Logistics and Programming
A firm has several factories that differ in terms of capacity and unit cost of production. The firm sells its product at customer places, each with its own fixed quantity demanded. How much does it ship from each factory to each customer place? To solve this problem, linear programming is introduced. In Model 3A, the firm incurs production costs, but unit shipping cost is zero everywhere. Model 3B includes a unit production cost and a unit shipping cost that varies from one customer place to the next for each factory. In addition to allocating production to customers, linear programs like 3A and 3B generate shadow prices: one for each constraint. The shadow price on the capacity constraint at factory i tells us how much money the firm could save (i.e., additional profit it could earn) if only it had one more unit of capacity there. This is a kind of opportunity cost. There was no congestion (i.e., restriction on production) in Chapter 2. The models in Chapter 3 help us to better understand congestion and its impact on locational decisions (how much, if any, to produce at each factory). In this chapter, localization and the shadow prices on capacity (one for each factory) are joint outcomes of cost-minimizing behavior.