Single-Facility Resource Allocation Under Capacity-Based Economies and Diseconomies of Scope

We consider the optimal allocation of a resource in a single-facility production environment in the presence of capacity-based economies and diseconomies of scope. This setting generalizes the usual approach to single-facility resource allocation by allowing for the effective capacity of a facility to be a (nonlinear) function of the number of different items produced or the services delivered by the facility. Economies or diseconomies of scope are attributable to factors such as production changeover time, overall process management requirements, and complementary production requirements that vary with the product or service mix. We consider the problem setting in which the effective capacity depends on the number of tasks assigned to the facility. The resulting model (SCOPE) generalizes the well-known 0--1 knapsack problem. We also consider the more general problem (GENCAP) in which capacity consumption depends on the specific set of tasks assigned to the facility. We define tabu-search heuristics, as well as exact branch-and-bound algorithms for SCOPE and GENCAP. On the basis of extensive computational experience, the solution procedures are seen to be extremely effective. In particular, the heuristics consistently obtain high-quality solutions to the test problems. Furthermore, the tractability of solving problems to optimality is demonstrated through the solution of SCOPE problems having as many as 500 tasks and GENCAP problems involving as many as 50 tasks and more than 16,500 nonlinear capacity interactions.