Optimal release times in single-stage manufacturing systems with finite production inventory

The paper concerns a due-date matching problem in single-stage manufacturing systems with limited production-inventory buffering capacity. The objective is to determine parts' release times so as to minimize a weighted sum of the discrepancies between products' completion times and given due dates. This scheduling problem is formulated as an optimal control problem whose "plant" is modeled by a deterministic queue with finite output buffer, its controls are the release times, and its associated cost function penalizes products' earliness as well as tardiness. Although the optimal control problem appears to be nonconvex and nondifferentiable, we show that it is equivalent to a differentiable, convex programming problem with linear constraints. The problem may have a large number of variables and inequalities, but we decompose it into a finite sequence of one-dimensional problems. We then develop an algorithm for computing the optimal controls and demonstrate its efficacy by means of computational examples.