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In this paper, we present an inventory model for deteriorating items with time varying demand and deterioration rates when the credit period depends on the retailer's ordering quantity. We also provide simple solution procedures for finding the optimal replenishment period and show in a rigorous way that the policy suggested is indeed optimal. Further, we use numerical examples to illustrate the model and conclude the paper with suggestions for possible future research.

Inventory models with deteriorating items have received considerable attention in recent years. In considering the deteriorating inventory with permissible delay in payments, most researchers pay attention to a single warehouse. Under conditions of permissible delay in payments, this paper develops a model to determine the optimal cycle time for a single deteriorating item that is stored in two different warehouses. A rented warehouse (RW) is used to store the excess units over the fixed capacity W of the owned warehouse (OW). The rented warehouse is assumed to charge higher unit holding cost than the OW. In this paper, we propose a two-warehouse inventory model for deteriorating items under permissible delay in payments. It is assumed that the deterioration rate in RW is the same as in OW, and the holding cost in RW is greater than that in OW. The stocks of RW are transported to OW in continuous release pattern and the transportation cost is ignored. Three theorems are developed to determine the optimal cycle time and numerical examples are given to illustrate these theorems.

Since the publication of the Goyal model in 1985, research on the modeling of inventory lot-size under trade credits has resulted in a body of literature. In this paper, we present a review of the advances in inventory literature under conditions of permissible delay in payments since 1985. We classify all related previous articles into five categories based on: (a) without deterioration, (b) with deterioration, (c) with allowable shortage, (d) linked to order quantity, and (e) with inflation. The motivations, extensions and weaknesses of various previous models have been discussed in brief to bring out pertinent information regarding model developments in the past two decades.

This study considers the supplier's warranty return and the buyer's rebate policy as business-return policy in the supplier–buyer supply chain. The policy as well as the displayed stock level influences the behavior of the buyer. Distinct from the traditional single-stage inventory model, we investigate a two-stage replenishment policy model for deteriorating item considering the effect of imperfect production process, product design, stock level and business-return. A mathematical model utilizing the time weighted inventory (TWI) approach and two-variables fixed point optimization technique is developed to derive the optimal inspection starting time, the number of deliveries, the optimal delivery-time interval and the optimal business-return period. A numerical example is presented to illustrate the model developed. The result shows that the fixed demand rate, the unit holding cost and the unit inspection cost are the critical factors affecting the scheduling and performance of the two-stage supply chain.

Considering the real dilemma of deteriorating items, we explore how to find a balance between the conflicting achievements of enhancing flexibility and reducing costs. We propose a general dynamic model to penetrate customer orders by decoupling point with objective to minimize the cost. The closed forms of optimal solutions are obtained for companies to deal with the integrated problem of customer order decoupling point (CODP) decision and production–inventory plan simultaneously. Applications and numerical experiments are performed to illustrate practical insights for managers. The results show that the truth of zero-inventory policy is to avoid unnecessary inventory instead of absolutely no inventory. The CODP will shift forward with the increasing of customer demand rate and shift backward with the increasing of deterioration rate under the production smoothing policy. However, although it encounters the same changes of demand, the CODP moves with a smaller extent in high deterioration rate than in low. In addition, we find that during the growth phase of product life cycle, the increase of time-sensitive degree of demand is coupled with forward shifting of CODP; while during the decline phase, it is coupled with CODP backward shifting.

A model is constructed for a type of multi-period inventory problem with deteriorating items, in which demands are assumed to be uncertain variables. The objective is to minimize the expected total cost including the ordering cost, inventory holding cost and deteriorating cost under constraints that demands should be satisfied with some service level in each period. To solve the model, two methods are proposed in different cases. When uncertain variables are linear, a crisp equivalent form of the model is provided. For the general cases, a hybrid algorithm integrating the 99-method and genetic algorithm is designed. Two examples are given to illustrate the effectiveness of the model and solving methods.

This paper presents an EPQ model which illustrates imperfect production and imperfect inspection processes for items that are subject to a constant rate of deterioration. The model considers two types of inspection errors, namely, Type I error of falsely screening out a proportion of nondefects, thereby passing them on for rework and Type II error of falsely not screening out a proportion of defects, thus selling those to customers which results in defect sales returns. The screened and returned items are then reworked and the proportion that could not be reworked successfully is scrapped. Shortages are allowed and are completely backlogged. Finally, we calculate the optimal production lot size and the optimal backordering quantity in order to minimize the total inventory cost per unit time. A numerical example is also considered to exemplify the obtained theoretical results which is followed by the complete sensitivity analysis of the involved parameters for even better managerial insights.

This paper focuses on imperfect manufacturing system with remanufacturing, manufacturing and product returned cycle for a single item which deteriorates with respect to time. The product has maximum fixed lifetime. To decrease deterioration of the product, manufacturer spends capitals on preservation technology to preserve the item. In this paper, the effect of inflation is also considered. Here, time-dependent quadratic demand is debated which is suitable for the products whose demand increases initially and afterward it starts to decrease. The objective is to minimize the total cost of manufacturer with respect to cycle time and investment for preservation technology. The model is supported with numerical example. Sensitivity analysis is done to derive insights for decision makers. Graphical result, in three dimensions, is exhibited with supervisory decision.

Inventory models are quite important when it comes to analyzing scenarios that occur in a variety of areas, including food, warehouses, vegetable markets, and other similar places. Within the scope of this study, we investigate both a linear and a nonlinear time-dependent inventory control model for things that are deteriorating. When it comes to conducting business in the modern day, the relationship that exists between retailers and customers is absolutely necessary for successful implementation. Consumers engage in commercial transactions with retailers in order to buy goods with the intention of increasing their earnings. The goal of this study is to calculate the number of times demand orders are placed by customers throughout the rotation time in order to achieve the highest possible overall profit for both the client and the merchant, both with and without the use of collaboration. In addition, it intends to investigate the disparity between the total profit obtained by the customer and the merchant in two different scenarios. Using analytical methods, the proposed model is evaluated in order to obtain the best possible solution to the problem. In the following section, a numerical example and a comparison study are discussed. Ultimately, a sensitivity analysis of the parameters is to be done to investigate the variations in the results of various parameters inside the model based on the optimal strategy.