A Discrete Time Average Cost Flexible Manufacturing and Operator Scheduling Model Solved by Deconvexification Over Time

A flexible manufacturing and operator scheduling problem is introduced and solved. The principal concern is to schedule operators over time to various activities of a manufacturing system for the purpose of optimizing some steady-state criteria. In mathematical terms, the problem is modeled as a deterministic, infinite horizon, discrete dynamic program. Our solution procedure is to convexify the problem to obtain a linear program, and then to deconvexify the solution of the linear program over time to arrive at an optimal solution. Apparent loss in objective value due to the deconvexifications is circumvented with buffer inventories. The procedure is reduced to solving a sequence of linear programs and the complexity is stated in these terms.