Asynchronous regulation of service speed in inventory-production systems with time-varying positive demand

This paper deals with an inventory-production system in which raw parts are transformed into processed parts, in order to satisfy a time-varying positive demand over a given time horizon. The production resource is capacitated whereas the inventory is unbounded; the external demand is known and is expressed as a piecewise constant function changing at asynchronous time instants. The objective is to find the optimal service speed pattern, assumed to be a piecewise constant function, which minimizes setup, production, and holding costs; hence, the decisions concern both the values of the service speed and the (asynchronous) time instants at which it changes. The optimization problem defined for this class of systems has a parametric structure and includes both nonlinear and combinatorial aspects. In the paper, some structural properties of any optimal solution are firstly proven, and then a solution procedure that allows finding an optimal solution in polynomial times is provided.