7. Assignment and Location Problems in Supply Chains

This chapter delves into problems that require assigning customer demands to supply sources. When no fixed cost exists for using a supply source and supply sources are capacitated, we have a generalized assignment problem (GAP). When fixed costs are incurred for using a supply source, then the problem is a classical facility location problem (FLP). We consider both capacitated and uncapacitated facility location problems, as well as the implications of requiring single sourcing constraints that do not allow splitting a demand between supply sources. Within these problem classes, we analyze two different forms of demand flexibility. The first type of flexibility corresponds to what we saw in the last two chapters, i.e., each demand must be either fully accepted or rejected. The second type of flexibility requires satisfying each demand, but the quantity (e.g., size, number of units) at which a demand is satisfied must fall between prespecified lower and upper limits, while revenue is proportional to the level at which the demand is satisfied. This chapter defines several such assignment and location models containing these dimensions of demand flexibility.