Thansportarlon problem with production costs (not the usual transportation problem). Two factories are manufacturing and supplying a single type of good to four warehouses in different parts of the country. The factories can produce al and 02 units of the good each month. and the warehouses need b1. B2,b3, and b4, units each month. The monthly total of goods available from the two factories exceeds the total of the monthly demands at the four warehouses.

The costs of supplying one unit of the good from factory i to warehouse/ is cij. So far the problem posed is the problem you have seen in this chapter. The twist in this problem is that the two factories have different factors of production. Their energy and labor costs are very different, with one of the factories having much higher electricity rates and employee wages. The costs of production of one unit of the good at factories 1 and 2 are d1 and d2. Structure the objective function and constraints for this problem in expanded form (without the summation signs).

A corporation is engaged in producing and marketing a consumer good. The company has two factories that produce the good and also four intermediate ware-houses from which the good is delivered to the final link in the chain. retail stores. of which there are many. Factories only ship to warehouses and not directly to retail stores. The warehouse intervenes in the supply chain so that rapid response (overnight truck delivery) can deliver the good to stores The warehouses are. of course, more geo-graphically dispersed than the plants are.

This dispersed supply network eliminates the need for the more distant, and hence slower. shipment that would occur if the stores ordered replenishment stock from the factory. The manufacturing plants are in place and producing goods; the maximum monthly production rates from factories I and 2 arc a, and 02. Warehouses are positioned in key locations and are currently in operation. The maximum monthly throughputs at the four warehouses are. kg. and th. The monthly demands at the 40 retail stores are di 42. dm. The cost of a unit shipped from plant i to warehouse j is cij and the cost of a unit shipped from warehouse j to store k is kip Each unit manufactured at plants I and 2 costs e1 and e2. respectively. to manufacture.

Processing and stocking costs at the warehouses all cost g per unit that moves through the warehouse each month. All goods that enter the warehouse in any month must exit it in that same month as there is not enough storage capacity to operate with carryover goods. Structure a linear programming optimization model.

using summation notation where it is convenient to do so. that seeks to manufacture and dis-tribute the gnarls in the supply chain at the least total cost. The decision variables will tell you which warehouses serve which plants and retail stores. Other than the set of assignments and minimum total cost, can you think of additional valuable information that would come from solution of this problem?