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考虑一个单周期的生产决策模型,在该模型中有一个制造商生产两种可替代的产品。面对随机的市场需求,制造商要在需求到来之前制定出两种产品的生产决策来最大化自己的期望利润。在制造商的资金有、无约束两种情形下,证明了制造商的收益函数的期望是关于两种产品生产数量的凹函数,探讨了资金的约束以及产品的替代给制造商的生产决策所带来的影响,给出了最优生产数量的若干性质。另外,针对需求分布为均匀分布的特殊情形给出了制造商最优生产决策的简单表达形式。
Consider a one-cycle production decision model in which one manufacturer produces two alternative products. Faced with random market demand, manufacturers need to come up with the decision-making before the two products to maximize their profit expectations. In the two cases of the manufacturer’s capital and the non-constraint, it proves that the expectation of the manufacturer’s income function is a concave function about the quantity of the two products, discusses the constraint of the capital and the substitution of the product to the manufacturer’s production decision-making place Brought some of the properties of optimal production quantities. In addition, for the special cases with uniform distribution of demand, a simple expression of manufacturer’s optimal production decision is given.