An inventory model for deteriorating items with shortages and stock-dependent demand under inflation for two-shops under one management

In this study, we propose an inventory model for a differential item, units of which are not in perfect conditions, sold from two-shops- primary and secondary shop, under one management is formulated with stock-dependent demand rate and inflation. Initially, items are purchased in lots and received at the primary shop with an infinite rate of replenishment, then perfect and defective units are separated, only the perfect/ good units are sold from the primary with a profit and its demand is a deterministic linear function of current stock level. The defective units spotted at the time of selling of the good products from the lot are transferred continuously to the adjacent secondary shop for sale at a reduced price and demand for these units is linearly proportional to the selling price. In both shops, shortages are allowed. In this study, there are three scenarios depending upon the time of occurrence of shortages at the shops. At the secondary shop, the time of shortages occurs: (1) exactly at the same time or (2) before or (3) after the time of shortages at the primary shop. In each case under each scenario, profit is maximized and optimum order quantities are evaluated using the computer algorithm based on a gradient method. Finally, a numerical example and sensitivity analysis is used to study the behavior of the model. © Operational Research Society of India 2011.