Optimal capacity planning for a manufacturing system with non-convex cost index and delayed growth dynamics

A manufacturing system is looked upon as a black box whose input vector is an r-tuple of planning decisions where each decision is a series of pulse functions in the time-domain, and whose output vector is an r-tuple of actual manufacturing capacities which is the response of the black box to the planning decisions. This response is described by a linear difference equation including transport lag (i.e., delay). The cost functional of the system is non-convex due to set up charges. In this paper, a method is discussed to determine the optimal planning decisions to minimize the cost using a discrete version of Pontryagin´s Maximum Principle that gets around the problem of the increase in dimensionality caused by the delay term in the system equation.