Abstract: 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.

Key words: finite horizon, deteriorating items, partial backlogging, production, pricing