MOD2_268-273 - 72106 MOD02 GGS 3/30/05 2:39 PM Page 268 M O...

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268 T EACHING S UGGESTIONS Teaching Suggestion M2.1: Overall Use of Dynamic Programming. Dynamic programming is a general approach that can be used to solve a number of different problems. The overall approach of breaking a larger problem into smaller stages is an important prin- ciple. In addition to being essential for the solution of a dynamic programming problem, this concept is a useful approach for gen- eral decision-making problems. Teaching Suggestion M2.2: Use of the Shortest-Route Problem. Dynamic programming can be a difFcult topic for some students to understand. The shortest-route problem was used in this chapter to show students how the principles of dynamic programming can be used to solve a familiar problem. Once students understand the use of dynamic programming to solve the shortest-route problem, more complex and difFcult problems can be undertaken. Teaching Suggestion M2.3: QA in Action Boxes in This Module. Because dynamic programming is a difFcult and advanced topic, we selected applications that might interest the average student. Teaching Suggestion M2.4: Use of Terminology. Understanding dynamic programming terminology is one ap- proach to handling larger and more complex problems. Learning how the terminology of dynamic programming is applied to the shortest-route problem can help students understand larger and more complex dynamic programming problems. A LTERNATIVE E XAMPLE Alternative Example M2.1: Darrell Washington would like to use dynamic programming to solve the shortest route problem shown in the following Fgure. Beginning with stage 1, we begin to solve the problem. The dis- tance from node 5 to node 7 is 4 and the distance from node 6 is 8. These values are put in boxes by the nodes. The results are shown in the following network. Next, we solve stage 2. The minimum distances between nodes 2, 3, and 4 and the ending node 7 are 12, 8, and 12. These distances are also put in boxes by the nodes. The results for stage 2 are shown in the following network. 2 MODULE Dynamic Programming 4 3 5 6 1 7 2 1 2 5 8 4 4 8 4 8 Stage 3 Stage 2 Stage 1 4 3 5 6 1 7 2 1 2 5 8 4 4 8 4 8 Stage 3 Stage 2 Stage 1 4 8 4 3 5 6 1 7 2 1 2 5 8 4 4 8 4 8 Stage 3 Stage 2 Stage 1 4 8 12 12 8 72106 MOD02 GGS 3/30/05 2:39 PM Page 268
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MODULE 2 D YNAMIC P ROGRAMMING 269 Finally, we solve stage 3. The minimum distance is through node 3. The distance from node 1 to node 3 is 2, and the minimum dis- tance from node 3 to the end of the network is 8 as seen in the re- sults for stage 2. Thus the shortest route through the network is 10. S OLUTIONS TO Q UESTIONS AND P ROBLEMS M2-1. A stage in dynamic programming is a period or a logical subproblem. Dynamic programming divides problems into a num- ber of decision stages, whereby the outcome of a decision at one stage affects the decision at each of the next stages.
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MOD2_268-273 - 72106 MOD02 GGS 3/30/05 2:39 PM Page 268 M O...

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