摘要
A mathematical model to determine the optimal production lot size for a deteriorating production system under an extended product inspection policy is developed. The last-K product inspection policy is considered so that the nonconforming items can be reduced, under which the last K products in a production lot are inspected and the nonconforming items from those inspected are reworked. Consider that the products produced towards the end of a production lot are more likely to be nonconforming, is proposed an extended product inspection policy for a deteriorating production system. That is, in a production lot, product inspections are performed among the middle K1 items and after inspections, all of the last K2 products are directly reworked without inspections. Our objective here is the joint optimization of the production lot size and the corresponding extended inspection policy such that the expected total cost per unit time is minimized. Since there is no closed form expression for our optimal policy, the existence for the optimal production inspection policy and an upper bound for the optimal lot size are obtained. Furthermore, an efficient solution procedure is provided to search for the optimal policy. Finally, numerical examples are given to illustrate the proposed model and indicate that the expected total cost per unit time of our product inspection model is less than that of the last-K inspection policy.
A mathematical model to determine the optimal production lot size for a deteriorating production system under an extended product inspection policy is developed. The last-K product inspection policy is considered so that the nonconforming items can be reduced, under which the last K products in a production lot are inspected and the nonconforming items from those inspected are reworked. Consider that the products produced towards the end of a production lot are more likely to be nonconforming, is proposed an extended product inspection policy for a deteriorating production system. That is, in a production lot, product inspections are performed among the middle K1 items and after inspections, all of the last K2 products are directly reworked without inspections. Our objective here is the joint optimization of the production lot size and the corresponding extended inspection policy such that the expected total cost per unit time is minimized. Since there is no closed form expression for our optimal policy, the existence for the optimal production inspection policy and an upper bound for the optimal lot size are obtained. Furthermore, an efficient solution procedure is provided to search for the optimal policy. Finally, numerical examples are given to illustrate the proposed model and indicate that the expected total cost per unit time of our product inspection model is less than that of the last-K inspection policy.
基金
supported by the National Natural Science Foundation of China(60874034).
作者简介
Hu Fei was born in 1977. He is the Ph. D. candidate in School of Electrical Engineering and Automation and a lecture in Department of Mathematics, Tianjin University. His research interests include system modeling and reliability analysis. E-mail： hfzdzy@126.comXu Genqi was born in 1959. Now he is a professor in Department of Mathematics, Tianjin University. He received his Ph.D. degree from the System Science In-stitute of Chinese Academy of Sciences. His research interests are spectral theory of linear operator, system stability and reliability analysis, etc.Ma Lixia was born in 1978. She is the Ph.D. candidate in School of Electrical Engineering and Automation and a lecture in Department of Mathematics, Tianjin University. Her research interest is in system stability analysis.
