In real life, many inventory goods, such as agricultural products, fashion goods, drugs and high-tech products, are subject to depletion through spoilage, shrinkage, decay and obsolescene . The deterioration is quite prevalent and should not be disregarded. Inventory management for deterioration goods has received many attentions from researchers and practitioners. Most of the existing researches focus on the EOQ-based inventory decision models. Ghare and Schrader  presented the EOQ model by considering the combined effects of demand, usage and linear decay. Covert and Philip used the variable deterioration rate of the two-parameter Weibull distribution, to formulate the inventory decision model under the assumptions of a constant demand rate, with no shortages allowed. Philip  modified this model by using the deterioration rate of the three-parameter Weibull distribution. Tadikamalla  adopted gamma distributed deterioration under constant demand over time, without shortages. Moon and Lee  presented the EOQ model with a normally distributed deterioration rate. Other deterioration inventory models have extended prior research by considering a time-varying demand function, with or without shortages. Dave and Patel  proposed an EOQ model under time-proportional demand, with no shortages allowed. Sachan  extended their model by considering shortages. Bahari-Kashani  generalized the problem by permitting variations in both replenishment cycle length and order quantity. Bose et al developed an EOQ model for deterioration items incorporating the effects of inflation, time value of money, a linearly time-dependent demand rate and shortages. Replenishment decision models under time-proportional demand and exponentially decaying deterioration rate was developed in .
It is observed that large quantities of consumer goods displayed in a supermarket generate higher demands. Silver and Peterson  noted that the sales at the retail level tend to be proportional to the inventory displayed. Gupta and Vrat , Mandal and Phaujdar , Baker and Urban , Datta and Pal , etc developed the EOQ models with stock-dependent demand rate. Mandal and Phaujdar , Pal et al.  developed the inventory models for deteriorating items with stock-dependent demand rate. In this paper, we have extended these works, on deteriorating inventory research, by considering deteriorating goods with stock-dependent demand in a two-echelon supply chain consisting one manufacturer and one retailer, the objective is to investigate the effects of supply chain coordination on profit increase in the supply chain, and study the impact of different parameters associated with the model, such as the rate of deterioration, the retailer's purchase cost, the manufacturer's production cost, the retailer's and manufacturer's holding cost on the supply chain profit increase percentages generated by the supply chain coordination.
2. Assumptions and Notations
(1) The retailer replenishes the stocks from the exclusive source on an EOQ basis. Replenishments are instantaneous.
(2) Lead time is assumed to be zero for the sake of simplicity.
(3) No backorders are allowed.
(4) Demand rate is dependent on the instantaneous inventory level. The demand rate d(I) of the item, when the inventory is I , is considered in the form d(I) = [alpha][I.sup.[beta]], where [alpha] > 0 and 0 < [beta] < 1 are scale and shape …