Transportation, Assignment, and Transshipment Problems
Transportation, Assignment, andTransshipment ProblemsIn this chapter, we discuss three special types of linear programming Problems : transporta-tion, assignment, and Transshipment . Each of these can be solved by the simplex algorithm,but specialized algorithms for each type of problem are much more 1Formulating Transportation ProblemsWe begin our discussion of transportation Problems by formulating a linear programmingmodel of the following has three electric power plants that supply the needs of four cities. Each powerplant can supply the following numbers of kilowatt-hours (kwh) of electricity: plant 1 35 million; plant 2 50 million; plant 3 40 million (see Table 1). The peak power de-mands in these cities, which occur at the same time (2 ), are as follows (in kwh): city1 45 million; city 2 20 million; city 3 30 million; city 4 30 million.
Dummy City 5 d 5 = 5 s 2 = 50 Plant 2 s 3 = 40 Plant 3 FIGURE 2 Graphical Representation of Unbalanced Powerco Problem and Its Optimal Solution (with Dummy Demand Point) c 11 c 12 c 1n c 21 c 22 c 2n c m1 c m2 c mn s 1 s 2 s m d 1 d 2 d n TABLE 2 ATransportation Tableau Supply Demand 8 6 9 9 12 7 45 3020 30 10 10 45 5 25 30 10 13 14916 5 35 50 ...
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