Joint Stocking and Product Offer Decisions Under the Multinomial Logit Model
Joint Stocking and Product Offer Decisions Under the Multinomial Logit Model
复制标题
多项Logit模型下的联合库存和产品报价决策
DOI：
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发表时间：
2013
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影响因子：
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通讯作者：
Huseyin Topaloglu
中科院分区：
文献类型：
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作者：
Huseyin Topaloglu
本文研究了一个联合进货与供货问题。我们有很多产品可以在有限的销售期限内满足需求。假设客户根据多项logit模型在提供的一组产品中进行选择，我们需要决定在销售范围内提供哪些产品，以及每种产品的库存数量，以使期望利润最大化。我们将问题表述为一个非线性规划，其中决策变量对应于每种产品的库存数量和每组产品的提供时间。该非线性规划具有决策变量数量多、目标函数不可分、不可凹等特点。我们利用多项式logit模型的结构，构造了一个决策变量数量可控、目标函数可分离的等效非线性规划。利用可分性，通过具有二维连续状态变量的动态规划求解等效非线性规划。由于动态规划的求解需要对状态变量进行离散化，我们研究了其他近似求解方法。我们的等效非线性规划和近似解方法产生了好的报价集的见解。
This article studies a joint stocking and product offer problem. We have access to a number of products to satisfy the demand over a finite selling horizon. Given that customers choose among the set of offered products according to the multinomial logit model, we need to decide which sets of products to offer over the selling horizon and how many units of each product to stock so as to maximize the expected profit. We formulate the problem as a nonlinear program, where the decision variables correspond to the stocking quantity for each product and the duration of time that each set of products is offered. This nonlinear program is intractable due to its large number of decision variables and its nonseparable and nonconcave objective function. We use the structure of the multinomial logit model to formulate an equivalent nonlinear program, where the number of decision variables is manageable and the objective function is separable. Exploiting separability, we solve the equivalent nonlinear program through a dynamic program with a two dimensional and continuous state variable. As the solution of the dynamic program requires discretizing the state variable, we study other approximate solution methods. Our equivalent nonlinear program and approximate solution methods yield insights for good offer sets.