Multiple-facility loading under capacity-based economies of scope

Multiple-facility loading (MFL) involves the allocation of products among a set of finite-capacity facilities. Applications of MFL arise naturally in a variety of production scheduling environments. MFL models typically assume that capacity is consumed as a linear function of products assigned to a facility. Product similarities and differences, however, result in capacity-based economies or diseconomies of scope, and thus the effective capacity of the facility is often a (nonlinear) function of the set of tasks assigned to the facility. This article addresses the multiple-facility loading problem under capacity-based economies (and diseconomies) of scope (MFLS). The authors formulate MFLS as a nonlinear 0-1 mixed-integer programming problem, and they discuss some useful properties. MFLS generalizes many well-known combinatorial optimization problems, such as the capacitated facility location problem and the generalized assignment problem. The authors also define a tabu-search heuristic and a branch-and-bound algorithm for MFLS. The tabu-search heuristic alternates between two search phases, a regional search and a diversification search, and offers a novel approach to solution diversification. The author also report computational experience with the procedures. In addition to demonstrating MFLS problem tractability, the computational results indicate that the heuristic is an effective tool for obtaining high-quality solutions to MFLS.