To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna M2-1 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Module 2 Dynamic Programming

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna M2-2 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Learning Objectives Students will be able to Understand the overall approach of dynamic programming Use dynamic programming to solve the shortest-route problem. Develop dynamic programming stages. Describe important dynamic programming terminology. Describe the use of dynamic programming in solving knapsack problems.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna M2-3 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Module Outline M2.1 Introduction M2.2 Shortest-Route Problem Solved by Dynamic Programming M2.3 Dynamic Programming Terminology M2.4 Dynamic Programming Notation M2.5 Knapsack Problem

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna M2-4 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Four Steps in Dynamic Programming Divide the original problem into subproblems called stages. Solve the last stage of the problem for all possible conditions or states. Working backward from that last stage, solve each intermediate stage. Obtain the optimal solution for the original problem by solving all stages sequentially.

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna M2-5 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Dynamic Programming George Yates Dixieville miles 10 miles 14 miles 2 miles 10 miles 6 miles 4 miles 2 miles 12 miles 5 miles Rice LakecityAthens HopeGeorgetown Brown

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna M2-6 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ George Yates Stages Dixieville miles 10 miles 14 miles 2 miles 10 miles 6 miles 4 miles 2 miles 12 miles 5 miles Rice LakecityAthens HopeGeorgetown Brown Stage 1 Stage 2Stage 3

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna M2-7 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ George Yates Stage miles 10 miles 14 miles 2 miles 10 miles 6 miles 4 miles 2 miles 12 miles 5 miles 14 2

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna M2-8 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ George Yates Stage miles 10 miles 14 miles 2 miles 10 miles 6 miles 4 miles 2 miles 12 miles 5 miles

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna M2-9 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ miles 10 miles 14 miles 2 miles 10 miles 6 miles 4 miles 2 miles 12 miles 5 miles George Yates Stage

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna M2-10 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Dynamic Programming Terminology 1. Stage - A logical subproblem 2. State Variable - Possible condition 3. Decision Variable - Alternative 4. Decision Criterion - Problem objective 5. Optimal Policy - A set of decision rules 6. Transformation - Relationship between stages

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna M2-11 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Roller Transport Problem

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna M2-12 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Roller Transport Problem Solution Final Solution StageOptimal Decision Optimal Return Total828

To accompany Quantitative Analysis for Management, 8e by Render/Stair/Hanna M2-13 © 2003 by Prentice Hall, Inc. Upper Saddle River, NJ Dynamic Programming Key Equations s n  Input to stage n d n  Decision at stage n r n  Return at stage n s n-1  Input to stage n-1 t n  Transformation function at stage n s n-1 = t n [s n d n ]  General relationship between stages f n  Total return at stage n