基于效用替代率的物资储备量模型与算法

研究在物资储备有容量限制且需求未知的情形下,考虑多种物资之间具有替代性时应如何决定各物资的储备量,使得所有储备物资在满足需求时带来的效用尽可能大的物资储备问题.对物资之间的替代性进行分析并给出了效用替代率的定义,在此基础上建立一般的物资储备量模型,分析了该模型与背包问题模型以及指派问题模型之间的区别和联系.针对该问题的一种特殊情形设计了效用替代率贪婪算法并进行了算法的性能分析.最后通过一个数值算例说明引入替代率可以改善物资储备的效用.

Model and algorithm of materials inventory based on substitution rate

This paper studied materials inventory problem based on substitution rate, while the inventory capacity was limited and the demand was unknown, and the objective was to maximize the effectiveness brought by the inventory. Firstly, this paper analyzed the phenomenan of substitution and defined substitute rate. Then, the model of materials inventory was eatablished, and the differences among this model, the model of knapsack problem and the model of assignment problem were discussed. For a special case of this problem, we proposed a substitute rate greedy algorithm and analyzed its performance. At last, an example shows the application of the substitute rate greedy algorithm.