Optimal Control Policy for a Supplier Management System with Stochastic Variability

The manufacturing of a product involves using several different kinds parts. Some of these parts are supplied by outside vendors. This adds a layer of complexity to the already challenging problem of managing the logistics of the production operation. It is important to efficiently control the ordering of parts from the outside vendors as their lead times tend to be relatively long (compared to the internal lead times) due to, among other things, the geographical distances of outside vendors from the production facility. Since the production of a product often requires interaction, it is crucial to develop a coordinated supplier management system for the entire operation to work efficiently. Just-in-time (JIT) production systems have been successfully implemented in many factories. To maintain the JIT production system, two kinds of kanbans, that is, a production-ordering kanban and a withdrawal kanban are used as tools to control the production and withdrawal quantities in each process. In particular, the withdrawal kanban used for withdrawing from a vendor is called a supplier kanban. The number of supplier kanbans attributed to a given part represents the maximum number of units of that part available in stock for the use in production. Once the number of kanbans is agreed upon, the system performs automatically. The purpose of this paper is to obtain the optimal control policy for a supplier management system under stochastic variability. The supplier management system has a single process with two kinds of kanbans. One is a production-ordering kanban used for production and the other is a supplier kanban used for ordering parts. We assume that there are line stoppages for machine maintenance in the process, which leads to a random production capacity. The problem is formulated into a Markov Decision Process(MDP). It is a class of stochastic sequential processes in which the reward and transition probability depend only on the current state of the system and the current action. The MDP models have gained recognition in such diverse fields as engineering, economics, communications and so on. We can obtain the optimal control policy for the supplier management system that minimizes the expected average cost per period. Comparisons between the optimal control policy and the kanban policy are shown numerically.