Nonlinear programming for multiperiod capacity planning in a manufacturing system

In this paper, we present nonlinear programming methods for capacity planning in a manufacturing system that consists of a set of machines or work stations producing multiple products. We model the facility as an open network of queues where capacity at each work station in the system may be changed in each of a finite number of time periods. To determine the timing and size of capacity changes, we present two nonlinear programming models and methods for solving the resulting problems. One model involves minimizing total capacity costs such that plant congestion is controlled via upper limits on work-in-process. The other model involves minimizing a weighted sum of product lead times subject to budget constraints on capacity costs. We present solution methods for continuous and discrete capacity options and convex and nonconvex (e.g., economies of scale) capacity cost functions. We use branch and bound and outer approximation techniques to determine globally optimal solutions to the nonconvex problems. Computational testing of the algorithms is reported.