有限时域内部分缺货的变质品生产-定价策略研究

研究有限时域内对变质产品同时安排生产计划和制定定价策略的问题。有限时域被划分成同等长度的多个周期，产品以固定的生产率间歇生产，并以固定的速率发生变质。需求同时依赖于时间和产品价格，在每个周期内都允许缺货且短缺量部分延迟订购。目的是要寻求一个使有限时域内系统的平均利润最大化的生产计划和定价策略。在算例中，分别讨论了需求随时间增大和减小两种不同的需求模式，采用Box复合算法，通过数值计算求得相应的最优生产计划和定价策略。分析表明：对于成长期或销售季初的产品，系统应采用“小批量多批次”的生产方式；而对于衰退期或销售季末的产品，应采用“大批量小批次”的生产方式。此外，不同类型的产品在不同需求模式下的定价策略有所不同：对于有限时域较短或变质率较高的产品，处于衰退期或销售季末的定价要低于成长期或销售季初的定价；相反，对于有限时域相对较长或变质率较低的产品，在衰退期或销售季末的最优定价要高于在成长期或销售季初的定价。

A Production-pricing Strategy for Deteriorating Items with Partial Backlogging Over a Finite Horizon

With the development of science and technology, the upgrade rate of products is faster than ever, and the trend of popularity varies continuously. All of these lead to the shorter sales period and production planning horizon. In addition, more and more products are possessed of the characteristic of perishability and limited lifetime. Therefore, the influence of the sales period and perishability of the products on the production planning and pricing cannot be neglected anymore. The issue of joint production planning and pricing decision for perishable items over a finite horizon is studied in this paper. The finite horizon, H, is divided into several cycles with the same interval, and the length of each cycle is H/n. The production rate, R and the deterioration rate, θ, are constants. The demand rate of the products denoted by D(t,p) is dependent on time and price linearly, and D(t,p)=a+bt+cp (a≥0,b≠0,c<0). The unsatisfied demand is partially backlogged, and the backlogging rate B(τ)=K₀e^-K₁τ, <1, k₁≥0. The aim of this paper is to find a joint production and pricing policy maximizing the average profit over the finite horizon. The Box complex algorithm is presented to obtain the optimal solution of the proposed model. To illustrate the effectiveness of the model and algorithm, some numerical examples are presented and two demand patterns are considered respectively: the demand is increasing or decreasing over time. The optimal production and pricing policies in the two situations are developed through the Box complex algorithm. It is indicated that for products in the growth stage or at the beginning of sales season, the system should adopt the‘low-volume multi-batch’mode of production. However, for products in the decline stage or at the end of the sales season,‘multi-volume small batch’mode of production is preferred. In addition, the pricing strategies for products with different characteristics and demand patterns are different. For products with shorter sale horizon or higher deterioration rate, the price in the decline stage or at the end of the sales season is lower than that in the growth stage or at the beginning of sales season; however, for products with longer horizon or lower deterioration rate, the price in the decline stage or at the end of the sales season is higher than that in the growth stage or at the beginning of sales season. The model and algorithm addressed in this paper can be used to help making joint decision of production planning and pricing for enterprise producing perishable items.