IELM_assignment_2

IELM_assignment_2 - IELM 202, Assignment #2 Solution Due...

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IELM 202, Assignment #2 Solution Due date: 5 October 2005, Wednesday, 12:00 noon Question 1 (25 marks): A company has two manufacturing plants ( A and B ) and three sales outlets ( I , II , III ). Shipping costs from the plants to the outlets in $/unit are as follows: Outlet Plant I II III A 4 6 8 B 7 4 3 The company wants to plan production, shipping and sales for the next two periods. The manufacturing and demand data for the two periods are shown in the following tables. The plants can store products produced in one period for sale in the next. The maximum storage at each plant is 50 units and the inventory cost is $1 per unit. Formulate the problem as Liner Programming to maximize the company profit. Manufacturing Data Plant A Plants B Period Unit cost ($/unit) Capacity Unit cost ($/unit) Capacity 1 8 175 7 200 2 10 150 8 170 Demand Data Selling price ($/unit) Maximum sales Period I II III I II III 1 15 20 14 100 200 150 2 18 17 21 150 300 150 VARIABLE DEFINITIONS P A-1 , P B-1 , P A-2 , P B-2 : production at A and B in the two periods S I-1 , S II-1 , S III-1 : sales in period 1 at three locations S I-2 , S II-2 , S III-2 : sales in period 2 at three locations x A-I-1 , x A-II-1 , x A-III-1 , x B-I-1 , x B-II-1 , x B-III-1 : shipments in period 1 x A-I-2 , x A-II-2 , x A-III-2 , x B-I-2 , x B-II-2 , x B-III-2 : shipments in period 2 I A , I B : Inventory storage at A and B
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CONSTRAINTS Conservation constraints of the production P A-1 - x A-I-1 - x A-II-1 - x A-III-1 - I A = 0 P B-1 - x B-I-1 - x B-II-1 - x B-III-1 - I B = 0 P A-2 + I A - x A-I-2 - x A-II-2 - x A-III-2 = 0 P B-2 + I B - x B-I-2 - x B-II-2 - x B-III-2 - I B = 0 Conservation constraints of the selling point
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IELM_assignment_2 - IELM 202, Assignment #2 Solution Due...

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