Abstract: Because of the stochastic fluctuations of man, machine, material, method and environment, defective items can not be avoided in the production process. Considering these characteristics, a more practical Mixed Integer Programming（MIP） model is presented for supply chain order allocation problem, so as to minimizing the transaction cost of purchasing from suppliers, purchasing cost, defective units, delivered units and maximizing the evaluation scores of the selected suppliers. Because of its difficulty, a Simulated Annealing（SA） algorithm combined with a heuristics rule is developed to solve the model and to avoid the illegal initial solutions and neighborhood solutions. Random instances show that the model provides systemic simulation for the whole decision-making process and reflects the product defect situation. And the results of SA are stable and acceptable in allowable CPU time. Computational experiments show that the SA heuristic algorithm outperforms LINGO with respect to solution quality and computational time when the instances become larger.

Key words: defect rate, order allocation, Mixed Integer Programming（MIP） model, Simulated Annealing（SA） algorithm

摘要： 受4M1E（人、机、料、法、环）因素的随机波动影响，产品的制造过程通常是不完美的，从而产生不良产品。针对已有研究多忽略不良产品的特点，建立了更加符合实际需求的订单分配多目标混合整数规划模型，其优化目标为最小化交易成本、采购成本、不良产品数量、产品延迟交付数量，以及最大化供应商信誉评价。考虑到模型求解的复杂度，设计了一种模拟退火算法，并结合启发式规则避免了大量非法初始解与邻点解的出现。实验算例表明所建立的模型能够反映订单分配过程中的产品缺陷现象，其算法能够在允许的运算时间内获得稳定的满意解，并且随着算例规模的增大，其计算时间与优化结果均优于LINGO软件。

关键词: 产品缺陷率, 订单分配, 混合整数规划模型, 模拟退火算法