Optimal control of pull manufacturing systems

We consider the problem of optimal control of pull manufacturing systems. We study a fluid model of a flow shop, with buffer holding costs nondecreasing along the route. The system is subject to a constant exogenous demand, thus incurring additional shortfall/inventory costs. The objective is to determine the optimal control for the production rate at each machine in the system. We exhibit a decomposition of the flow shop into “sections” of contiguous machines, where, in each section, the head machine is the bottleneck for the downstream system. We exhibit the form of an optimal control and show that it is characterized by a set of “deferral times”, one for each head machine. Machines which are upstream of a head machine simply adopt a “just-in-time” production policy. The head machines initially stay idle for a period equal to their deferral time and thereafter produce as fast as possible, until the initial shortfall is eliminated. The optimal values of these deferral times are simply obtained by solving a set of quadratic programming problems. We also exhibit special cases of re-entrant lines, for which the optimal control is similarly computable