On Server Allocation in Multiple Center Manufacturing Systems

We study the problem of allocating a given number of identical servers among the work centers of a manufacturing system. The problem is formulated as a nonlinear integer program of allocating servers in a closed queueing network to maximize throughput. We show that the throughput of the closed queueing network has a monotonicity property, such that any optimal allocation must give more servers to stations with a higher workload. The number of allocations that satisfy this property is much smaller than the total number of feasible allocations. This property and a bounding technique for the throughput of the closed queueing network are combined to develop a search algorithm to obtain an optimal allocation of servers. A greedy heuristic is also developed, and its optimality proven in the special case of a two-center system (in the general case, its optimality remains a conjecture).