Optimal numbers of two kinds of kanbans in a JIT production system

The production-ordering and withdrawal kanbans are used in a Just-in-Time (JIT) production system. In particular, a withdrawal kanban used for a vendor is called a supplier kanban. This paper deals with the JIT production system with the production-ordering and supplier kanbans under stochastic demand. A necessary and sufficient condition, called a stability condition, is derived under which the JIT production system has a stationary distribution of the backlogged demand. An algorithm is devised for determining optimal numbers of two kinds of kanbans that minimize an expected average cost per period. In other words, it determines optimal values of the safety stocks included in the popular formulas for computing the numbers of kanbans. Numerical results are given to show its efficiency.