An EOQ model with delay in payments and time varying deterioration rate

In this paper, economic order quantity (EOQ) models without shortages for single item and multi-items are presented. Here, the holding cost of the item is a continuous function of the order quantity. The costs involved in this model are imprecise in nature. The main contributions of this research are as follows: The proposed EOQ model is discussed in two cases by describing the model in an uncertain environment. In case-1, EOQ models with fuzzy parameters (like ordering cost, holding cost, and unit product cost) are considered. Here all the fuzzy parameters are represented by trapezoidal fuzzy numbers. The said EOQ model is carried out by using the signed-distance method. In case-2, EOQ models with interval parameters (like ordering cost, holding cost, unit product cost, and the total money investment for the quantities) are considered. This proposed model is solved by using interval linear programming problem (ILPP) technique based on the best and the worst optimum values of the objective function. Numerical examples are given to exemplify the proposed model and also the results of different models are compared.KeywordsEOQTrapezoidal fuzzy numberInterval numberSigned-distance methodInterval linear programming problem (ILPP)

Optimal pricing and ordering policies for retailers under order-size-dependent delay in payments

In the economic order quantity models, it is often assumed that the payment of an order is made on the receipt of items by the inventory system. Such assumption is usually not fulfilled in practice. The phenomenon that a supplier may offer a credit period to the retailers in order to stimulate demand is very common in the market. In this paper, the stock-dependent demand rate and conditions of permissible delay in payments used in conjunction with the economic order quantity model are the focus of discussion. We shall be concern with finding the optimal replenishment cycle under conditions of permissible delay in payments. Numerical examples are presented to illustrate the proposed models.

We developed an economic order quantity (EOQ) model with a learning effect and carbon emissions under inflationary conditions and inspection for retailers where the items deteriorate naturally. Finally, the total profit of the retailer is maximized with respect to cycle length. A sensitivity analysis was also performed to understand the robustness of the model. In the sensitivity analysis, we discuss the impact of learning rate, inflation rate, and deterioration rate on lot size and length of the cycle, as well as the retailer’s entire profit function. Observations and managerial insights are discussed. The effect of inventory parameters on the total profit is shown in the sensitivity section.

A study on an inventory model for non-instantaneous deteriorating items with permissible delay in payments

Most researchers established their inventory lot-size models under trade credit financing by assuming that the supplier offers the retailer fully permissible delay in payments and the products received are all non-defective. However, in the real business environment, it often can be observed that the supplier offers the retailer a fully permissible delay in payments only when the order quantity is greater than or equal to the predetermined quantity Q d . In addition, an arriving order lot usually contains some defective items due to imperfect production processes or other factors. To capture this reality, the paper extends Huang (2007) economic order quantity (EOQ) model with partially permissible delay in payments to consider defective items. We formulate the proposed problem as a profit maximization EOQ model in which the replenishment cycle time is the decision variable. Then we use the arithmetic-geometric mean inequality approach to determine the optimal solution under various situations. An algorithm to obtain the optimal solution is also provided. Finally, the numerical examples and sensitivity analysis are given to illustrate the results.

In this article, we extended Goyal's model to develop an Economic Order Quantity (EOQ) model in which the supplier offers the retailer the permissible delay period M, and the retailer in turn provides the trade credit period N (with N ≤ M) to his/her customers. In addition, we assume that (1) the retailer's selling price per unit is necessarily higher than its unit cost, and (2) the interest rate charged by a supplier or a bank is not necessarily higher than the retailer's investment return rate. We then establish an appropriate EOQ model with trade credit financing, and provide an easy-to-use closed-form solution to the problem. Furthermore, we find it is possible that a well-established buyer may order a lower quantity and take the benefit of the permissible delay more frequently, which contradicts to the result by the previous researchers. Finally, we perform some sensitivity analyses to illustrate the theoretical results and obtain some managerial results.

Abstract. Effective and efficient inventory management is crucial for the sustainability of businesses in the culinary industry. Brebes Lembang Restaurant, as a culinary business providing food and beverages, requires proper inventory management to increase efficiency and reduce costs.This study aims to determine the Economic Order Quantity (EOQ) method in managing chicken broiler raw material inventory at Brebes Lembang Restaurant and to evaluate the effectiveness of the EOQ method in improving inventory management efficiency.This study employs a mixed-method approach, combining qualitative and quantitative methods. Data were collected through interviews, observations, and analysis of secondary data. Data analysis used the EOQ method to determine the optimal order quantity and minimum total cost.The resultsshow that Brebes Lembang Restaurant has effectively applied the EOQ method in managing chicken broiler raw material inventory. The analysis reveals that the EOQ method can improve inventory management efficiency and reduce total costs.This study concludes that the EOQ method can be used as a tool to support inventory management of chicken broiler raw materials at Brebes Lembang Restaurant. The findings of this study are expected to contribute to the development of inventory management theory and practice in the culinary industry. Abstrak. Pengelolaan persediaan bahan baku yang efektif dan efisien sangat penting bagi keberlangsungan usaha di bidang kuliner. Rumah Makan Brebes Lembang sebagai salah satu usaha kuliner yang bergerak di bidang penyediaan makanan dan minuman, memerlukan pengelolaan persediaan bahan baku yang tepat untuk meningkatkan efisiensi dan mengurangi biaya. Penelitian ini bertujuan untuk mengetahui metode Economic Order Quantity (EOQ) dalam pengelolaan persediaan bahan baku ayam gantung di Rumah Makan Brebes Lembang, serta untuk mengetahui efektivitas metode EOQ dalam meningkatkan efisiensi pengelolaan persediaan. Penelitian ini menggunakan metode campuran, yaitu kombinasi antara metode kualitatif dan kuantitatif. Data yang dikumpulkan melalui wawancara, observasi, dan analisis data sekunder. Analisis data menggunakan metode EOQ untuk mengetahui jumlah pesanan optimal dan biaya total yang minimal. Hasil penelitian menunjukkan bahwa Rumah Makan Brebes Lembang telah menggunakan metode EOQ dengan baik dalam pengelolaan persediaan bahan baku ayam gantung. Hasil analisis menunjukkan bahwa metode EOQ dapat meningkatkan efisiensi pengelolaan persediaan dan mengurangi biaya total. Penelitian ini menyimpulkan bahwa metode EOQ dapat digunakan sebagai alat bantu dalam pengelolaan persediaan bahan baku ayam gantung di Rumah Makan Brebes Lembang. Hasil penelitian ini diharapkan dapat memberikan kontribusi pada pengembangan teori dan praktik manajemen persediaan di bidang kuliner.

This paper presents EOQ (Economic Order Quantity) model with stock- level dependent demand and different types of holding cost function. We show that the total relevant inventory cost per unit time is convex with respect to cycle time. Mathematical models are established to determine optimal order quantity and total relevant inventory cost. Numerical examples are provided for two different models i.e. (i): Instantaneous replenishment with inventory dependent holding cost and (ii) Instantaneous replenishment with quadratic time dependent carrying cost. Numerical examples are provided to illustrate the proposed model. Sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out. The second order approximation is used for finding closed form optimal solution. Mathematica 5.2 software is used to find numerical results.

An inventory model under two levels of trade credit and limited storage space derived without derivatives

This study aims to determine whether the calculation of Economic Order Quantity (EOQ) can be used as Control of Raw Material Inventory at PT. X. This research was conducted by comparing between inventory control methods according to company policy with the Economic Order Quantity (EOQ) method. The research method used is descriptive quantitative, do to collect techniques used are interviews, observation, and documentation. Data analysis techniques used in this study are steps (1) gathering information about the amount of raw material inventory in 2018. (2) processing these data determine the control of raw material inventory based on company policy. (3) analyzing the precessed data using the Economic Order Quantity (EOQ) method. The results of the study prove that Economic Order Quantity (EOQ) is more efficient than the method used by the company. The application of the Economic Order Quantity (EOQ) method can reduce the total costs that must be incurred by the company. Which is IDR 299,399,040. with this (EOQ) method, it can avoid delays in the supply of raw materials, because the supply of raw materials can be ensured constant and according to lead time. Then reaching the research objectives, companies should use the Economic Order Quantity (EOQ) method.

The main purpose of this paper wants to investigate the effect of trade credit policy with limited storage capacity within the economic order quantity (EOQ) framework. Goyal is frequently cited when the inventory systems under conditions of permissible delay in payments are discussed. But Goyal assumed that the retailer’s storage capacity is unlimited. This assumption is debatable. So, we want to extend Goyal’s model to the case that the retailer’s storage capacity is limited. Then, two theorems present solution procedures to locate the optimal cycle times of the annual total relevant cost function. In essence, the inventory model discussed in this paper generalizes that of Goyal. Finally, numerical examples are given to illustrate all theorems obtained in this paper.

The inventory models under conditional trade credit in a supply chain system

Economic order quantity and sampling inspection plans for imperfect items

Study of memory effect in an inventory model for deteriorating items with partial backlogging