alternatives
• Perform cost/benefit comparisons.

Suppose you have been accepted by five MBA programs. (Hopefully, you would have many alternatives.) Which one would you attend? The selection process is based on several (multiple) criteria, ranging from quality to location. A simplified selection situation is summarized in Table W5-B.1. Below, we work this problem in Expert Choice.
 
 

Developing the Hierarchy

The first step is developing the hierarchy (an upside down tree that looks like a traditional organization chart), as shown in Figure W5.8. The goal is entered as the first node with a total weight of 1.000. This is followed by entering the main criteria nodes directly beneath the goal node. The total goal weight is initially divided equally among the criteria. (In the professional versions of the Expert Choice software, subcriteria may be added.) Simple editing commands are used to create and edit the nodes (from the Edit drop-down menu -- usually just Edit Insert).

Next, typically all the alternatives are entered beneath each criterion node. Normally, you just enter the alternatives beneath the first criterion node (move the cursor to the leftmost criterion node and select Edit Insert). Then, move the cursor up the hierarchy to the criterion containing the alternatives. Through the Edit drop-down menu, select Edit Replicate to Peers to copy the alternatives to the other criteria.

Comparing the Importance of the Criteria Against the Goal

The next step in the process is to verbally compare the criteria, two at a time (say, quality and location). The user needs to specify which criterion is more important and by how much (moderately more important, strongly more important, etc.). Alternatively, a numerical comparison can be done (e.g., quality is 7 times more important than location -- see Table W5-B.2). Once quality is compared to location, type, size and payoff; the second criterion, location, is compared to type, size and payoff. Then the third criterion, type, is compared to size, and payoff, and the fourth, size, is compared to payoff. All possible pairs of criteria are compared to ensure consistency of the decision maker (more on this later). To activate this mode, the user selects Compare Importance. Then, Skip the preliminary questions. If the second of the pair is more important, just hit the down arrow once to invert the comparison (the second becomes more important than the first). The verbal mode goes quickly once you get the hang of it. (The verbal mode will create the numeric matrix.) Note that when you only have two items to compare, Expert Choice switches to a graphical mode.
 
 

This pairwise comparison information is sufficient for the program to calculate the relative importance of each criterion (given in fractions, totaling 1.00; for example, quality = 0.411, location = 0.043, etc.). The program also calculates an inconsistency level; this level should typically be less than 0.10, or if you like more accuracy, then use 0.05. If the inconsistency index exceeds the threshold, you can adjust relative importance until a desired consistency is achieved. Typically, if the inconsistency ratio exceeds 0.20, then it indicates that you forgot to invert at least one pairwise comparison. When it is between 0.10 and 0.20, then it may be the result of an error, an error in judgement, or it may be OK. Some inconsistency is expected in human beings performing decision making. (Note: consistency may not be a good characteristic of a good decision maker. Bad decision makers can be notoriously consistent, e.g., consider Ivan the Terrible.)
 
 

Comparing Alternatives for Each Criterion

The process just described is now repeated for all alternatives against each criterion. We start with "quality" and compare two alternatives at a time. Say we compare the quality of School 1 to that of School 2 (are they equal? or which one is of a higher quality?). Use the down arrow to switch between the first being more important than the second or back.

When comparing numerical values (for example, the payoff could be an estimated dollar value), you can use a numerical comparison instead of the verbal one. For example, the payoff of School 1 might be 10 percent, that of 2 might be 35 percent, and so on. The program can compute the relative percentage (or cost, profit, etc.) on a scale totaling one in a linear calculation. Alternatively, the numerical comparison can be done on a nonlinear scale. (We use the latter approach here. We consider the payoff in terms of low through extremely high.) In real-world situations involving hard numerical comparisons, it turns out that the verbal mode is usually as accurate as the numerical mode. The numerical mode is useful for debugging the model when the inconsistency index is too high (note again -- usually an inconsistency index greater than 0.2 usually indicates that a comparison should have been inverted). To toggle between verbal and numerical modes, while comparing, use ‘V’ and ‘N.’

We start this process by comparing the schools under quality, then location, until we complete payoff.

Overall Ranking. Using a "weighted average" approach, the overall ranking is obtained by multiplying the preferences in each criterion for each alternative by the relative importance of each criterion and totaling the weights for each alternative. The end product is a weighted average for each alternative. The alternatives then are ranked from the best to the worst. This is done by the Synthesis command. Select Synthesis and include details if you want them (do so the first couple of times you use the software).

An example of the overall ranking of the MBA program selection problem, executed with Expert Choice, is shown in Figure W5.10. Note that a graphical view is also provided. This is the result of the Synthesis of all the weights. School 4 is the clear winner with a total weight of 0.380. The inconsistency index is 0.02.

Rating Utility - Model 2

For a large number of alternatives, the pairwise comparison of each two alternatives for all criteria can be very cumbersome (not to mention that more than 7 nodes will not fit on the screen). In this case, a utility approach (ratings) is applied. The ratings approach requires the definition of intensities (or measures) for each criterion. For example, "quality" can be extreme, high, medium, or low. "Size" can be small, medium, or large. So, the key difference between the first model described above and the ratings approach model is that beneath each criterion we do not have the alternatives, but a definition of possible ‘values’ (symbolic, not numeric) that each could take on. The relative importance of these intensities is then assessed, using a numerical comparison similar to that shown in Table W5-B.1. An example of such a hierarchy is shown in Figure W5.11. The criteria are the same, and the criteria comparisons yield the same results at this level as those of the first model. In the next level, possible values of each criterion appear (for example, "size" may be large, medium, or small). Once the criteria and their symbolic values are entered, pairwise comparisons are performed as described above. Then, in the Comparison drop-down menu, select Ratings. A spreadsheet structure will appear. In it, you enter the alternatives (one per row) followed by the symbolic values that each criterion (in the columns) can have. This table essentially looks like the original model data shown in Table W5-B.1. Once the data are all entered (once you list the alternatives, select the criterion values off of the list at the top of the screen), the weighted average of each alternative is calculated and presented on screen. For this example, the Schools 1 through 5 rated 0.259, 0.622, 0.364, 0.919, and 0.171 respectively. No pairwise comparisons yielded an inconsistency index above 0.02, with an overall index of 0.01.
 
 

Sensitivity Analysis

Expert Choice enables the user to see how the final priorities will change if the user changes the relative importance of the criteria. This option is supported by graphics.

Caution: A few words of caution are in order. If you have two (or more) very similar alternatives, you might want to use only one in the model. Then, once you have finished your evaluation, if it wins, create a new model to compare the two similar items. Otherwise, if you include both, they may split the overall weight, so that a normally second place item may win. Also, if you do not get a clear winner, that is the top two choices are close (within .05, say), then, you might want to drop some of the lesser preferred choices; or you may add a few criteria to help break the tie. This rank reversal problem has fueled much debate and controversy over the effectiveness, accuracy, and viability of the AHP. Check it out in the literature!

Overall, though, using the methodology and software generally assists a decision maker by allowing him or her to apply managerial judgments directly in the model. It helps decompose the model and helps the decision maker to focus better, and make an expert choice!

Software Availability

A demo version along with a tutorial of Expert Choice are available directly from Expert Choice Inc., Pittsburgh, PA, directly over the Web (www.expertchoice.com).
 

References for Appendix W5-B

Saaty, T. L. (1990). Decisions for Leaders: The Analytical Hierarchy Process. Pittsburgh, PA: University of Pittsburgh Press.

Saaty, T. L. (1995). Decision Making for Leaders: The Analytic Hierarchy Process for Decisions in a Complex World. Revised. Pittsburgh, PA: RWS Publishers.

Saaty, T. L. (1996). Decision Making for Leaders. Vol. II. Pittsburgh, PA: RWS Publishers.

Appendix W5-C: Waiting Line Modeling (Queueing) in a Spreadsheet

Introduction to Waiting Lines

Waiting lines describe one of the most common decision-making situations with which many people are familiar. They occur everywhere - theme parks, airports, movie theaters, banks, supermarkets, etc. This model class also describes many industrial situations, such as telephone / communication system design, forklift scheduling, and textile spool replacements. Any time customers ‘line up’ (‘queue up’ in England) for service, there is a queue. Essentially, whenever there are fewer servers (tellers in a bank, forklifts, etc.) than customers (people, items to be moved, etc.), there is a waiting line.

In basic waiting line theory, the arrival rate of customers (or alternatively the interarrival times) and the service times are considered to be stochastic (random), with certain, well-known probability distributions (Poisson, exponential, respectively) that accurately describe them. Here, we focus on the ‘standard’ queuing model, which might be found in a bank or movie theater (we ignore extensions that include balking, waiting line size limits, etc.). In our example, the Main Street Bank (MSB), customers arrive according to a Poisson process (e.g., characterized by a Poisson probability distribution) with a mean arrival rate of l = 15 customers per hour. The service time for an individual server is assumed to be exponentially distributed. Its inverse has a mean of m = 20 customers per hour. There is a single waiting line with one server. Fortunately, the assumptions are not too restrictive and cover a wide variety of situations. Further, there are relatively easy to state the formulas that describe a simple waiting line system’s performance. See Hillier and Lieberman (1995) and Turban and Meredith (1994) for details on the theoretical models and other examples of waiting lines.

Performance Measures for Waiting Line Models

The following formulas describe a set of standard performance measures (potential result variables) of the single waiting line system:

L = expected line length (number of customers) in the system, including those being serviced,

L_q = expected number of people waiting for service (in line only),

W = expected total time a customer is in the system (including service time),

W_q = expected waiting time of a customer (excluding service time).

P(W_q<t) = probability that the waiting time in the system (excluding service) exceeds t,

r = effectiveness of the system (a utilization parameter used in calculations),

s = number of servers.

For a single server, these performance measures are determined by the formulas:

(Note, e = 2.7182818 is the natural logarithm.)

Using the performance measures, we can evaluate service levels for the waiting line system. We next show a simple spreadsheet model to describe the complicated nature of waiting lines (queues). We then extend it into a decision making spreadsheet model.

Excel Spreadsheet Waiting Line Model Implementation

Situation 1

In Figure W5.13, we show an Excel spreadsheet model that evaluates the performance measures for a single server waiting line (s = 1) for the Main Street Bank (a very small bank), in which an analyst has spent several days observing the real system to determine the following parameters: the mean arrival rate is l = 15 customers per hour, the mean service rate is m = 20 customers per hour. The parameters of the spreadsheet waiting line model are clearly defined at the top, while the results are shown at the bottom. The text boxes on the spreadsheet describe the details of the waiting line performance measure formulas (the numbers and labels are clearly shown in the rest of the cells). (Note that in Lotus 1-2-3, formulas are preceded by the ‘@’ symbol rather than by the equals sign (=) as in Excel.)
 
 

Situation 2

Susan Sanders, the bank manager, is very sensitive to customers waiting in line too long because the bank’s largest depositor complained about having to wait in line for 45 minutes yesterday. We can determine the probability that a customer waited more than 45 minutes (.75 hour) in the section of the spreadsheet close to the bottom where the P(Wq>t) (for t=.75 hour) calculation is performed. Note that the performance is not too bad (0.0176). But, there is a finite probability that a customer may experience a very long wait (say 1.5 hours at 0.000415), so, these expected times should be considered carefully in managing a waiting line.

Situation 3

Main Street Bank can lease some new computer hardware for $20 per hour to speed up the teller’s performance to 30 customers per hour. We can determine the value of this new hardware by evaluating the cost of the system. Clearly the hourly cost of tellers is known (the salary), but the customers’ waiting costs must be factored into the evaluation. There is a difficulty, however, in establishing the customer waiting cost. We recommend that demographic data (check census data for your local area or MSA -- see the Exercises and Internet Exercises in Chapter 4) be used to determine how much a customer’s time is worth, with an added quantity to compensate the customer for lost goodwill due to waiting. In our example, a teller earns $17 per hour (including fringe benefits), and a customer’s waiting cost is $100 per hour. To determine the customers’ waiting cost, we multiply by the customer hourly waiting cost by the expected number of customers waiting in line = $100 L_q . The total cost is then TC = $37 s + $100 L_q . This case is easily solved and the total cost of the new system is compared to the old one in Figure W5.13. The new hardware should definitely be leased, but, if it were to cost more than $ 175 per hour, it should not.

Interesting extensions to the basic waiting line model are called for in the Group Exercises below.
 
 

Appendix W5-C References

Hillier F. S. and G. Lieberman. (1995). Introduction to Operations Research, 6th. ed. New York: Irwin.

Turban, E. and J. Meredith (1994). Fundamentals of Management Science. 6th ed. Homewood, IL: Irwin.
 

Appendix W5-C Exercises

1. Download and open the spreadsheet waiting line models. Why is $175 per hour the breakeven point for deciding whether or not to lease the new equipment?

2. What happens to the bank’s performance (especially the probability of waiting more than 6 minutes in line for service) if the manager installs an Automatic Teller Machine outside the bank which cuts the arrival rate inside the bank to 10 customers per hour? Is there a significant difference in the probability that a customer would wait more than 45 minutes? Would the bank be servicing more customers? Consider the issue of attracting customers who generally do their banking when the bank is closed.

3. Suppose there is no Automatic Teller Machine. What if the manager were to hire a faster teller who can service an average of 25 customers per hour? How do the performance measures change? What if this new teller were to earn $22 per hour? Should the manager replace the original teller with the faster one?

During rush hour, a manager of a fast food restaurant may attempt to minimize the total system cost of a waiting line. But, the number of servers may not be sufficient for the system to remain stable. For example, if customers arrive on average one per minute, but the average service time is 2 minutes, after one hour, there will be (on average) 30 people waiting in line. The utilization parameter r = l / sm > 1, indicates that in the long run, more customers arrive than can be served.

1. In this case, what performance measures should a manager examine, and how can this seemingly unstable situation be managed?

2. Clearly, this situation occurs in reality (check out a fast food restaurant at lunch time, or examine rush hour traffic). What is really happening?

3. How do managers really handle this situation?

1. Refer to one of the two references on waiting line models. In this exercise, the decision variable is the number of tellers, s.

a. Develop a spreadsheet model that accommodates the basic model for a single line with more than one server (s > 1) (Caution - this is a much more difficult task than the creation of the original model). For the basic case in Situation 1, evaluate the performance measures for values of s = 1, 2, 3, ... , 10. Plot the results. When does the decrease in the expected customer waiting time and the expected number of customers waiting become insignificant? How small is the improvement? What happens if you use multiple lines (one per server)? Which is better, a single line or multiple lines?

b. Suppose Susan has decided that an average waiting time (before service) in excess of 6 minutes (0.1 hours) is excessive. She wants to reach a desired service level for the bank. Knowing that as s increases, the performance measures will decrease, how many tellers (what value of s) yields an average waiting time of W_q £ 0.1? On average, what is the probability of waiting more than 0.1 hours? Is this reasonable? How many tellers would be necessary to get this probability down to 0.15?

c. The nature of waiting lines is such that one cannot absolutely minimize any of the standard performance measures as a function of s. As the decision maker increases the number of servers, the quantities all decrease. When s is very large, an increase in s decreases the measures a very tiny amount. In fact, the servers will start to interact and their efficiency will drop - thus being very counterproductive (or there may not even be room in the facility for all the servers - just imagine a bank with 5,000 tellers). So, it would be prudent to consider another performance measure, that of the cost of the system. The total cost of the system is the tellers’ salaries plus the customer waiting cost. Suppose a teller earns $17 per hour and the customer waiting cost is $100 per hour (just consider the waiting time, not the service time). Then, the hourly system cost is $17 s + $100 L_q . Evaluate the teller cost, the customer waiting cost and the total system cost for s =1, 2, 3, ... , 10. Plot the total cost versus s. How many tellers (s) yields a minimum total system cost?

d. What If Analysis: How sensitive is the decision in part c to the customers’ hourly waiting cost (i.e., if it increases, when does s; similarly, if it decreases, at what value does s change and in which direction)? Over what range is s = 1 optimal, s = 2 optimal, and so on up to s = 5?

e. Now, consider the dynamic nature of the problem. Use the spreadsheet model developed in part c to determine how many tellers are needed over the course of an 8 hour day, where the mean customer arrival rates are
 
 

f. For the models developed in parts a and c, what is the effect of using multiple lines, one per teller for s = 1, 2, 3, ..., 10?

2. Find a real business that has waiting lines (fast food restaurant, bank, train station, post office, airport, university registration) and examine their waiting lines (get permission from the business owner or manager first). Describe the waiting line situation. Do they use one line or many? Do they have specialty servers, and if so, how many and what kinds? Do they control the arrivals in any way (e.g., airlines control their flights to some degree, and university registration often involves specific time slots for each student)? For a relatively busy hour, observe the operations and record the time of arrival, time that service begins and time that service ends for each customer. Are both the interarrival times and service times exponentially distributed (do customers arrive and leave according to Poisson processes)? Plot a histogram of the interarrival times and service times. Do they ‘look’ exponential? If not, explain why not. Using the means of the interarrival and service rates, make an estimate of the servers’ hourly wages and the customer waiting time to determine (in a spreadsheet model) the optimal number of servers. Is this sensitive to changes in the customer waiting cost?

(A small amount of this material is condensed from Gray, P. (1996). Visual IFPS / PLUS for Business. Upper Saddle River, NJ: Prentice Hall, Inc.).
(We apologize in advance for the quality of the IFPS figures. These were created from paper scans.)

Introduction

Visual IFPS/PLUS (from Comshare Inc., Ann Arbor, MI, www.comshare.com) is a complete modeling language. Visual IFPS/PLUS (IFPS for short) is a financial planning language - a fourth generation programming language (4GL). IFPS (the Interactive Financial Planning Language) was originally designed to be a programming language for managers and executives. It uses a more natural syntax than traditional, third generation programming languages use, and handles much of the work that programmers must do to get the computer to do anything practical. Estimates of the efficiency improvements in terms of the amount of work done by an IFPS model (also called a program) range from a factor of 10 to 100 times over traditional languages. For example summing the digits from 1 to 10 can be done in the following two line IFPS model:

COLUMNS 1..10

TOTSUM = TOTSUM + COLNUM

An IFPS model is organized like a spreadsheet. The rows represent variables defined using algebraic style expressions, and the columns contain values that are determined by solving the model.

Our intent of this appendix is to explain briefly the main features of Visual IFPS/PLUS and the basics of how to use it. Refer to Gray (1996) for details about installation and for subtler details about the software and its use. For commercial use, contact Comshare Inc. directly at www.comshare.com.

Features of IFPS

Although most business students today already know how to use spreadsheets, there are certain features that make IFPS much more effective, once the user gets past the initial part of the learning curve. One should remember that the first release of IFPS preceded the development of the computer spreadsheet by nearly a decade.

We show a simple IFPS model (MOD5A1) in Figure W5.15 and its solution in Figure W5.16. This example aptly illustrates the many built-in features of IFPS. IFPS derives its versatility and strength from these built-in features, which include the following:

Natural Language. The language statement structure is VARIABLE = EXPRESSION. For example, ANNUAL REVENUE = UNIT PRICE * SALES, is a valid model line. This natural format makes the relationships among variables clear. Furthermore, it leads to very compact models. Variable names are in English (or whatever language you speak), may include multiple words and effectively have no length limits, so models are self-documenting. Variable names are NOT case sensitive. If comments are needed, a backslash (\) precedes a comment.

The first statement of every IFPS model is the COLUMNS statement. It is the only data statement and defines the number of columns to be used. The number of rows is determined by how many lines are in the model (except for a few special cases). The natural model structure involves each model line repeating its last expression (separated by commas) until the last column is reached (e.g., INVESTMENT = 1000, 0 means that the first column has 1000, but columns 2 through the last one are 0).

No Order Restriction. You can organize the lines (variables) of a model in any order that fits the way you view the problem. For example, in model MOD5A1, we use the UNIT PRICE and SALES in defining ANNUAL REVENUE in the fifth line of the model, but the UNIT PRICE and SALES are not defined until the Model Parameter section at the bottom. When you direct IFPS to solve a model, it finds what it needs, when it needs it. (No Muss! No Fuss!)

Spreadsheet Solution. The results of an IFPS model, when solved, appear in tabular form as shown in Figure W5.16.

What if. Once a model is solved, scenarios may be tested and saved or incorporated directly into the model. The model can easily be reset to its original structure.

Goal Seeking. Two forms of goal seeking are available: line-to-line or entire expressions (over all columns) or point-to-point. In the former case, you specify an entire new expression for the Goal Variable and select All columns to change; and for the Adjust Variable, select All columns to adjust. In the latter case, you specify a specific column for the Goal Variable and a single value expression; then the Adjust Variable and its specific column to adjust.

Built-in Functions. IFPS has many financial, statistical, and mathematical functions including those of net present value, internal rate of return, amortization, and a number of depreciation options. It also includes forecasting functions such as moving averages, trend extrapolation, and regression. Standard mathematical functions such as absolute value, maximum, minimum, etc., are available. There is also a logical IF THEN ELSE statement for setting values of variables (e.g., SALES = IF UNIT PRICE .GT. 100 THEN 50 ELSE 75).

Reserved Words. There are a number of built-in reserved words that refer to specific columns in variable expressions. These include PREVIOUS, FUTURE, FOR and [ ]. They are used as follows:

SALES = 100, PREVIOUS * 1.04

indicates that sales in column 1 are 100, and increase by 4% per year thereafter (when no variable is specified, it is assumed to be the same as the variable in the row).

SALES = 100, 120, PREVIOUS 2 + 25

indicates that the SALES in columns three and thereafter are 25 more than the SALES two columns back in time.

ESTIMATED TAX PAYMENT = .2 * FUTURE PROFIT

looks ahead one column in the PROFIT row to determine the ESTIMATED TAX PAYMENT

SALES = 4200 FOR 6, PREVIOUS * 1.08

keeps the SALES at 4200 for 6.

TAX RATE = FINAL TAX RATE[10]

sets the TAX RATE in every column to the FINAL TAX RATE in column 10.

Other common reserved works include COLNUM (a variable that always equals the column number), THRU (for specifying variables or columns), and all the command, functions and subroutine names.

Other. Other IFPS features include model consolidation, reports and data files, the profile, and command files. Model consolidation is easily handled by the command structure. Meaningfully formatted reports can be created through predefined report files. IFPS models may be linked to data from a database directly through data files. The profile is used to customize the operation of IFPS for an individual user. Command files are programs of IFPS commands that can be used to automate its operations for repetitive tasks.

A Simple Visual IFPS/Plus Model

Refer to the model shown in Figure W5.15. This is a six-year investment model.

Line 1: COLUMNS 1..6

Specifies that the model has 6 columns, numbered 1 through 6. (There can be variations on this. You can number columns QTR1, QTR2, etc.; or A, B, C, D; or 2001..2006, etc.)

Line 2: \ Sample Investment Model 5A1

This is a comment.

Line 3: INVESTMENT = 1000, 0

Sets the variable INVESTMENT to 1000 in year 1 and 0 in years 2 through 6.

Line 4: SALES = 100, PREVIOUS * 1.08

SALES are set to 100 in year 1, then increase by 8% per year.

Line 5: ANNUAL REVENUE = UNIT PRICE * SALES

The ANNUAL REVENUE in every column is equal to UNIT PRICE times SALES.

Note that the UNIT PRICE is not specified until line 12.

Line 6: ANNUAL COST = UNIT COST * SALES

The ANNUAL COST in every column is equal to UNIT COST times SALES.

Again, note that a variable has not been defined yet: UNIT COST.

Line 7: ANNUAL NET PROFIT = ANNUAL REVENUE - ANNUAL COST

This is a simple algebraic expression to define the ANNUAL NET PROFIT.

Line 8: NET PRESENT VALUE = NPVC(ANNUAL NET PROFIT, DISCOUNT RATE, INVESTMENT)

The NET PRESENT VALUE is set to a function that relates three other variables. NPVC performs a cumulative net present value calculation. In column k, it sums the ANNUAL NET PROFIT, assumed at the end of each year, for years 1 through k, taken back in time using the DISCOUNT RATE. It subtracts from that result, the sum of the INVESTMENT over columns 1 through k, but assuming that these streams of cash are at the start of the year. Note that financial functions assume that columns represent years. The PERIODS statement indicates how many periods are in a year (12 for months, etc.).

Lines 9-11: Comments

\
\ MODEL PARAMETERS
\

Lines 12-14:

Line 12: UNIT PRICE = 10
Line 13: UNIT COST = 7
Line 14: DISCOUNT RATE = 8%

These lines simply set these parameters to their defined values. Note that the discount rate can be specified as 8% or .08.

TIP: If goal seeking is to be done, where the discount rate is expected to repeat in every column, line 14 should be replaced with:

DISCOUNT RATE = 8%, PREVIOUS
 

How to Create and Solve a Visual IFPS/Plus Model

Visual IFPS/Plus has many features and capabilities that are impossible to cover in depth here. Our intent is to explain how to start the system, create and solve a model, and print results.

System Operation. Visual IFPS/Plus must be installed on your PC system. It uses a client / server operation mode. Some of the work is done on the client - on your PC’s desktop, while part of the work (file management and solution of certain advanced models) is done on the server. The student version on the PC uses the same PC as the client and the server, so, the screen will toggle between each as is required. The Visual IFPS/Plus graphical user interface will be intuitive to users of Microsoft Windows 3.1 or higher. For example, the use of buttons, drop-down menus and rudimentary editing are from the Windows user interface. If you are not familiar with Windows, you should learn it before using Visual IFPS/Plus (generally good advice before using Windows-based software!).

Visual IFPS/Plus System Requirements. The basic system requirements are a personal computer that is 100 percent IBM / PC compatible with an Intel 386 processor chip or higher (a math coprocessor is recommended for the 386 chip), a hard disk with at least 10 megabytes of free space, a 3.5" floppy drive, 8 Mb of RAM (16 Mb is recommended), and a VGA monitor. Visual IFPS/Plus runs under Windows 3.1 or Windows NT. Note: later releases may require different minimum configurations.

Getting Started. Activate Windows and double-click on the IFPS Program Group on the desktop. Double-click on the Visual IFPS/Plus icon in the folder. (The IFPS/Plus icon will activate the IFPS server, which is a nonvisual version of IFPS/Plus. It requires that commands be typed directly.) When you see the Copyright / Restricted Rights Notice screen, click on the IFPS+ button. You may get a message about a Model and Reports Filename. If so, click on OK. In the Visual IFPS/Plus window, you will see a menu bar with the following pull-down menus:

File View Tools Server Help ;

and a button bar with four buttons:

New Open Context Server.

More buttons will appear once a model is active.

Model and Reports File. IFPS stores all of its models in umbrella files called Model and Reports Files (M/R). These are ‘megafiles’ that contain collections of related models and other files. Click on the Context button (which opens a Set Entity Context Window) and select an M/R file from the list, or create one at this time. The open M/R File is indicated in the Status Bar at the bottom of the Visual IFPS/Plus window.

Creating a New Model. Next, to create a new file, click on the New button. You will see a window open on the screen. Using the IFPS rudimentary visual editing commands, type in your model line by line (type in the model in Figure W5.15). (Note, to continue a variable definition statement to the next line, use a ‘ at the end of the first line.) When you are done, select File, Save As (use Save if you already have saved it) and give it a name. It will actually be stored in the Model and Reports File.

Opening an Existing Model. If your model already exists, click on Open and select your model from the list.

Menus and Commands. Once an M/R File is active and a model is created or opened, the available menus have expanded to include:

File Edit View Format Tools Options Analysis Window Server Help .

The buttons now include

New Open Templates Solve Using What If Goal Seek Report Server .

Solving the Model. To solve the model, click on the Solve button. IFPS will ask you which columns and variables you want. Select OK for All. If the model has an error, IFPS will report it next, and give you a hint as to how to fix it. Otherwise, it will solve the model and produce a tabular output screen as shown in Figure W5.16. When does this investment break even?

What If. What if analysis can be performed by closing the solution window and, with the model still active, clicking on the What If button. A Case window will open. In this Case window, you type in new model lines. Then, select Solve to solve the case. The solution appears quickly in a What If solution window. You may save the Case for later use (with the Case window open, select File, Save as), or replace the existing model lines with those specified in the Case window. What would happen if the investment required an additional infusion of capital - a payment of $500 at the start of year 5? The new What If statement would be INVESTMENT = 1000, 0 FOR 3, 500, 0 . You can save this (or any) What If Case or Append it to the model (which eliminates the original model lines for the variables in the Case).

Goal Seeking. As mentioned above, there are two kinds of goal seeking, but both work the same way. Either with an open solution window to the model, or just the model window open, click on the Goal Seek button. You will see a Goal Seek window containing a tablet with three columns labeled ‘Goal Variable,’ ‘Goal Expression,’ ‘Adjust Variable,’ with boxes for selecting the Column for each variable. Before attempting to Goal Seek with model MOD5A1, change the DISCOUNT RATE = 8% line to DISCOUNT RATE = 8%, PREVIOUS and Save as MOD5A2. To perform a line-to-line Goal Seek, to determine the DISCOUNT RATE that yields a NET PRESENT VALUE initially at -800 and rising by 300 per year, select NET PRESENT VALUE for the ‘Goal Variable’ (use the arrow button to find it), select All columns, and for the expression use = -800, PREVIOUS + 300. For the ‘Adjust Variable,’ select DISCOUNT RATE. You must select All columns. Then click on the Solve button. The results appear in a Goal Seek solution window.

For a point-to-point Goal Seek, say we want to know the internal rate of return (actually, we could have used the IRR function). The IRR is the discount rate that yields a zero net present value. We could use trial and error via What If to find it, or, simply activate Goal Seek, select NET PRESENT VALUE for the ‘Goal Variable’ (use the arrow button to find it), select column 6, and for the expression use ‘= 0. For the ‘Adjust Variable’, select DISCOUNT RATE. You must select a single column - for this example, column 1. Then click on the Solve button.

Printing: From any screen, selecting File Print will print the information (model, solution, etc.) of the current screen. Tip: to capture an entire screen in Windows, use the ‘Alt’ + ‘Print Screen’ keys. This copies the screen into the Windows clipboard. You can then close Visual IFPS/Plus, open a word processor, and paste the screen image into a file.

For More Information

Refer to Gray (1996) for details about installation and for subtler details about the software and its use. For commercial use, contact Comshare Inc. directly at www.comshare.com.

Appendix W5-E: Visual IFPS/Plus and Spreadsheet Simulation Models

(A small amount of this material is condensed from Gray, P. (1996). Visual IFPS / PLUS for Business. Upper Saddle River, NJ: Prentice Hall, Inc.).

Introduction

Visual IFPS/Plus supports Monte Carlo simulation. You create the model in the same way that you create a deterministic model described above. There are several random number distributions in IFPS to specify stochastic (random) variables like demand, price, etc. IFPS Monte Carlo simulation only allows for equal time interval models (ideal for cash flow models), and must run on the server (but, a Monte Carlo model may be solved deterministically on the client for debugging). You are basically running the mainframe version of IFPS/Plus after you create the model. Recall though that the Student Version will have both the client and server running on the PC.

Here, we provide a simple example, and the basic steps one follows to create and run a Monte Carlo simulation model in Visual IFPS/Plus. We also provide a comparable simulation implementation in Excel (alternatively, Lotus 1-2-3 may be used). If you haven’t done so, you should read the previous appendix and implement a couple of Visual IFPS/Plus models.
 

A Visual IFPS/Plus Monte Carlo Model

In Figure W5.17, we show model MONTE1. It is an investment model over 10 years, where the SALES are randomly distributed in each time period. The SALES follows a normal (Gaussian) distribution with a mean of AVERAGE SALES (starts at 100 in year one and increases by 4% per year) and a standard deviation of AVERAGE SALES / 10 ). This is implemented as the SALES model line:

SALES = NORRANDR(AVERAGE SALES, AVERAGE SALES / 10)

The normal random number NORRANDR(mean, standard deviation) is used. To repeat the same value in every column, use NORRAND(mean, standard deviation) (e.g., drop the final R).
 
 

This model is created by the same procedure described in Appendix W5-C. When model MONTE1 is solved directly on the client (or even on the server with the SOLVE command) as a deterministic model, the average values for the random numbers are used. Its deterministic solution is shown in Figure W5.18.

Built-in Probability Distributions of IFPS/Plus

VISUAL IFPS/Plus has the following built-in random number generators:
 
 

These distribution functions all repeat the number generated in the first column over all columns. To generate a different random number in every column, add an R to the end of the distribution function’s name (e.g., UNIRANDR, TRIRANDR, etc.).
 

Monte Carlo Solution of the Model

At this point, we assume model MONTE1 has been typed in and saved. It has been debugged by solving it on the client (Visual mode). To solve model MONTE1 as a stochastic model, click on the Server button. You will see the Command Session window. (Note - variable names are now case sensitive.) Type the following:

MODEL MONTE1

to activate the model

LOGOUTPUT MONTE1DO.LOG

to create a log file called MONTE1DO.LOG of the activities of the session.

If you want to see the model, type

LIST

(Caution: don’t try to edit the model on the server.)

You can get a list of commands by typing

HELP TOPICS

If you want to solve the model as you did in the Visual mode (deterministically using the average values), you type

SOLVE

ALL

to see the solution of all columns. The information will scroll on the screen like a mainframe terminal session in the window.

There are two ways to solve an IFPS/Plus Monte Carlo model:

1. Deterministic Scenarios. Random variables can be set to their HIGH, LOW, MEAN, or MEDIAN values. This way the best and worst conditions may be tested to help validate the model. For example, HIGH UNIT COST and LOW UNIT PRICE and HIGH SALES (if we are losing money on each sale) might be a worst case situation, while LOW UNIT COST, HIGH UNIT PRICE and HIGH SALES might be a best case situation (if we are making money on each sale). Note that just solving a model means that the mean values are used. Also, for normally distributed random variables, the mean +/- 2.5 standard deviations is considered to be a HIGH and LOW value.

For model MONTE1, we are interested in the behavior of the NET PRESENT VALUE relative to the values of the SALES. An example of HIGH SALES is shown in Figure W5.19. After the model was activated and solved as described above (following the SOLVE and ALL commands), the scenario was created by typing

2. Stochastically. We perform several hundred runs of the simulation model with random numbers and collect statistics on specific variables in specific columns. Here, we are interested in the statistical behavior of the NET PRESENT VALUE in column 10.

One important feature about simulation in IFPS/Plus is the compactness of the model. This is best illustrated by examining how one can create a simulation model directly in a spreadsheet. In this subsection, we show the implementation of a spreadsheet simulation model comparable to the IFPS/Plus model MONTE1. The spreadsheet simulation model is shown in Figure W5.21.
 
 

The main advantage to such an implementation is that most managers already understand how to use a spreadsheet, so that such a model would be more palatable. Note that each cell must be specified, and special macro programming must be done to capture the results of several runs. Results for each year and the statistics must be explicitly coded into the cells. Documentation of the model is performed by explicit comments, separate from cell entries. Graphs of the results must be explicitly defined as well. Of course, some of this can be automated by using specialized packages like @Risk (Palisade Corp. Newfield, NY, www.palisade.com).
 

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Palvia, S., and S. R. Gordon. (1992, October). "Tables, Trees, and Formulas in Decision Analysis." Communication of the ACM.

Pearl, J. (1984). Heuristics. Reading, MA: Addison-Wesley.

Pirlot, M. (1996, August 9). "General Local Search Methods." European Journal of Operational Research. Vol. 92. No. 3. 493-511.

Raiffa, H. (1970). Decision Analysis: Introductory Lectures on Choices Under Uncertainty. Reading, MA: Addison-Wesley.

Sage, A. P. (1989). Decision Support Systems Engineering. New York: Wiley.

Savage, S. L. (1993). Fast QM: Fundamental Analytic Spreadsheet Tools for Quantitative Analysis. New York: McGraw-Hill.

Schrage, L. (1996). Optimization Modeling with Lindo. 5th ed. Chicago, IL: Lindo Systems, Inc.

Shim, J. K. (1994). Strategic Business Forecasting: The Complete Guide to Forecasting Real-World Company Performance. Chicago, IL: Probus Publishing Company.

Sinclair, M. (1993, September). "Comparison of the Performance of Modern Heuristics for Combinatorial Optimization on Real Data." Computers & Operations Research. Vol. 20. No. 7. 687-695.

Stewart, G. (19094, June). "Forecasting the Future." Byte. (www.byte.com/art/9406/sec9/art6.htm)

Swain, J. J. (1993, December). "Simulation Software Survey." OR/MS Today.

Tavana, M. and S. Banerjee. (1995). "Strategic Assessment Model (SAM): "A Multiple Criteria Decision Support System for Evaluation of Strategic Alternatives." Decision Sciences. Vol. 26. No. 1. 119-143.

Teach, R. D. (1990). "Demand Equations for Business Simulations with Market Segments." Simulation and Gaming. Vol. 21. No. 4. 423-442.

Thalmann, N. and D. Thalmann. (1997). Interactive Computer Animation. Upper Saddle River, NJ: Prentice Hall PTR.

Thierauf (1995). Virtual Reality Systems for Business. Westport, CT: Quorum Books.

Tolvanen, J. - P. and K. Lyytinen. (1994). "Modeling Information Systems in Business Development: Alternative Perspective on Business Process Re-engineering." The IFIP Trans A Comput Sci Teechnol. No. A-54, 567-579.

Walkenbach, J. (1992, June). "Spreadsheets: The Next Generation." PC World.

Watson, H. J., and J. H. Blackstone, Jr. (1989). Computer Simulation, 2nd ed., New York: Wiley.

Whitten, J., L. D. Bentley and V. M. Barlow. (1994). Systems Analysis & Design Methods. 3rd ed. Burr Ridge, IL: Richard D. Irwin, Inc.

Wittkemper, H-G. and M. Steiner. (1996, May). "Using Neural Networks to Forecast the Systematic Risk of Stocks." European Journal of Operational Research. Vol. 90. No. 3. 577-588.
 

Animation

Bayarri, S., M. Fernandez and M. Perez. (1996 May). "Virtual Reality for Driving Simulation." Communications of the ACM. Vol. 39. No. 5. 72-76.

Hurrion, R. D. (1993 July). Using 3D Animation Techniques to Help with the Experimental Design and Analysis Phase of a Visual Interactive Simulation Project. Journal of the Operational Research Society. Vol. 44. No. 7. 693-700.

Thalmann, N. and D. Thalmann. (1997). Interactive Computer Animation. Upper Saddle River, NJ: Prentice Hall PTR.
 

Visual Interactive Simulation

Eriksson, I. and A. Finn@ s. (1991). "Creating a Visual Simulation Model of an Inventory System." in van den Besselaar, P., A. Clement and P. J@ rvinen. (eds.). Information System, Work and Organization Design. 239-257. See also www.abo.fi/fak/mnf/infbeh/publications/journals/abstracts/Eriksson91a.html (10/11/96, 12:19:14 p.m.).

Hansen, G. (1996). Automating Business Process Re-engineering: Using the Power of Visual Simulation Strategies to Improve Performance and Profit. 2nd ed. Upper Saddle River, NJ: Prentice Hall PTR.

Lyu, Jr. J. and A. Gunasekaran. (1993). Developing a Visual Interactive Simulation Model for Flexible Manufacturing Systems. International Journal of Operations & Production Management. Vol. 13. No. 6. 59-67.

Robinson, S. L. (1994, February). "An Introduction to Visual Interactive Simulation in Business." International Journal of Information Management. Vol. 14. No. 1. 13-23.

Rohrer. M. (1996 May/June). "Visualization and its Importance in Manufacturing Simulation." Industrial Management. Vol. 38. No. 3. 15-18.

"Spatial Databases and Automated Construction of Virtual Worlds," www-cgi.cs.cmu.edu/afs/cs/usr/maps/www/research/databases.html, 10/11/96, 12:18:01 p.m.

Thav, O. (1996, June). "Insights via Interactivity: The Right Simulation Package Furthers Corporate Goals." Manufacturing Systems. Vol. 14. No. 6. 36-37.
 

Environmental Scanning / Analysis:

Auster, E. and C. W. Choo. (1994, September/October). "How Senior Managers Acquire and Use Information in Environmental Scanning." Information Processing & Management. Vol. 30. No. 5. 607-618.

Boyd, B. K. and J. Fulk. (1996). "Executive Scanning and Perceived Uncertainty: A Multidimensional Model." Journal of Management. Vol. 22. No. 1. 1-21.

Costa, J. (1995). "An Empirically-based Review of the Concept of Environmental Scanning." International Journal of Contemporary Hospitality Management. Vol. 7. No. 7. 4-9.

Matthews, C. H. and S. G. Scott. (1995, October). "Uncertainty and Planning in Small and Entrepreneurial Firms: An Empirical Assessment." Journal of Small Business Management. Vol. 33. No. 4. 34-52.

Xu, X. -Z. and G. R. Kaye. (1995). "Building Market Intelligence Systems for Environment Scanning." Logistics Information Management. Vol. 8. No. 2. 22-29.
 

Model Management

Blanning, R. W. (1993). "Model Management Systems: An Overview." Decision Support Systems. Vol. 9. 9-18.

Chang, A-M., C. W. Holsapple and A. B. Whinston (1993). "Model Management Issues and Directions." Decision Support Systems. Vol. 9. 19-37.

Liang, T. P. and B. Konsynski (1993). "Modeling by Analogy: Use of Analogical Reasoning in Model Management Systems." Decision Support Systems. Vol. 9. 113-125.
 

BPR Modeling

Tolvanen, J. - P. and K. Lyytinen. (1994). "Modeling Information Systems in Business Development: Alternative Perspective on Business Process Re-engineering." The IFIP Trans A Comput Sci Technol. No. A-54, 567-579.
 

Object-Oriented Business Modeling: - Business Processes

Barnett, W. A. Presley, M. Johnson and D. H. Liles. (1994, October). "Architecture for the Virtual Enterprise." Proceedings of the IEEE International Conference on Systems, Man and Cybernetics, Part 1. San Antonio, TX.

Briccarello, P., G. Bruno and E. Ronco. (1995). "REBUS: An Object-oriented Simulator for Business Processes." Proceedings of the IEEE Annual Simulation Symposium, Los Alamitos, CA. 269-277.
 

Simulation / Modeling and Expert System - BPR

Archetti, F., E. Fagiuoli, P. Confalonieri and F. Zannetti. (1992). "A Knowledge-based Diagnostic System for the Business-Process Ordering of a Plant." Expert Systems Applications. Vol. 4. No. 3. 315-322.
 

Database Design Modeling and Heuristics

Cerpa, N. (1995). " Pre-physical Data Base Design Heuristics." Information Management. Vol. 28. No. 6. 351-359.
 

Modeling - Evaluating

Labys, W. C. (1990). "Evaluating Models." Energy. Vol. 15. No. 3-4. 155-162.
 

Modeling - Database

Bohoris, G. A. and J. M. Thomas. (1995). "A Heuristic for Vehicle Routeing and Depot Staffing." Journal of the Operational Research Society. Vol. 46. 1184-1191.

Campbell, J. F. and A. Langevin. (1995). "The Snow Disposal Assignment Problem." Journal of the Operational Research Society. Vol. 46. 919-929.

Kilov, H. and L. Cuthbert. (1995). "Model for Document Management." Computer Communications. Vol. 18. No. 6. 408-417.
 

Modeling Languages

Brooke, A., D. Kendrick and A. Meeraus. (1992). GAMS Release 2.25: A User’s Guide. South San Francisco, CA: The Scientific Press.

Fourer, R., D. M. Gay and B. W. Kernighan. (1993). AMPL A Modeling Language for Mathematical Programming. South San Francisco, CA: The Scientific Press.

Lindo Systems, Inc. (1996). LINGO: Optimization Modeling Language. Chicago, IL: Lindo Systems, Inc.
 

Forecasting

Ainscough, T. L. and J. E. Aronson. (1997a). "A Neural Network Approach for the Analysis of Scanner Data." Journal of Consumer Retailing. forthcoming.

Ainscough, T. L. and J. E. Aronson. (1997b). "Neural Networks in Business." Journal of Business and Entrepreneurship. forthcoming.

Broadie, M. and P. Glasserman. (1996, February). "Estimating Security Price Derivatives using Simulation. Management Science. Vol. 42. No. 2. 269-285.

Coates, J. F. (1995 September/October). "How to Recognize a Sound Technology Forecast." Research-Technology Management. Vol. 38. No. 5. 11-12.

Collopy, F. and J. S. Armstrong. (1992). "Rule-Based Forecasting: Development and Validation of an Expert Systems Approach to Combining Time Series Extrapolations." Management Science. Vol. 38. No. 10. 1394-1414.

de Gooijer, I. G. and K. Kumar. (1992). "Some Recent Developments in Non-Linear Modelling, Testing, and Forecasting." International Journal of Forecasting. Vol. 8. 135-156.

DeLurgio, S. and C. Bhame. (1991). Forecasting Systems for Management. Homewood, IL: Business One Irwin.

Donaldson, R. G. and M. Kamstra. (1996, Jan). "Forecast Combining with Neural Networks." Journal of Forecasting. Vol. 15. No. 1. 49-61.

Geurts, M. D. and ED. B. Whitlark. (1996, August). "Using Diffusion Models to Forecast New Product Sales." Marketing & Research Today. Vol. 24. No. 3. 202-204.

Hill, T., M. O’Connor and W. Remus. (1996, July). "Neural Network Models for Time Series Forecasts." Management Science. Vol. 42. No. 7. 1082-1092.

Jain, B. A. and B. N. Nag. (1995) "Artificial Neural Network Models for Pricing Initial Public Offerings." Decision Sciences Vol. 26, No. 3. 283-302.

Jain, C. L. (1996 Summer). "Monthly Corporate Forecast Meeting." Journal of Business Forecasting Methods & Systems. Vol. 15. No. 2. p. 2, 28.

Rao, R. D. and J. K. Parikh. (1996 June). "Forecast and Analysis of Demand for Petroleum Products in India." Energy Policy. Vol. 24. No. 6. 583-592.

Wittkemper, H-G. and M. Steiner. (1996, May). "Using Neural Networks to Forecast the Systematic Risk of Stocks." European Journal of Operational Research. Vol. 90. No. 3. 577-588.
 

Simulation

Aggarwal, A. K. (1990). "Simulation as a DSS Modeling Technique." Information Management. Vol. 19. No. 5. 295-305.

Bertsche, D., C. Crawford and S. E. Macadam. (1996). "Is Simulation Better than Experience?" McKinsey Quarterly. No. 1. 50-57.

Chapman, R. G. (1995). BRANDS: A Marketing Game. Englewood Cliffs, NJ: Prentice Hall.

Cho, K., I. Moon and W. Yun. (1996, July). "System Analysis of a Multi-product, Small-lot-sized Production by Simulation: A Korean Motor Factory Case." Computers & Industrial Engineering. Vol. 30. No. 3. 347-356.

Ezingeard, J-N. and P. Race. (1995). "Spreadsheet Simulation to Aid Capacity Management of Batch Chemical Processing using JIT Pull Control." International Journal of Production & Operations Management. Vol. 15. No. 10. 82-88.

Fishwick, P. (1995). Simulation Model Design and Execution: Building Digital Worlds. Englewood Cliffs, NJ: Prentice Hall.

Pidd, M., F. N. de Silva and R. W. Eglese. (1996 May 10). "A Simulation Model for Emergency Evacuation." European Journal of Operational Research. Vol. 90. No. 3. 413-419.

Rao, R. D. and J. K. Parikh. (1996 June). "Forecast and Analysis of Demand for Petroleum Products in India. Energy Policy. Vol. 24. No. 6. 583-592.

Teach, R. D. (1990). "Demand Equations for Business Simulations with Market Segments." Simulation and Gaming. Vol. 21. No. 4. 423-442.
 

Object-Oriented Simulations

Ninios, P. K. Vlahos and D. W. Bunn. (1995). "Industrial Simulation: System Modelling with an Object Oriented / DEVS Technology." European Journal of Operational Research. Vol. 81. 521-534.
 

Simulation for Training and Games

Bertsche, D., C. Crawford and S. E. Macadam. (1996). "Is Simulation Better than Experience?" McKinsey Quarterly. No. 1. 50-57.

Hill, L. D. and K. L. Bender. (1996, July/August). "Market Simulation for Teaching Commodity Trading Skills." Agribusiness. Vol. 12. No. 4. 403-410.

Sim Wireless. (1996, July). "Sim Wireless: The Simulation Game for Serious Decision Makers." Telecommunications (Americas Edition). Vol. 30. No. 7. 34.

Trippi, R. R. (1996 May/June). "The AIM Game: Learning Investment Management Principles through Monte Carlo Simulation." Interfaces. Vol. 26. No. 3. 66-76.

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