1. Stevenson and Ozgur First Edition Introduction to Management Science with Spreadsheets McGraw-Hill/Irwin Copyright © 2007 by The McGraw-Hill Companies, Inc. All rights reserved. Chapter 7 Integer Programming Part 2 Deterministic Decision Models

2. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–2 Learning Objectives 1.Tell how integer programming problems differ from general linear programming problems. 2.Explain the difference among pure, mixed, and 0–1 integer programming problems. 3.Formulate and use Excel to solve integer programming problems. 4.Formulate and use Excel to solve 0–1 integer programming problems. 5.Formulate specialized integer programming problems including knapsack, set covering, fixed charge, and facility location problems. After completing this chapter, you should be able to:

3. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–3 Types of Integer Programming 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 0 or 1, such as situations in which decision variables are of the yes-no type.

4. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–4 Figure 7–1Graph of an Integer Programming Problem

5. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–5 Example 7-1

6. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–6 Example 7-1 (cont’d)

7. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–7 Exhibit 7-1Input and Output Worksheet for the Boat-Manufacturing Example

8. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–8 Exhibit 7-2Solver Parameters Screen for the Boat-Manufacturing Problem

9. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–9 Exhibit 7–3Integer Requirement Specification Exhibit 7–4Solver Results Screen

10. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–10 Exhibit 7–4Solver Results Screen

11. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–11 Integer Programming Problems and Sensitivity Analysis Integer programming problems do 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.

12. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–12 Formulating Integer Programming Problems with 0–1 Constraints Either-Or Alternatives k-Out-of-n Alternatives If-Then Alternatives Either-Or Constraints Variables That Have Minimum Level Requirements

13. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–13 Specialized Integer Programming 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.

14. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–14 Exhibit 7–5Worksheet for the 0–1 Integer Programming Set Covering Problem

15. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–15 Exhibit 7–6Solver Parameters Screen for the Set Covering Problem

16. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–16 Exhibit 7–7Binary Requirement Specification

17. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–17 Exhibit 7–8Excel Worksheet for Example 7-7 (Traveling Salesperson Problem)

18. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–18 Exhibit 7–9Solver Parameters Screen for the Traveling Salesperson Problem Exhibit 7–10Specification of the Binary Variables

19. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–19 Exhibit 7–11Excel Worksheet for Solved Problem 1, Part a (Shopping Mall Problem)

20. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–20 Exhibit 7–12Solver Parameters Screen for Solved Problem 1 (Shopping Mall Problem) Exhibit 7–13Specification of the Binary Variables

21. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–21 Exhibit 7–14Excel Worksheet for Solved Problem 1, Part b (Shopping Mall Problem)

22. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–22 Exhibit 7–15Excel Worksheet for Solved Problem 2 (Cargo Plane Problem)

23. Copyright © 2007 The McGraw-Hill Companies. All rights reserved. McGraw-Hill/Irwin 7–23 Exhibit 7–16Solver Parameters Screen for Solved Problem 2 (Cargo Plane Problem) Exhibit 7–17Specification of the Integer Variables