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Topic 11

Dynamic Programming: A Breakdown Solution Approach. Overview: Dynamic programming (DP) is perhaps the most fascinating tool of Management Science. It can be used to solve certain types of difficult problems which are not solvable, or which are difficult to solve, by other tools. DP is an approach r

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Topic 11

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    1. Topic 11 Dynamic Programming (DP)

    2. Dynamic Programming: A Breakdown Solution Approach Overview: Dynamic programming (DP) is perhaps the most fascinating tool of Management Science. It can be used to solve certain types of difficult problems which are not solvable, or which are difficult to solve, by other tools. DP is an approach rather than a structured tool. It decomposes problems to sub problems in a certain manner. The tool is also capable of handling multi-period sequential decision situations.

    3. Dynamic Programming: A Breakdown Solution Approach Overview: Dynamic programming is a technique that can be used to solve many optimization problems. In most applications, dynamic programming obtains solutions by working backward from the end of a problem toward the beginning, thus breaking up a large unwieldy problem into a series of smaller, more tractable problems.

    4. Two Puzzles Now, we show how working backward can make a seemingly difficult problem almost trivial to solve. Example 1 Suppose there are 30 matches on a table. I begin by picking up 1, 2, or 3 matches. Then my opponent must pick up 1, 2, or 3 matches. We continue in this fashion until last match is picked up. The player who picks up the last match is the loser. How can I (the first player) be sure of winning the game?

    5. Two Puzzles Example 2 I have a 9-oz cup and a 4-oz cup. My mother has ordered me to bring home exactly 6-oz of milk. How can I accomplish this goal? By starting near the end of the problem, I cleverly realized that the problem can easily be solved if I can somewhat get 1 oz of milk into a 4-oz cup. Then I can fill the 9-oz cup and empty 3-oz from the 9-oz cup into the partially filled 4-oz cup. At this point, I will be left with 6-oz of milk. After I have this flash of insight, the solution to the problem may easily be described as (initial situation is written last, and the final situation is written first).

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