随机生产中拖后需求的变质产品最优生产策略

针对部分短缺量拖后的变质产品,建立随机生产状态下的生产-库存模型.所谓随机生产状态,是指生产过程会随机地从一种可控状态向另一种不可控状态转移,当生产处于不可控状态时,会生产出一定比例的次品.其中,生产状态的转移服从均匀分布.通过生产-库存模型得到了随机生产状态下总成本函数,分析得到,该总成本函数是一个关于生产次数的凹函数,并由此提出了最优生产次数算法.最后给出了算例.算例结果表明,最优生产次数算法能够有效地将一个4n 1维的最优问题转化为一个一维问题,为变质商品的生产-库存决策提供了简便有效的方法.

Optimal production policy for deteriorating items with backlogging demand in stochastic production process

A production-inventory model in a stochastic production process is established for deteriorating items with partial backlogging demand.It is assumed that the process is subject to a random imperfection from an in-control state to an out-of-control state with an arbitrary distribution and,thus,produces some proportion of imperfect items.At the same time,an elapsed time to the out-ofcontrol state is uniformly distributed.Through the production-inventory model, the total cost function which is concave in a stochastic production process is obtained,and a production number algorithm which determines an optimal production number is derived.Finally,a numerical example is given.The results indicate that the optimal algorithm can effectively transform a 4n 1 dimension optimal problem into a one dimension optimal problem,and it can also present a simple and effective method for making production-inventory policy of deteriorating items.