This paper studies the effect of inflation and customer returns on joint pricing and inventory control for deteriorating items. We adopt a price and time dependent demand function, also the customer returns are considered as a function of both price and demand. Shortage is allowed and partially backlogged. The main objective is determining the optimal selling price, the optimal replenishment cycles, and the order quantity simultaneously such that the present value of total profit in a finite time horizon is maximized. An algorithm has been presented to find the optimal solution. Finally, we solve a numerical example to illustrate the solution procedure and the algorithm. 1. Introduction Recently, many researchers have studied the problem of joint pricing and inventory control for deteriorating items. Generally, deterioration is defined as decay, damage, spoilage, evaporation, and loss of utility of the product. Most physical goods undergo decay or deterioration over time such as medicines, volatile liquids, blood banks, and others [1]. The first attempt to describe optimal ordering policies for deteriorating items was made by Ghare and Schrader [2]. Later, Covert and Philip [3] derived the model with variable deteriorating rate of two-parameter Weibull distribution. Goyal and Giri [4] presented a detailed review of deteriorating inventory literatures. Abad [5, 6] considered a pricing and lot-sizing problem for a perishable good under exponential decay and partial backlogging. Dye [7] proposed the joint pricing and ordering policies for a deteriorating inventory with price-dependent demand and partial backlogging. Dye et al. [8] developed an inventory and pricing strategy for deteriorating items with shortages when demand and deterioration rate are continuous and differentiable function of price and time, respectively. Chang et al. [9] introduced a deteriorating inventory model with price-time-dependent demand and partial backlogging. Nakhai and Maihami [10] developed the joint pricing and ordering policies for deteriorating items with partial backlogging where the demand is considered as a function of both price and time. Tsao and Sheen [11] proposed the problem of dynamic pricing and replenishment for a deteriorating item under the supplier’s trade credit and the retailer’s promotional effort. Sarkar [12] extended the model with finite replenishment rate, stock-dependent demand, imperfect production, and delay in payments with two progressive periods. Sarkar [13] proposed an EOQ (economic order quantity) model for finite replenishment rate with delay
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