设备多状态、多类顾客制造系统的生产速率和库存分配联合决策

在生产制造系统中, 设备状态严重制约系统产能, 并增加生产过程的不确定性. 为应对不确定性对系统的影响, 对顾客进行细分, 实施差异化服务. 在顾客泊松达到、 缺货不补的假设下, 研究了设备多状态、多类顾客制造系统的生产和库存分配联合决策问题. 利用马尔科夫决策理论, 建立了系统在无限期期望折扣总成本准则和平均成本准则下的最优方程, 并证明了最优策略具有相似的结构性质. 最优生产速率策略是生产阈值水平随设备状态非增的阈值策略, 即当库存水平降至该阈值水平之下时, 以允许的最大生产速率生产, 否则不生产. 最优库存分配策略是分配阈值水平随设备状态非增的阈值策略. 另外, 缺货成本大的顾客具有较低的分配阈值.

Optimal control of production rate and inventory in a manufacturing system with multiple machine states and multiple demand classes

In manufacturing system, machine state constrains the production capacity and increases the manufacturing uncertainty. Customer differentiation, which provides different services to different customers, arises to cope with this uncertainty. This paper considered the optimal production and inventory allocation control of a multi-state production-inventory system with Poisson arrival and lost sales. The demand that can't be satisfied immediately is lost and incurs a lost sale cost, which varies from class to class. The production rate depends on the machine state. By formulating the system as a Markov decision process, we obtained that the structural properties of the optimal control policies under the expected total discounted cost criterion are similar with that under the average cost criterion. The optimal production rate policy is the threshold policy with the threshold level non-increasing in the machine state, that is, if it is optimal to produce, produce with highest rate. The optimal inventory allocation policy is the rationing policy with the rationing level non-increasing in the machine state. The demand with higher lost sale cost has lower rationing level.