OPTIMIZATION OF A CONDITION-BASED DURATION-VARYING PREVENTIVE MAINTENANCE POLICY FOR THE STOCKLESS PRODUCTION SYSTEM BASED ON QUEUEING MODEL

摘要

A stockless production system is considered, in which the products are not produced until the orders are accepted. Due to this character, the duration of the preventive maintenance has an influence on the lead time. In addition, in this stockless production system, the cost of the preventive maintenance depends on its duration; if the lead time exceeds to the quoted lead time, some penalty cost should be considered; and the non-conforming products can still be sold by a discount. A condition-based duration-varying preventive maintenance policy is designed for the stockless production system, by making a tradeoff among the duration of the preventive maintenance, the time for the machine continuously producing, and the lead time of the order. According to the characters of the stockless production system with the designed preventive maintenance policy, it can be modeled by a BMAP/G/1 infinite-buffer queueing model with gated service and queue-length dependent vacation. Based on this queueing model, the stationary probability distributions of four performance measures for the stockless production system are analyzed, including, the number of the products produced in a production cycle, the number of the unfulfilled orders at arbitrary time, the time required to fulfill the tasks present at arbitrary time, and the lead time of the order accepted at arbitrary time. Moreover, based on some information of these performance measures, a profit function, which represents the average profit of the manufacture in a production cycle, is constructed to optimize the designed preventive maintenance policy according to specific conditions. Finally, given an example with the purchasers having different sensitivities to the lead time, some numerical experiments are carried out; and from the numerical experiments, some general results can be inferred for the stockless production system with the designed preventive maintenance policy.