On the stochastic sequential and non‐sequential production planning problem
研究了随机需求下顺序与非顺序生产计划问题，分析了近似解的最坏情况误差，并给出了两期问题的上界，在均匀分布下误差在23%以内。
This dissertation examines a stochastic sequential and a non-sequential capacitated production planning problem (Bitran and Yanasse, Operations Research, 32, 5, 1984) where the demand of each period is a continuous random variable. The stochastic non-sequential production planning problem is at first examined with sequence independent and then with sequence dependent set-up costs and the worst case error determined when an approximate solution is obtained by solving the deterministic equivalent. We prove in general that the worst case error is not dependent on the nature of the set-up cost. Based on a result due to Huang, Ziemba and Ben-Tal (Operations Research, 25, 2, 1977) we identify a family of approximations for both the stochastic sequential and the stochastic non-sequential production planning problem. We find a problem which bounds the stochastic sequential problem of two period from above: the upper bound coupled with Bitran and Yanasses' (Operations Research, 32, 5, 1984) lower bound enable us to perform worst-case analysis. Given uniformly distributed demand, this analysis produces results within 23% of optimality. Finally, we derive conditions such that an order-up-to the service level policy is optimal for the T-period stochastic sequential capacitated production planning problem.