Explain how you could model sole sourcing for markets 2 and 5 from distribution centre 2

1. ACME Manufacturing serves a number of markets from the company's manufacturing plants and distribution centres. The distribution manager must decide on a plan for shipping product A from the manufacturing plants and the distribution centres to the markets. Table 1.1 below shows the available units of product A to be shipped from the two plants and the two warehouses. Table 1.1 Facility Manufacturing Plant A Manufacturing Plant B Warehouse 1 Warehouse 2 Units available (Product A) 100 200 45 90 The market demands are given in the table 1.2 below together with the transportation cost per unit. These transportation costs include handling costs at the facilities and at the markets, and trucking (mileage) costs. Table 1.2: Demand and transportation cost data From/to M1 M2 M3 M4 M5 M6 M7 M8 M9 M10 Plant A 14 24 21 20 21 19 17 30 23 26 Plant B 13 23 19 18 22 23 19 28 24 22 DC 1 1 24 15 28 20 24 22 19 18 22 27 DC 2 23 16 26 21 24 26 20 19 23 25 Demand 44 57 32 32 30 43 52 44 48 53 The distribution manager at ACME wishes to investigate the potential benefits of locating a cross docking facilities near the markets 4, 5, 6 and 8,9,10. The facilities would receive products from the plants and the distribution centres and immediately dispatch them to the ten markets offering 100% service level. Table 1.3, contains the relevant new transportation cost data. In addition, there is a handling charge of 2 for each product A transhipped through the cross dock facility 1 and of 3 for each product through the cross dock facility 2. Each cross dock facility has a maximal flow capacity of 60 units of product A per week. Table 1.3: Additional transportation cost data From/to Cross dock 1 From/to MARKET 4 MARKET 5 MARKET6 Plant A 10 Cross Dock 1 6 5 5 DC 1 11 From/to Cross dock 2 From/to MARKET 8 MARKET 9 MARKET 10 Plant B 9 Cross Dock 2 5 6 7 DC2 12