生产与存储问题的数学模型讲解.pdfVIP

生产与存储问题的数学模型 生产与存储问题的数学模型 摘 要 在一定时期内,生产的成本费与库存费一直是厂家最关心的优化指标。本文根据题 中的条件针对如何满足市场需要的条件下,使总成本最小，利用了多目标动态规划的方 法，建立了生产与存储的优化模型。 我们知道增大生产量可以降低成本费，但如果超过市场的需求量,就会因积压增加 存贮费而造成损失。相反，如果减少生产量，虽然可以降低存贮费，但又会增加生产的 成本费，同样会造成损失。故可以找到一个生产计划使得生产的生产费与存贮费之和达 到一个最小值。 4  根据该题目我们可以建立一个目标函数：minw (h c)，其中 为第 次的h i i i i i1 库存费用， 为第 次的生产成本费用。在对目标函数进行规划，建立数学模型求解。c i i 并对该模型进行分析。 关键词：生产与存储；建模；动态规划；线性规 生产与存储问题的数学模型 THE MATHEMATICAL MODEL OF PRODUCTION AND STORAGE PROBLEMS ABSTRACT In a certain period of time, cost and inventory cost of production has been optimized index manufacturers are most concerned about. According to the questions of the conditions on how to meet the needs of the market conditions, to minimize the total cost, using the method of multiobjective dynamic programming, establishes the optimization model of production and storage. We know that increase the production capacity can reduce the cost, but if the amount exceeds market demand, there will be a loss is caused due to the backlog of increased storage cost. On the contrary, if the production is reduced, although can reduce the storage cost, but it will increase production costs, will also cause the loss of. So we can find a production plan making production fee and storage cost of production and reach a minimum value. According to the topic we can establish an objective function ：