Why and How to Teach Modeling

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Why and How to Teach Modeling

• Stephen G. Powell
• Tuck School of Business
• Dartmouth College
• INFORMS Teaching of Management Science Workshop
• July 16, 2006

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Teaching models vs teaching modeling

• Examples of models
• resource allocation model (LP)
• newsvendor model (simulation)
• M/M/1 queue (stochastic modeling)
• Examples of modeling techniques
• problem framing
• simplification
• prototyping
• sensitivity analysis
• problem exploration for insight

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Question for Participants

• Do you teach models or modeling?
• Why?

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A Typical Optimization Problem

• Veerman Furniture Company makes three kinds of
  office furniture chairs, desks, and tables. Each
  product requires some labor in the parts
  fabrication department, the assembly department,
  and the shipping department. The furniture is
  sold through a regional distributor, who has
  estimated the maximum potential sales for each
  product in the coming quarter. Finally, the
  accounting department has provided some data
  showing the profit contributions on each product.
  The decision problem is to determine the product
  mixthat is, to maximize Veerman's profit for the
  quarter by choosing production quantities for the
  chairs, desks, and tables. The data shown below
  summarize the parameters of the problem
• Hours per Unit Hours
• Department Chairs Desks Tables Available
• Fabrication 4 6 2 1850
• Assembly 3 5 7 2400
• Shipping 3 2 4 1500
• Demand Potential 360 300 100
• Profit 15 24 18

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A Typical Simulation Problem

• In November, Jeff Hastings of the fashion skiwear
  manufacturer Hastings Sportswear, Inc., faces the
  task of committing to specific production
  quantities for each skiwear item the company will
  offer in the coming years line. Commitments are
  needed immediately, in order to reserve space in
  production facilities located throughout Asia.
  Actual demand for these products will not become
  known for at least six months. Production costs
  for a typical parka run about 75 percent of the
  wholesale price, which in this case is 110.
  Unsold parkas can be sold at salvage for around 8
  percent of the wholesale price. Demand is
  normally distributed with a mean of 1,017 units
  and a standard deviation of about 200 units.
  Based on this information, Jeff must decide on an
  order quantity for this model of parka.

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An Ill-defined Problem

• The Red Cross provides about 40 percent of the
  replacement blood supply for the United States.
  The available donor base has been shrinking for
  years, and although increased advertising has
  kept Red Cross supplies adequate, the time is
  approaching when demand will outstrip supply. For
  many years, the Red Cross has refused to pay
  donors for blood, on the grounds that to do so
  would put the blood supply of the country at
  risk. However, Red Cross management has begun to
  consider changing its policy. Evaluate the
  impacts of a policy under which the Red Cross
  would pay each of its donors a set fee.

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Another Ill-defined Problem

• The Boeing Company faces a critical strategic
  choice in its competition with Airbus Industries
  for the long-haul flight segment should it
  design and build a super-747 model that can carry
  550 passengers at speeds around 350 mph, or a
  plane that can fly at 95 of the speed of sound
  but carry only about 350 passengers? As a member
  of Boeings Planning Group, your task is to build
  a model to investigate the trade-offs involved in
  this decision.

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Question for Participants

• Do you teach well-defined or ill-defined problem
  solving?
• Why?

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Questions for Participants

• What pitfalls do your students face in
  formulating linear programs?

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Questions for Participants

• What pitfalls do your students face in
  formulating simulation models (Monte Carlo or
  discrete-event)?

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Pitfalls in Novice Problem Solving

• Over-reliance on available data
• Taking shortcuts to an answer
• Insufficient use of abstract variables and
  relationships
• Ineffective self-regulation
• Overuse of brainstorming relative to structured
  problem solving

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How to Teach Ill-structured Problem Solving

• Teach problem formulation with no data and with
  excessive data
• Teach abstraction
• algebra
• spreadsheets
• influence charts
• Teach self-regulation
• Teach structured problem solving
• parameterization
• prototyping

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Influence Charts - Example

• Determine the price we should set for our product
  so as to generate the highest possible profit
  this coming year.

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Influence Chart
Price
Quantity Sold
Total Revenue
Variable Cost
Profit
Total Cost
Unit Cost
Fixed Cost
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National Leasing Your Assignment

• Management at NLI would like to know how best to
  set residual values on automobile leases.
• Can a modeling approach help?
• Sketch an influence chart for a prototype model.
  
• Include uncertainty or not?
• Optimize or simulate?
• Generic lease or specific lease?

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National Leasing Modeling choices

• Model a portfolio of leases or a single lease?
• Model dynamics or statics?
• Include uncertainty or not?
• Optimize or simulate?
• How to model market share?
• How to model consumer behavior at lease end?

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National Leasing Influence Chart
Competitive Lease Terms
Cost of Borrowing
Contract Residual Value
Leases Sold
Lease Revenue
Profit
Monthly Payment
Term
Money Factor
Residual Gain/Loss
Used Car Price
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Prototyping

• What is it?
• How do you do it?
• What role does it play in modeling?

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Definition of Prototyping

• Prototyping is an approach to design that
  involves building a sequence of artifacts.
• Each member of the sequence is closer to the
  ultimate product.
• Each member of the sequence reveals the
  weaknesses that will be addressed in the next
  prototype.

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Power of Prototyping

• The essence of prototyping is learning.
• Effective prototyping reveals the true
  requirements for the design.
• Effective prototyping in modeling suggests
• which approaches will work
• what data is important
• what the answer might be
• how sensitive the answer is to assumptions

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Results from Pricing Prototype
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Results from Leasing Prototype
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Summary

• Modeling is fundamental
• Modeling is not learned effectively through
  models
• Modeling can be taught
• Two key tools in teaching modeling
• influence charts
• prototyping
• How to learn more.

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References

• How Novices Formulate Models Part I Qualitative
  Insights and Implications for Teaching, S. G.
  Powell and T.W. Willemain, Journal of the
  Operational Research Society, forthcoming 2006.
• How Novices Formulate Models Part II A
  Quantitative Description of Behavior, T.W.
  Willemain and S. G. Powell, Journal of the
  Operational Research Society, forthcoming 2006.
• Six Key Modeling Heuristics, S.G. Powell,
  Interfaces, 254, July-August, 1995, pp. 114-125.
• The Studio Approach to Teaching the Art of
  Modeling, S. G. Powell, Annals of Operations
  Research, Vol. 82, 1998, pp. 29-147.