Performance evaluation of SCM in JIT environment

Under stochastic demand and deterministic processing times, we discussed a single-stage JIT production system with the production-ordering and supplier kanbans and derived a probability generating function (p.g.f.) of the stationary distributions of the backlogged demand. In this paper, we extend the system to supply chain management (SCM) in JIT environment with two kinds of kanbans under stochastic demand, deterministic processing times and withdrawals with lead time. These conditions are more realistic than the previous papers. We develop an algorithm for the exact performance evaluation of the SCM such as the stationary distributions of the inventory level, production quantities and total backlogged demand in each stage, using discrete-time Markov process. Optimal numbers of two kinds of kanbans in the system are determined by minimizing a general total cost function. Numerical examples are given to show the efficiency of the proposed approach.