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Unformatted text preview: Worked Examples for Chapter 10 Example 1 for Section 10.3 The Build-Em-Fast Company has agreed to supply its best customer with three widgits during each of the next 3 weeks, even though producing them will require some overtime work. The relevant production data are as follows: Week Maximum Production, Regular Time Maximum Production, Overtime Production Cost per Unit Regular Time 1 2 2 $300 2 3 2 $500 3 1 2 $400 The cost per unit produced with overtime for each week is $100 more than for regular time. The cost of storage is $50 per unit for each week it is stored. There is already an inventory of two widgets on hand currently, but the company does not want to retain any widgets in inventory after the 3 weeks. Management wants to know how many units should be produced in each week to minimize the total cost of meeting the delivery schedule. Let us solve this by using dynamic programming. Application of Dynamic Programming The decisions that need to be made are the number of units to produce each week, so the decision variables are x n = number of widgets to produce in week n, for n = 1, 2, 3. To choose the value of x n , it is necessary to know the number of widgets already on hand at the beginning of week n. Therefore, the state of the system then is s n = number of widgets on hand at the beginning of week n, for n = 1, 2, 3.= number of widgets on hand at the beginning of week n, for n = 1, 2, 3....
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- Spring '08