Inventory of multi-deteriorating items sold from two shops under single management with constraints on space and investment

In this study, we propose an inventory model for several continuously deteriorating items, sold from two shops – primary and secondary shops, under single management dealing with limitations on investment and total floor-space area. Initially items are purchased in lots and received at the primary shop, then fresh and deteriorated units are separated, only the fresh units are sold from the primary shop with a profit and its demand is a deterministic linear function of instantaneous stock level and the selling price of the units. The deteriorated units are transferred to the adjacent secondary shop for sale at a reduced price and the demand for these units is linearly proportional to the selling price only. In both the shops, shortages are not allowed. There may be six scenarios depending upon the time periods of two shops and altogether there will be 6ⁿ (n ⩾ 2) different cases for n items. In each case optimum order quantities are evaluated maximizing the corresponding average profit function. Models are illustrated with numerical examples for two items only.