Mathematical models for Business Strategies in Direct Mail

本研究建立了数学模型，用以解决直邮中的三类问题：* 目录投递的缩减问题 * 根据目录发布后的需求量预测产品的需求量。一种判断新产品是否为快速消费品的方法针对上述第一个问题，本研究提出了一个基于更新报酬理论的数学模型，重点研究了经常购买的顾客。对于第二个问题，将累积需求用均值函数为H（t）的非齐次Poisson过程表示.提出了一种利用过去均值函数与目录发布后均值函数之间的关系进行需求预测的方法;最后提出了利用测试目录对新产品进行销售测试的方法。如果测试目录中的需求数量等于或大于k，则新产品被视为将在正常目录中采用的快速移动产品。当测试目录中的需求数量小于k时，视为滞销产品，不纳入正常目录。为了获得k的最优值，用公式表示了期望成本。

This study has built mathematical models for solving the following three kinds of problems in direct mail :*Curtailment problems of catalog delivery*Demand forecasting of a product based on the demand immediately after the publication of catalog.*A method for judging whether or not the new product is a fast moving productFor the first problem in the above, this study proposed a mathematical model based on renewal reward theory, focusing on customers who have frequently purchased. Under the proposed model, the catalog delivery is curtailed for the customers who have not responded to the recent K successive catalog deliveries.For the second problem, the cumulative demand was expressed by means of non-homogeneous Poisson process with mean value function H (t). A method was then proposed for demand forecasting, which used the relationship between the mean value function in the past and that immediately after the publication of the catalog.For the final problem, it was proposed to conduct a sales test for a new product using a test catalog. If the number of demands in the test catalog is equal to k or more, the new product is regarded as a fast moving product to be adopted in the normal catalog. When the number of demand in the test catalog is less than k, it is regarded as a slow moving product not to adopt in the normal catalog. The expected cost was formulated for the purposed of obtaining a optimal value of k.