DMOR_HW4_fall10_solutions

DMOR_HW4_fall10_solutions - ESI 6314 Deterministic Methods...

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Fall 2010 HW 4 Solutions 1. Problem 21, page 410 The demand for a given day (Day j) can be satisfied by either 1. A newly purchased napkin that is being used for the first time. 2. A napkin that was used to satisfy Day k's demand that returns from laundry service in time to satisfy Day j demand. Thus the supply points are as follows: New=Purchased napkins that are used for the first time (at most 15 + 12 + 18 + 6 = 51) new napkins will be purchased so New has a supply of 51) Day 1=Napkins used to meet Day 1 demand that can be used to meet later demands(this point has a supply of 15) Day 2=Napkins used to meet Day 2 demand that can be used to meet later demands (this point has a supply of 12) Day 3=Napkins used to meet Day 3 demand that can be used to meet later demands (this point has a supply of 18. We obtain the following balanced transportation problem (optimal solution is also given). Day 1 Day 2 Day 3 Day 4 Dummy New 20 15 20 3 20 20 0 33 51 Day 1 M 10 9 6 6 6 0 15 Day 2 M M 10 12 6 0 12 Day 3 M M M 10 6 0 12 18 15 12 18 6 45 Thus Day 1 demand is met with 15 newly purchased napkins. Day 2 demand is met with 3 new napkins and 9 napkins that were used for Day 1 demand and were laundered via Fast Service. Day 3 demand is met by 6 napkins that were used to meet Day 1 demand and are laundered by Slow Service and 12 napkins that were used to meet Day 2 demand and are laundered by Fast Service. Day

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This note was uploaded on 12/14/2010 for the course ESI 6314 taught by Professor Vladimirlboginski during the Spring '09 term at University of Florida.

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DMOR_HW4_fall10_solutions - ESI 6314 Deterministic Methods...

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