A profit maximization inventory model for a differential item, units of which are not in perfect conditions and are sold from two shops (primary and secondary shops) that are owned by a single management is formulated with variable demand. Here, differential units (both perfect and defective) are received at the primary shop with an infinite rate of replenishment. At the primary shop, the perfect/good products whose demand is a deterministic linear function of current stock level are sold and the defective units spotted at the time of selling the good products from the lot are transferred continuously to the secondary shop for sale at a reduced price and demand for these units is linearly proportional to the selling price only. In both the shops, shortages are allowed and fully backlogged out of a differential lot which is sorted out into good and defective units in "no-time" at the beginning of the subsequent schedule. For this model, there are three scenarios depending upon the time of occurrence of shortages at the shops. The time of shortages at the secondary shop occurs (i) exactly at the same time or (ii) before or (iii) after the time of shortages at the primary shop. Again, in each scenario, there are three different cases when the defective units spotted "in-no-time" sorting at the beginning of subsequent schedule are (i) exactly equal to or (ii) less than or (iii) greater than the actual backlogged units at the secondary shop. Thus, for each case under each scenario, profit is maximized and optimum order quantities are evaluated using the computer algorithm based on a gradient method (generalised reduced gradient method). The models are illustrated with numerical examples. (C) 2003 Elsevier Science Inc. All rights reserved.
