Lecture2_331 - Class Notes Due to reasons beyond my control...

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Class Notes Due to reasons beyond my control, the course webpage will be on Google Groups I have to add you manually, so please send your email address to [email protected] with the subject “msci 331”. I will post course slides and the syllabus to the group page.
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01/08/09 Operations Research Lecture 1 2 Lecture 2:  Introduction to Modeling Jim Ostrowski
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01/08/09 3 Introduction to modeling • A decision is a choice between conflicting or  competing alternatives • Situation                   Analysis                  Decision                        Implementation                    Payoff                                                           Monetary or qualitative
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01/08/09 4 Models A model is an abstraction of reality    Physical (iconic)   Analog   Mathematical
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01/08/09 5 OR methodology 1.  Problem formulation diagnose the situation: start with a “mess”, end with  a “problem” 2.  Model construction translate the formulation into the appropriate quantitative form, called the model 3.  Solve the model  use a computer package to solve the problem  small problems might be solved using a spreadsheet solver,
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01/08/09 6 OR methodology 4. Test the model and solution  perform sensitivity analysis and/or restructuring  examine the solution to assess how well it would likely perform in the real problem  attempt to estimate effects that were omitted from the initial analysis 5. Implement the model  perhaps develop a user-friendly graphical interface if model is to be used frequently  issues of model documentation and maintenance should be addressed.
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01/08/09 7 The modeling Process Symbolic model Solution Real-life situation Assumptions Management Decision Methodology
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01/08/09 8 Example Your store is selling calendars, which cost you $6.00 and sell for $9.99 Calendars which remain unsold after January are returned to the publisher for a $3.50 "salvage" credit. There is only one opportunity to order the calendars. What is the right number of calendars to order? Tradeoff between ordering a large number and ordering an insufficient number.
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01/08/09 9 Example (continued) Objective:  maximize profit Parameters: unit cost :6$ /calendar sales price: $9.99 /calendar salvage price : $3.5/calendar Demand for calendars
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01/08/09 10 Example (Continued) Decision Variables: calendars  ordered
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01/08/09 11 A symbolic Model c : unit cost : $ 6 p : unit sales price: $9.99 s : unit salvage price : $3.5 D : Demand for calendars x : calendars ordered Ns : Calendars sold Nr : Calendars returned × - - × - - × - = D x if x c p D x if D x s c D c p profit ) ( ) ( ) ( ) ( ) , 0 max( 5 . 2 ) , min( 99 . 3 ) , 0 max( ) ( ) , min( ) ( D x x D D x s c x D c p profit - - = - × - - × - = Notice: Number of calendars sold Number of calendars returned ) , 0 max( ) , min( D x x D - = =
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01/08/09 12
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  • Winter '09
  • Ostrowski
  • Optimization, Harshad number, ij, decision variables, feasible set, Giapetto

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