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中文摘要：
研究了允许需求延迟，制造商生产能力有限情形下，价格对多产品批量模型的影响。制造商处于垄断地位，具有定价主导权。分析了曩优解的性质乖特征．蛤出了基于拉格朗日松驰的启发式算法，耙原问题转换成若干个单产品无能力受限批量与定价协调问题．在算法中设计了拉格朗日下界问题和上界问题，通过在上、下界问题问的反复速代，得到曩优价格序列和相应的曩优生产策略．实验结果表明，与分散策略相比，显著降低了计算量；制定更为合理的价格，增加了制造商的利润。
英文摘要：
The effects of pricing on production decisions were studied. The dynamic prices as the decision variables were introduced into multi-item capacitated lot sizing problem with backlogging. The problem was formulated as a mixed-integer program. Lagrangean relaxation was used to decompose the capacitated problem into a set of simple uncapacitated sub-problems. A heuristic method based on Lagrangean smoothing multipliers was proposed to solve the original problem. Although multi-item capacitated lot sizing problem （MCLSP） is an NP-hard problem, the model appears to be easier to solve than MCLSP from a numerical point of view. The model also improves the finn＇s profit in comparison with the decentralized policy.
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