A two-commodity deteriorating inventory model with price-dependent demand

Recently, inventory models considering deteriorating items have attracted much more attention in that almost all commodities in real life deteriorate over time. This study deals with a two-commodity deteriorating inventory model when the demand of each commodity depends linearly on the selling prices of both two commodities. Deterioration rate of each commodity is assumed to be time-proportional and the time to deterioration follows a two-parameter Weibull distribution. The objective of this study is to find the joint optimal pricing strategies and replenishment policies to maximize the total average net profit in a replenishment cycle. This problem can be finally formulated as a nonlinear programming and the optimal solution is proved to exist. Solution procedure and algorithm of searching for the optimal solution are developed in detail. A numerical example is given at last which illustrates the results of the model. The optimal solutions and some useful curves are obtained by simulating with Matlab 7.0.