Question: Example in Section 10.1 The transportation problem is balanced because the total supply = total demand Total supply = 5000 + 6000 + 2500 =

Example in Section 10.1 The transportation

Example in Section 10.1 The transportation problem is balanced because the total supply = total demand Total supply = 5000 + 6000 + 2500 = 13500 units Total demand = 6000 + 4000 + 2000 + 1500 = 13500 units Decision variables: Xij = number of units shipped from plant i to distribution center i where i = 1, 2, and 3 and j = 1, 2, 3, and 4. Following Figure 10.1, plant 1 is located in Cleveland, plant 2 is located in Bedford, and plant 3 is located in York. Similarly, distribution center 1 is located in Boston, etc. There are 12 (or 3*4) decision variables because there are 12 distribution routes (arcs). Objective function: Minimize the total transportation cost where the total transportation cost = (3)X11 + (2)x12 + .....+ (4)X33+ (5)X34 Supply constraints: The total number of units sent from Cleveland plant must be less than or equal to the plant capacity in Cleveland. Thus, X11+X12 + X13 + X14 = 0; i = 1, 2, 3; j = 1, 2, 3, 4

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