A Study on Stochastic Dynamic Production Cycling Problem

Abstract

A production system to process multi-item products by using a single machine by turns to meet time-varying stochastic demand in finite horizon consisting of discrete periods is considered and a new optimization model and its calculation procedure are proposed. The problem is to determine the item and the production amount to minimize the expectation of the total of production costs, inventory-holding costs, shortage costs and set-up costs. The problem can be formulated as a Markov decision process, but it is not practical because its dimension becomes too large. Therefore an eclectic model is built, where the item is treated as a variable to be determined at the beginning of the planning horizon and the production amount is determined as a policy. Two propositions to make the characteristics of the problem clear are introduced and the method for obtaining the lower bound to the partial problem is proposed based on the propositions. A calculation procedure using the branch and bound method is developed. Meaning and validity of the proposed model are clarified by the numerical example.