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Multi-item inventory model for deteriorating items with stock dependent demand under two-warehouse system is developed in fuzzy environment (purchase cost, investment amount and storehouse capacity are imprecise ) under inflation and time value of money. For display and storage, the retailers hire one warehouse of finite capacity at market place, treated as their own warehouse (OW), and another warehouse of imprecise capacity which may be required at some place distant from the market, treated as a rented warehouse (RW). Joint replenishment and simultaneous transfer of items from one warehouse to another is proposed using basic period (BP) policy. As some parameters are fuzzy in nature, objective (average profit) functions as well as some constraints are imprecise in nature, too. The model is formulated so to optimize the possibility/necessity measure of the fuzzy goal of the objective functions, and the constraints satisfy some pre-defined necessity. A genetic algorithm (GA) is used to solve the model, which is illustrated on a numerical example

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.

In this paper, a deterministic inventory model for deteriorating items with two warehouses and shortages is developed. It is observed that in supermarkets, the demand rate is usually influenced by the amount of the stock level, i.e., the demand rate may go up or down with the on-hand inventory level. Influenced by this, we develop a model where the demand is dependent on the present stock level. Trade credit is provided to the customer to attract them and boost up the demand. A rented warehouse (RW) is used when the ordering quantity exceeds the limited capacity of the own warehouse. Due to different storage conditions, deterioration rate in two warehouses may be different. In addition, shortages are neither completely backlogged nor completely lost assuming the backlogging rate to the inversely proportional to the waiting time for the next replenishment. The associated cost minimisation is illustrated by numerical example and also its sensitivity analysis is carried out by using Mathematica-5.2 for the feasibility and applicability of our model. Keywords:two-warehouse inventory model; shortage; stock-dependent demand rate; time-dependent partial backlogging rate; permissible delay in payments. S.R. Singh et al.Reference to this paper should be made as follows: Singh, S.R., Kumari, R. and Kumar, N. (2011) 'A deterministic two warehouse inventory model for deteriorating items with stock-dependent demand and shortages under the conditions of permissible delay', Int.