Reverse logistic model for deteriorating item with preservation technology investment and learning effect in an inflationary environment

Recycling is essential for the existence of the environment. Nowadays, recycling is also being promoted by the governments of numerous countries in the world. In the recycling process, the used items are collected from the customers and sent back to the remanufacturing unit. In the literature, many authors have assumed that the remanufactured items are as good as the freshly produced ones, but this is not really practical. The remanufactured items are of lower quality than the freshly produced ones. For purposes of studying the recycling process we have developed a reverse logistic model for the deteriorating items. The deterioration rate is treated as a controllable variable, which is controlled by investing in preservation technology. The demand rate is taken as exponential function of time with demand dependent manufacturing and remanufacturing rates. The fresh products are sold in the primary market and the remanufactured products are sold in the secondary market at a low selling price, in view of the low quality of remanufactured products. The whole study is carried out under the effect of learning in an inflationary environment and the learning coefficients are associated with production cost and set-up cost. The main objective of this study is to find the optimal cost value and the optimal operating times. At the end of this article numerical illustration is presented and sensitivity analysis is performed. The whole of the mathematical calculations is done with the use of the mathematical software Mathematica7.