Lecture Introduction to Management Science with Spreadsheets: Chapter 7 - Stevenson, Ozgur

Chapter 7 Integer programming, after completing this chapter, you should be able to: Tell how integer programming problems differ from general linear programming problems; explain the difference among pure, mixed, and 0–1 integer programming problems; formulate and use Excel to solve integer programming problems;...

Introduction to Management Science with Spreadsheets Stevenson and Ozgur First Edition Part Deterministic Decision Models Chapter 7 Integer Programming McGraw­Hill/Irwin Copyright © 2007 by The McGraw­Hill Companies, Inc. All rights reserved Learning Objectives After completing this chapter, you should be able to: Tell how integer programming problems differ from general linear programming problems Explain the difference among pure, mixed, and 0–1 integer programming problems Formulate and use Excel to solve integer programming problems Formulate and use Excel to solve 0–1 integer programming problems Formulate specialized integer programming problems including knapsack, set covering, fixed charge, and facility location problems Copyright © 2007 The McGraw­Hill  McGraw­ Companies. All rights reserved.   Hill/Irwin  7–2 Types Types of of Integer Integer Programming Programming Problems Problems • Pure-Integer Problems – require that all decision variables have integer solutions • Mixed-Integer Problems – Require some, but not all, of the decision variables to have integer values in the final solution, whereas others need not have integer values • 0–1 Integer Problems – Require integer variables to have value of or 1, such as situations in which decision variables are of the yes-no type Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–3 Figure Figure7–1 7–1 Graph Graphofofan anInteger IntegerProgramming ProgrammingProblem Problem Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–4 Example Example7-1 7-1 Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–5 Example Example7-1 7-1(cont’d) (cont’d) Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–6 Exhibit Exhibit7-1 7-1 Input Inputand andOutput OutputWorksheet Worksheetfor forthe theBoat-Manufacturing Boat-ManufacturingExample Example Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–7 Exhibit Exhibit7-2 7-2 Solver SolverParameters ParametersScreen Screenfor forthe theBoat-Manufacturing Boat-Manufacturing Problem Problem Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–8 Exhibit Exhibit7–3 7–3 Integer IntegerRequirement RequirementSpecification Specification Exhibit Exhibit7–4 7–4 Solver SolverResults ResultsScreen Screen Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–9 Exhibit Exhibit7–4 7–4 Solver SolverResults ResultsScreen Screen Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–10 Integer Integer Programming Programming Problems Problems and and Sensitivity Sensitivity Analysis Analysis • Integer programming problems not readily lend themselves to sensitivity analysis as only a relatively few of the infinite solution possibilities in a feasible solution space will meet integer requirements • Trial-and-error examination of a range of reasonable alternatives involving completely solving each revised problem is required Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–11 Formulating Formulating Integer Integer Programming Programming Problems Problems with with 0–1 0–1 Constraints Constraints • Either-Or Alternatives • k-Out-of-n Alternatives • If-Then Alternatives • Either-Or Constraints • Variables That Have Minimum Level Requirements Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–12 Specialized Specialized Integer Integer Programming Programming Problems Problems • Integer programming problems with 0–1 decision variables – Fixed-charge problem: minimize total costs – Set covering problem: minimize coverage costs – Knapsack problem: capacity-profit maximization – Facility location problem: multiple facility locations with capacity considerations – Traveling salesperson problem: minimize total costs of departing and returning the same location Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–13 Exhibit Exhibit7–5 7–5 Worksheet Worksheetfor forthe the0–1 0–1Integer IntegerProgramming ProgrammingSet SetCovering Covering Problem Problem Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–14 Exhibit Exhibit7–6 7–6 Solver SolverParameters ParametersScreen Screenfor forthe theSet SetCovering CoveringProblem Problem Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–15 Exhibit Exhibit7–7 7–7 Binary BinaryRequirement RequirementSpecification Specification Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–16 Exhibit Exhibit7–8 7–8 Excel ExcelWorksheet Worksheetfor forExample Example7-7 7-7(Traveling (TravelingSalesperson Salesperson Problem) Problem) Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–17 Exhibit Exhibit7–9 7–9 Solver SolverParameters ParametersScreen Screenfor forthe theTraveling TravelingSalesperson Salesperson Problem Problem Exhibit Exhibit77–10 –10 Specification Specificationofofthe theBinary BinaryVariables Variables Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–18 Exhibit Exhibit7–11 7–11 Excel ExcelWorksheet Worksheetfor forSolved SolvedProblem Problem1,1,Part Partaa(Shopping (ShoppingMall Mall Problem) Problem) Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–19 Exhibit Exhibit7–12 7–12 Solver SolverParameters ParametersScreen Screenfor forSolved SolvedProblem Problem11(Shopping (Shopping Mall MallProblem) Problem) Exhibit Exhibit7–13 7–13 Specification Specificationofofthe theBinary BinaryVariables Variables Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–20 Exhibit Exhibit7–14 7–14 Excel ExcelWorksheet Worksheetfor forSolved SolvedProblem Problem1,1,Part Partbb(Shopping (ShoppingMall Mall Problem) Problem) Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–21 Exhibit Exhibit7–15 7–15 Excel ExcelWorksheet Worksheetfor forSolved SolvedProblem Problem22(Cargo (CargoPlane PlaneProblem) Problem) Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–22 Exhibit Exhibit7–16 7–16 Solver SolverParameters ParametersScreen Screenfor forSolved SolvedProblem Problem22(Cargo (CargoPlane Plane Problem) Problem) Exhibit Exhibit7–17 7–17 Specification Specificationofofthe theInteger IntegerVariables Variables Copyright © 2007 The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin  7–23 ... McGraw­ Hill/Irwin ? ?7? ??16 Exhibit Exhibit7–8 7? ??8 Excel ExcelWorksheet Worksheetfor forExample Example7 -7 7 -7 ( Traveling (TravelingSalesperson Salesperson Problem) Problem) Copyright © 20 07? ?The McGraw­Hill ... McGraw­ Hill/Irwin ? ?7? ? ?7 Exhibit Exhibit 7-2 7- 2 Solver SolverParameters ParametersScreen Screenfor forthe theBoat-Manufacturing Boat-Manufacturing Problem Problem Copyright © 20 07? ?The McGraw­Hill ... Hill/Irwin ? ?7? ??4 Example Example 7-1 7- 1 Copyright © 20 07? ?The McGraw­Hill  Companies. All rights reserved.   McGraw­ Hill/Irwin ? ?7? ??5 Example Example 7-1 7- 1(cont’d) (cont’d) Copyright © 20 07? ?The McGraw­Hill  Companies. All rights reserved.