A Fuzzy Inventory System with Deteriorating Items under Supplier Credits Linked to Ordering Quantity

[[abstract]]The inventory problem associated with trade credit is a popular topic in which interest income and interest payments are important issues. Most studies related to trade credit assume that the interest rate is both fixed and predetermined. However, in the real market, many factors such as financial policy, monetary policy and inflation, may affect the interest rate. Moreover, within the environment of merchandise storage, some distinctive factors arise which ultimately affect the quality of products such as temperature, humidity, and storage equipment. Thus, the rate of interest charges, the rate of interest earned, and the deterioration rate in a real inventory problem may be fuzzy. In this paper, we deal with these three imprecise parameters in inventory modeling by utilizing the fuzzy set theory. We develop the fuzzy inventory model based on Chang et al.'s [1] model by fuzzifying the rate of interest charges, the rate of interest earned, and the deterioration rate into the triangular fuzzy number. Subsequently, we discuss how to determine the optimal ordering policy so that the total relevant inventory cost, in the fuzzy sense, is minimal. Furthermore, we show that Chang et al.'s [1] model (the crisp model) is a special case of our model (the fuzzy model). Finally, numerical examples are provided to illustrate these results.[[notice]]補正完畢[[journaltype]]國內[[incitationindex]]SCI[[incitationindex]]EI[[ispeerreviewed]]Y[[booktype]]紙本[[countrycodes]]TW

Optimal Order Policy for Deteriorating Items in Response to Temporary Price Discount Linked to Order Quantity

[[abstract]]This paper investigates the possible effects of a temporary price discount offered by a supplier on a retailer's replenishment policy for deteriorating items, whereby the price discount rate depends on the order quantity. The purpose of this study is to develop a decision process for retailers to assist in determining whether to adopt a regular or special order policy. Furthermore, the optimal quantity of a special order policy for a selected case is determined by maximizing the total cost saving between special and regular orders for the duration of the depletion time. This research establishes an algorithm to determine the optimal solution and utilizes several numerical examples to illustrate the theoretical results and subsequently conducts a sensitivity analysis of the optimal solution with respect to the main parameters. Finally, the results reveal that (1) the optimal special order quantity is determined by trading off the benefits of the price discount against the additional holding cost, (2) the retailer benefits in terms of total cost saving if the remnant inventory is as low as possible when adopting a special order policy, (3) for the retailer it is preferable to adopt the special order policy if the unit purchase cost, market demand rate and/or ordering cost increase, and (4) the retailer will order a lower quantity and the total cost saving will decrease when either the holding cost rate or deterioration rate is high. Thus, this study provides the basis for enterprises to make inventory decisions.[[booktype]]紙

Optimal credit period and lot size for deteriorating items with expiration dates under two-level trade credit financing

[[abstract]]In a supplier-retailer-buyer supply chain, the supplier frequently offers the retailer a trade credit of S periods, and the retailer in turn provides a trade credit of R periods to her/his buyer to stimulate sales and reduce inventory. From the seller’s perspective, granting trade credit increases sales and revenue but also increases opportunity cost (i.e., the capital opportunity loss during credit period) and default risk (i.e., the percentage that the buyer will not be able to pay off her/his debt obligations). Hence, how to determine credit period is increasingly recognized as an important strategy to increase seller’s profitability. Also, many products such as fruits, vegetables, high-tech products, pharmaceuticals, and volatile liquids not only deteriorate continuously due to evaporation, obsolescence and spoilage but also have their expiration dates. However, only a few researchers take the expiration date of a deteriorating item into consideration. This paper proposes an economic order quantity model for the retailer where: (a) the supplier provides an up-stream trade credit and the retailer also offers a down-stream trade credit, (b) the retailer’s down-stream trade credit to the buyer not only increases sales and revenue but also opportunity cost and default risk, and (c) deteriorating items not only deteriorate continuously but also have their expiration dates. We then show that the retailer’s optimal credit period and cycle time not only exist but also are unique. Furthermore, we discuss several special cases including for non-deteriorating items. Finally, we run some numerical examples to illustrate the problem and provide managerial insights.[[incitationindex]]SCI[[booktype]]紙

A note on “Optimal replenishment policies for non-instantaneous deteriorating items with price and stock sensitive demand under permissible delay in payment”

[[abstract]]Soni 2013. Int. J. Prod. Econ., 146 (1), 259–268 proposed optimal replenishment policies for non-instantaneous deteriorating items (i.e., the product starts deteriorating after a period of no-deterioration) with price and stock sensitive demand. With a stock-dependent demand, it is desirable to have non-zero ending inventory due to potential profit resulting from the increased demand. However, Soni 2013. Int. J. Prod. Econ., 146 (1), 259–268 treated those ending inventory as fresh stocks to go through another period of non-deterioration again. Additionally, he assumed for simplicity that the replenishment cycle time T must be longer than the period of non-deterioration td(i.e., T＞td). In reality, one should consider all possible replenishment cycle time to maximize the profit. In this note, we complement the shortcomings of his model by (i) selling those ending inventory as salvages, and (ii) considering all possible replenishment cycle time, which may be shorter than the period of non-deterioration. With these modifications the repeatability of the replenishment cycle is ensured and the applicability of Soni′s model is strengthened. The numerical examples indicate that the global optimal solution is indeed possible in the case of T≤td.[[notice]]補正完畢[[booktype]]紙

Advance sales system with price-dependent demand and an appreciation period under trade credit

[[abstract]]With globalization, companies are facing fierce competition. Offering an appreciation period has become a commonly adopted method by retailers to sustain competitive advantage. During the appreciation period, customers can request to return products for any reason. In addition, retailers provide advance sales to attract additional customers. The supplier usually provides the retailer with a trade credit, which they can use as a type of price reduction to attract additional customers. Price is viewed as an important vehicle to sell products and enhance revenues. Therefore, in this article, we establish an inventory model with price-dependent demand for a retailer who simultaneously receives trade credit from its supplier, and offers advance sales and an appreciation period to its customers. We first establish a proper model and then provide an easy-to-use method to obtain an ordering policy for the retailer to achieve its maximum total profit. Finally, numerical examples are given to illustrate the solution procedure

An integrated inventory model with capacity constraint and order-size dependent trade credit

[[abstract]]Trade credit has many forms in today’s business practice. The most common form of trade credit policy that is used to encourage retailers to buy larger quantities is order-size dependent. When the number of ordered units exceeds the capacity of the own warehouse, an additional rented warehouse is required to store the excess units. Therefore, to incorporate the concept of order-size dependent trade credit and limited storage capacity, we proposed an integrated inventory model with capacity constraint and a permissible delay payment period that is order-size dependent. In addition, the unit production cost, which is a function of the production rate, is considered. Three theorems and an algorithm are developed to determine the optimal production and replenishment policies for both the supplier and the retailer. Finally, numerical examples are presented to illustrate the solution procedure and the sensitivity analyses of some key parameters are provided to demonstrate the proposed model.[[notice]]補正完畢[[incitationindex]]SCI[[incitationindex]]EI[[booktype]]電子

Impacts of collaborative investment and inspection policies on the integrated inventory model with defective items

[[abstract]]For an imperfect production system, to reduce quality-related costs, a manager may consider investing capital in quality improvement. In general, the investment expense in reducing the defective rate of items is often paid by the vendor. On the other hand, the buyer may inspect the product quality as the order is received which implies it incurs an inspection cost. In a supply chain integrated system, to accomplish global optimisation, the vendor and buyer can agree to jointly invest capital to improve the imperfect production processes, and the buyer can remove the inspection programme as the defective rate reaches a certain low-level. Hence, this paper investigates the impacts of collaborative investment and inspection policies on an integrated inventory model with defective items. The objective of this study is to seek the optimal order quantity, shipping times from the vendor to the buyer per production run, and the defective rate that minimise the joint total cost per unit time. An algorithm is developed to find the optimal solution. Several numerical examples are presented to demonstrate the proposed model and solution procedure, and then several management insights are obtained from the numerical examples.[[incitationindex]]SCI[[incitationindex]]EI[[booktype]]紙

Optimal strategy for an integrated system with variable production rate when the freight rate and trade credit are both linked to the order quantity

[[abstract]]This paper presents an integrated inventory model with variable production rate and price-sensitive demand rate. The buyer's purchases trade credit linked to the order quantity offered by the supplier. In addition, the buyer pays the freight charge according to a weight schedule. This paper attempts to offer a best policy that aims at maximizing the joint total profit while the trade credit and freight rate are simultaneously linked to the order quantity. The same policy also incorporates considerations on the optimal retail price, order quantity and delivery decision. We provide possible solutions for the buyer and the supplier to collaboratively agree on inventory control, warehouse management, transportation logistics, delivery and billing. Our study demonstrates that significant profit increase for the entire supply chain can be achieved by linking both trade credit policy and freight rate policy to order quantities. An algorithm is furnished to determine the optimal solution. In addition, numerical examples and sensitivity analysis are presented to illustrate the theoretical results.[[notice]]補正完畢[[incitationindex]]SCI[[incitationindex]]SSCI[[incitationindex]]EI[[booktype]]紙

An economic order quantity model for deteriorating items with partially permissible delay in payments linked to order quantity

[[abstract]]To attract more sales suppliers frequently offer a permissible delay in payments if the retailer orders more than or equal to a predetermined quantity W. In this paper, we generalize [Goyal, S.K., 1985. EOQ under conditions of permissible delay in payments. Journal of the Operational Research Society 36, 335–338] economic order quantity (EOQ) model with permissible delay in payment to reflect the following real-world situations: (1) the retailer’s selling price per unit is significantly higher than unit purchase price, (2) the interest rate charged by a bank is not necessarily higher than the retailer’s investment return rate, (3) many items such as fruits and vegetables deteriorate continuously, and (4) the supplier may offer a partial permissible delay in payments even if the order quantity is less than W. We then establish the proper mathematical model, and derive several theoretical results to determine the optimal solution under various situations and use two approaches to solve this complex inventory problem. Finally, a numerical example is given to illustrate the theoretical results.[[notice]]補正完畢[[incitationindex]]SCI[[incitationindex]]EI[[booktype]]紙

An optimization approach for joint pricing and ordering problem in an integrated inventory system with order-size dependent trade credit

[[abstract]]Under a business trading environment, it is common for the trade credit to depend on the order size. Therefore, it is important to discuss the single-supplier and single-buyer supply chain problem which includes order-size dependent trade credit. In this study, an integrated inventory model with a price sensitive demand rate, determining jointly economic lot size of the buyer’s ordering and the supplier’s production batch, are developed to maximize the total profit per unit time. An efficient algorithm is provided to obtain the optimal solution, and then numerical examples are presented to illustrate the theoretical results. Finally, the comparison between whether an optimal solution is jointly or independently determined is also provided.[[incitationindex]]SCI[[incitationindex]]SSCI[[booktype]]紙