Deteriorating inventory models are used as decision support tools for managers primarily, although not exclusively, in the retail trade. The mathematical modeling of deteriorating items allows managers to analyze their inventory management systems to identify areas that can be improved and to measure the corresponding potential benefits. This study develops an enhanced deteriorating inventory model for optimizing the inventory control strategy of companies operating in sectors with deteriorating products. In contrast with previous studies, our model holistically accounts for the overall financial effect of a company’s policies on product price discounting and on inventory shortages while considering the time value of money (TVM). We aim to find the optimal replenishment strategy and the optimal price reductions that maximize the discounted profit function of this analytical model over a fixed planning horizon. To this end, we use an economic order quantity model to study the effects of the TVM and inflation. The model accounts for pre- and post-deterioration discounts on the selling price for non-instantaneous deteriorating products with the demand rate being a function of time, price-discounts and stock-keeping units. Shortages are allowed and partially backordered, depending on the waiting time until the next replenishment. Additionally, we consider the effect of discounts on the selling price when items have either an instant deterioration or a fixed lifetime. We propose five implementable solutions for obtaining the optimal values, and examine their performance. We present some numerical examples to illustrate the applicability of the models, and carry out a sensitivity analysis. The study reveals that accounting for TVM and inventory shortages is complex and time-consuming; nevertheless, we find that accounting for TVM and shortages can be valuable in terms of increasing the yields of companies. Finally, we provide some important managerial implications to support decision-making processes.

The present study investigates an inventory model for non-instantaneous deteriorating items under inflationary conditions with partially backlogged shortages. In today’s market structure consumers are looking for goods for which there is a delay in deterioration. At the same time, the consumers’ willingness to wait has been decreased over time, which leads to lost sales. Moreover in financial decision-making, the effects of inflation and time value of money cannot be oblivious to an inventory system. In this scenario, managing inventory of goods remains a challenging task for the decision makers, who may also have to rent warehouse under different prevailing factors such as, bulk discount, limited space in the retail outlet, or increasing inflation rates. With a focus on reduction of costs and increasing customer service, warehouse decision models are crucial for an organization’s profitability. Hence a mathematical model has been developed in the view of above scenario, in order to determine the optimal policy for the decision maker, by minimizing the present worth of total cost. The optimization procedure has been illustrated by a numerical example and detailed sensitivity analysis of the optimal solution has been performed to showcase the effect of various parameters. Managerial implications has also been presented to aid the decision making process.

This study is an inventory model with consideration of price, stock dependent demand, partially backlogged shortages, and two constant deterioration rates. In this model, demand function depends on price and stock while during the shortage time, demand depends only on price of the product. The deterioration is taken into account as a non-instantaneous, once the item is stocked in retailer’s house, any time deterioration can start with a constant rate for a certain period, then this deterioration rate increases. Shortages are allowed and it is partially backlogged. The corresponding inventory problem constitutes a non-linear constraint optimization problem. Here this problem has been solved using Lingo 15 software and also give 3D graph with the help of MATLAB2010a to show the convexity of the objective function. Finally, to illustrate and validate the inventory model, a numerical example is used considering fixed price. To study the effect of changes of different inventory parameters, a sensitivity analysis has been carried out changing one parameter at a time holding other parameters unchanged.

This study investigates optimal pricing and inventory policies for non-instantaneous deteriorating items with permissible delay in payment. The demand rate is as known, continuous and differentiable function of price while holding cost rate, interest paid rate and interest earned rate are characterized as independent fuzzy variables rather than fuzzy numbers as in previous studies. Under these general assumptions, we first formulated a fuzzy expected value model (EVM) and then some useful theoretical results have been derived to characterize the optimal solutions. An efficient algorithm is designed to determine the optimal pricing and inventory policy for the proposed model. The algorithmic procedure is demonstrated by means of numerical examples.