IE 495 – Final Exam

IE 495 – Final Exam

Due Date: May 1, 2003

Do the following problems. You must work alone on this exam. The only reference

materials you are allowed to use on the exam are the textbook by Birge and

Louveaux, the Stochastic Programming book by Kall and Wallace:

http://www.unizh.ch/ior/Pages/Deutsch/Mitglieder/Kall/bib/ka-wal-94.pdf,

the class notes and materials on the course web page, and references to help you

with AMPL syntax. You may use whatever software tools you find necessary (e.g.

AMPL, Excel, Maple, NEOS). If you feel you need other reference materials to

correctly answer any problem, contact Prof. Linderoth.

Please show your work. You may attach printouts of AMPL files, Maple worksheets,

and Excel worksheets, or you may email them to Prof. Linderoth.

1 You Say To-MAY-To, I Say To-MAH-To

Linear Programming1

Teresa’s Terrific Tomatoes (ttt) is in the business of selling a set P of tomato-related

products (e.g salsa, ketchup, tomato paste). In order to create these products,

resources from a set R are required (e.g. tomatoes, sugar, labor, spices). To be

specific, the parameter apr is the amount of resource r ∈ R that is required to

produce one unit of product p ∈ P. There is a limit br on the amount of each

resource r ∈ R that can be used in a production period. The company can pay for

extra resources at a cost of γr, r ∈ R.

ttt management is trying to determine the optimal way to meet an estimate

of its demand dpt for each of its products p ∈ P in each planning period t over a

horizon T. The regular production costs for each product are cpt, p ∈ P, t ∈ T. Any

surplus production of a product p ∈ P must be stored at a cost of αp per unit.

ttt management also considers unmet demand important, so it imposes a penalty

cost of βp for each unit of unmet demand for product p ∈ P. ttt carries no initial

inventory of products.

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