On-line production control using the EVPI approach

Abstract

This paper deals with the on-line control of a dynamic production system by integrating an off-line nonlinear programming solution with the EVPI (Expected Value of Perfect Information) principle. We consider a production system subjected to random disturbances which has to produce a given target amount by a given due date. There are several possible production speeds to process the target amount, each speed is randomly distributed with a pregiven probability law. The system is observed at discrete points during the course of production. At each such control point, given the observed accumulated amount already produced, the system controller has to set up the speed to be used and to determine the timing of the next control point. The objective is to maximize the expected net profit. The costs considered are: the cost of a single control observation, the penalty cost per unit shortage of the output at the due date and the operating costs per time unit for each speed. The algorithm developed here involves two stages: first we solve the off-line problem which determines the length of time that each speed should be used if there is no control during the course of production. The off-line problem is nonlinear. In order to determine which speed to use first, we apply the EVPI principle. After determining the speed to be used, the system operates with that speed during the corresponding time duration, until the next control point. At this point the actual output is observed and the off-line problem is resolved with the target amount left. The efficiency of the algorithm is evaluated by using extensive simulations.