Stochastic Properties and Optimality of a Supplier Kanban System

Abstract

A supplier Kanban system controls the orders to a vender in a Just-In-Time (JIT) production system. In our previous paper, we have proposed an algorithm for determining an optimal number of supplier Kanbans and an optimal withdrawal cycle that minimize an expected average cost per period under stochastic demand. This paper deals with stochastic properties of the supplier Kanban system and its optimality. First, we show behavior of the backlogged demand using the stochastic ordering and convex ordering in the case where the number of supplier Kanbans, production capacity and demand distribution change, respectively. Next, a problem of deter-mining an optimal ordering policy without using supplier Kanbans that minimize the expected average cost per period is formulated into a Markov decision process (MDP). Finally, an optimality of the supplier Kanban system with the optimal number of Kanbans is discussed through numerical comparisons between the supplier Kanban policies and the optimal ordering policies computed by the MDP.