A-I - Optimization Models Draft of August 26, 2005 I....

Info iconThis preview shows pages 1–4. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Optimization Models Draft of August 26, 2005 I. Formulating an Optimization Model: An Introductory Example Robert Fourer Department of Industrial Engineering and Management Sciences Northwestern University Evanston, Illinois 60208-3119, U.S.A. (847) 491-3151 4er@iems.northwestern.edu http://www.iems.northwestern.edu/ 4er/ Copyright c 19892005 Robert Fourer A2 Optimization Models 1.0 Draft of August 26, 2005 A3 1. A Simple Model To introduce the fundamentals of our subject, we begin with a simple exam- ple, the diet problem: choosing from a menu of available foods to produce a diet that meets daily nutritional requirements. Since there are many different combinations of foods that meet the requirements, our goal will be to identify a combination that does the job at the lowest possible cost. This is the character- istic goal of any optimization problem: to find a preferred arrangement among all that are acceptable. This chapter works through the basic steps of generating and solving a diet problem. In the process, we show how to formulate a mathematical model that describes diet problems in a general way, and how to submit a model and data to a software package that computes minimum-cost diets and related in- formation. Then in Chapter 2, your intuition for diets will enable you to see how our model must be refined to produce sensible results. You will also see how certain refinements can make the optimal diet harder to compute. These are characteristics that you will encounter repeatedly as you study different op- timization problems and models for them. Diet problems are only one example of the general idea of a minimum-cost input problem. Chapter 3 will take a tour through a variety of other applications of this idea, including blending, scheduling, and cutting. Then Chapter 4 will extend the idea even further to encompass output and input-output problems. 1.1 A small diet problem When approaching any unfamiliar kind of optimization problem, its best to start with a version thats small and simple. Thus lets begin by imagining that your diet is limited to a selection of items from a well-known fast food restaurant. Well give each food a nickname to assist in referring to it: QP: Quarter Pounder FR: Fries, small MD: McLean Deluxe SM: Sausage McMuffin BM: Big Mac 1M: 1% Lowfat Milk FF: Filet-O-Fish OJ: Orange Juice MC: McGrilled Chicken Suppose also that you are interested in providing your diet with appropriate amounts of seven nutrients: Prot: Protein Iron: Iron VitA: Vitamin A Cals: Calories VitC: Vitamin C Carb: Carbohydrates Calc: Calcium Your problem is to find the lowest-cost combination of the foods that will pro- vide a days requirements for the nutrients....
View Full Document

Page1 / 33

A-I - Optimization Models Draft of August 26, 2005 I....

This preview shows document pages 1 - 4. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online