This paper presents a literature review for inventory control of deteriorating items since 2018. A classification including 18 classes and 33 subclasses is offered to categorize inventory control models, constraints, and solution methods used in previous studies. Providing standard classes in this field, such as demand, deterioration, shortages, number of warehouses, and time value of money alongside new classes, for example, the type of model costs and supply chain, inventory constraints, number of supply chain levels, time horizon, lead time, considering multi-item models, preservation technology, financial conditions, non-instantaneous deteriorating items, environmental issues, and solution methods made this classification more comprehensive. A brief history and explanation are given to understand each class better, and related articles are grouped in these classes. The research gaps and a crucial aspect that paves the way for future research are presented in each category. A broad view of the future of this topic is provided, and exciting opportunities are highlighted for researchers to contribute to this field and inspire them to explore these potential areas of research. The potential for future research in this subject is vast and promising; this article offers numerous opportunities for researchers to make significant contributions. The results show that the best ways to extend this topic are using variable deterioration rates, costs, and demand functions, considering realistic assumptions, including allowable shortages with partial backlogging, two warehouses, inflation and discounts, preservation technology, uncertain lead time, and environmental issues. Developing cyclic (if possible), multi-item, and production models with financial conditions and various inventory constraints is an excellent way to develop existing models. Finally, solving the proposed models using exact methods to find the global answer is a great effort to contribute to this field.

This paper deals with a pricing and production-distribution model for a deteriorating item in a two-echelon supply chain. The profit function for the manufacturer and retailer in the integrated supply chain is derived. The manufacturer's production batch size is regulated to an integer multiple of the discrete delivery lot quantity to the retailer. The objective is to maximize the total profit per unit time by finding the optimal selling price, production lot size, total cycle time, number of deliveries, and delivery lot size, simultaneously. Based on the notion of optimal interval, we outline an effective algorithm for finding the optimal solution. Finally, the authors present a numerical example to illustrate the theoretical results of the model. Sensitivity analysis for the optimal solution with respect to major parameters is also carried out. The results show that, when the deterioration rate increases, both the optimal production lot size and cycle time decrease. It is interesting to note that an increase in the deterioration rate also tends to reduce the delivery lot size without affecting the number of deliveries per production batch. Also, the optimal interval for N does not change when deterioration rate changes. Reductions in the inventory cycle times for both parties demonstrate the negative effects of deterioration on the supply chain.

When a supplier announces a price increase at a certain time in the future, for each retailer it is important to choose whether to purchase supplementary stock to take benefit of the current lower price or procure at a new price. This article focuses on the possible effects of price increase on a retailer’s replenishment strategy for constant deterioration of items. Here, quadratic demand is debated; which is appropriate for the products for which demand increases initially and subsequently it starts to decrease with the new version of the substitute. We discuss two scenarios in this study: (I) when the special order time coincides with the retailer’s replenishment time and (II) when the special order time falls during the retailer’s sales period. We determine an optimal ordering policy for each case by maximizing total cost savings between special and regular orders during the depletion time of the special order quantity. Scenarios are established and illustrated with numerical examples. Through, sensitivity analysis important inventory parameters are classified. Graphical results, in two and three dimensions, are exhibited with supervisory decision.

Trade credit mainly signifies increase in order quantity when retailer offers a trade credit to the customer. From the customer’s view, granting trade credit not only increases sales and revenue but also increases opportunity cost. So, the choice to offer trade credit is an important managerial consideration. Moreover another significant decision on purchasing is to include (or not to include) cash discount benefits and the motivations behind it. Therefore, the major objective of this article is to derive the inventory models for deteriorating items by maximizing the total profit of the retailer. The models includes the cash discount for the retailer depending on ordering quantity and also cash discount for the customer depending on the time. The customer’s demand is expressed as a function of time and price, which is appropriate for the products for which demand increases initially and after sometime it starts to decrease. Lastly, numerical examples along with sensitivity analysis are done, which extracts some fruitful managerial insights.

Inventory control of deteriorating items constitutes a large part of the world’s economy and covers various goods including any commodity, which loses its worth over time because of deterioration and/or obsolescence. Vendor managed inventory (VMI), which is a win-win strategy for both suppliers and buyers gains better results than traditional supply chain. In this research, we study an economic order quantity (EOQ) with shortage in form of partial backorder under VMI policy. The model is concerned with multi-item subject to multi-constraint including storage space, time period and budget constraints. Two metaheuristic algorithms, namely Simulated Annealing and Tabu Search, are used to find a near optimal solution for the proposed fuzzy nonlinear integer-programming problem with the objective of minimizing the total cost of the supply chain. Furthermore, the sensitivity analysis of the metaheuristic parameters is performed and five numerical examples containing different numbers of items are conducted in order to evaluate the performance of the algorithms.

The objective of this work is to generalize the three echelon supply chain model proposed by Jaber and Goyal (2008) [Jaber, M. Y., & Goyal, S. K. (2008). Coordinating a three-level supply chain with multiple suppliers, a vendor and multiple buyers. International Journal Production Economics, 116, 95-103.] for multi-items where single item was considered in production and distribution. This paper develops the coordination amongst different parties in a three-echelon supply chain with a centralized decision process. Producer, suppliers and retailers are the parties of the supply chain where multiple suppliers deliver various types of raw materials to a producer; producer produces different types of items, multi-items, in different units of the factory and supplies the items to multiple retailers. Different deterioration rates for finished items and raw materials are also considered. The model developed of this paper guarantees that the local costs for the members either remain the same as before coordination, or decrease as a result of coordination. A numerical example along with graphical illustrations is considered and the sensitivity analysis is provided to test the feasibility of the proposed model.

The present study reviews different studies on inventory control of deteriorating items in chain supply published over the period 1963- 2013. The study investigates supply chain of the items in terms of various perspectives. Finally, the summary of the studies is shown in two tables for one-echelon and multi-echelon supply chain including the main information and assumptions of each paper. In the mentioned tables, the papers were classified in terms of the type of demand rate, deterioration rate, solution procedure and findings. It can be said that no analysis on the results was done in the present study and it can be only used as a good reference in the study field for other researchers.

This paper deals with developing an inventory model for two warehouses. In today’s business era, there are various types of conditions such as discounts, bulk storage and seasonal products forcing the buyer to purchase the order more than owned warehouse capacity. To store the excess unit of purchase order, buyer arrange additional storage space called as rented warehouse. It is known that the demand of the seasonal products (as woolen garments) increases at the beginning of the season up to a certain time and then stabilizes to a constant rate for the remaining time of the season. The ramp type demand rate forces the buyer to store a higher quantity of the product at the beginning of the season. Most of the physical goods undergo decay or deterioration over time so we study deteriorating seasonal products in this paper. This two warehouse inventory model is developed with inflation and shortages. The model starts with rent warehouse, in first rent warehouse’s inventory level is depleted due to demand and deterioration. At this time own warehouse is depleted due to deterioration only. But after that the inventory level of owned warehouse is depleted due to both demand and deterioration. The shortages are considered in owned warehouse, which is partially backlogged. Numerical solution of the model is obtained to verify the optimal solution. Comprehensive sensitivity analysis has been carried out for showing the effect of variations in the parameters. The model is solved analytically by minimizing the total cost.

This paper formulates a multi-level supply chain network with a single producer, multi distributors and multi retailers during a finite planning horizon. The demand rate is assumed to be exponential function of time; shortages are allowed and completely backlogged. The stock is assumed to undergo deterioration as soon as it is produced. The production rate is dependent on demand rate and greater than the demand rate. Optimal solution for the proposed model is derived and using a numerical example, the behavior of the model is analyzed.

Keeping in view the concern about environmental protection, the study investigates effects of remanufacturing in an integrated production inventory model consisting of forward and reverse supply chain over infinite planning horizon. This article is developed for the deteriorating products with stock dependent demand under shortages. To make the model more realistic, flexibility of production system has been incorporated during forward manufacturing. We derive total cost function and using the results of calculus, optimum production policy is derived, which minimizes the total cost incurred. The results are discussed with a numerical example to illustrate the theory.