Labor Assignment as a Dynamic Control Problem

A problem of labor assignment in a labor and machine limited production system is formulated as a dynamic control problem. The criterion function employed is total in-process inventory cost over a time period [O, T]. The Pontryagin maximum principle is applied to obtain necessary and sufficient conditions for the optimal control. Specifications defining the admissible set of control vectors leads directly to the constrained optimal solution that is found to be a time-dependent control determined by both the queue lengths and transitions among production centers. Some examples are given to illustrate the nature of the resulting priority policies in tandem and network type systems. A number of limiting assumptions and omissions that facilitated analytical resolution of the problem are discussed to suggest challenging possibilities for extensions of the model.