An analysis of multi-level lot-sizing problems with a bottleneck under a rolling schedule environment

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)

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.

PT. XYZ is a company that produces cardboard packaging. The product that is most in demand by customers is snack packaging. Snack packaging products have an erratic demand that affects the production process and ordering of raw materials. Therefore, companies need a more effective improvement proposal design starting from forecasting, inventory, distribution, production planning, and ERP simulation. The data needed to start the research are the raw materials used, data on demand for snack packaging products for the past 1 year, lead times for raw materials, machines used, and other data. Data processing begins with forecasting using the Double Moving Average, Single Moving Average, Weight Moving Average, Double Exponential Smoothing, Single Exponential Smoothing, Cyclic, Linear Regression, and decomposition methods followed by validation and verification of forecasting methods Mean Absolute Deviation, Mean Square Error, Mean Absolute Percent Error, and Standard Error of Estimate. Forecasting results that have been verified are followed by aggregate planning, Rough Cut Capacity Planning with Capacity Planning using Overall Factors, Bill of Labour Approach, Resource Profile Approach, safety stock methods, Material Requirement Planning with the Least Unit Cost, Lot for Lot, Silver Meal, Economic Order Quantity, Period Order Quantity, Capacity Requirement Planning, Distribution Requirement Planning, and Enterprise Resource Planning methods. The proper forecasting method used is the decomposition method which has the least error compared to PT. XYZ methods. The calculation of mixed aggregate planning (overtime and shifts) is the right method because it costs the least total cost, namely ${\$}$ 34023.54. The results of Capacity Requirement Planning and Rough-Cut Capacity Planning calculations do not indicate a lack of capacity to meet the demand for the Master Production Schedule. The proper Material Requirement Planning method is the Period Order Quantity lotsizing method with a 47.6% savings compared to PT. XYZ. Proper distribution planning using the Distribution Requirement Planning method with a savings of 36.3% compared to PT. XYZ methods.

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 conducts an in-depth analysis of three models derived from economic order quantity (EOQ) model in an effort to reduce high inventory cost associated with the IT commodities sold in one of the Carrefour supermarket outlets. These three models are: 1. model of lots ordered and delivered independently, 2. model of lots ordered and delivered jointly, and 3. model of lots ordered and delivered for a selective subset. Mathematically, these three models are carefully discussed and compared in this paper. The third EOQ-based model contains more selective procedures combining the commodities to be ordered jointly in an order schedule and with that may lead to an optimal solution for its lowest cost.

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.

Economic order quantity and sampling inspection plans for imperfect items

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

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.

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

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.

Environmental sustainability EOQ model for closed-loop supply chain under market uncertainty: A case study of printer remanufacturing

An economic order quantity model with reverse logistics program

The effects of inflation and time-value of money on an economic order quantity model with a random product life cycle

The classical economic order quantity (EOQ) model assumes that items produced are of perfect quality and that die unit cost of production is independent of demand. Product quality is not always perfect but directly affected by the reliability of the production process used to produce the products. In addition, a relationship between unit production cost and demand may exist under certain circumstances. We propose an EOQ model with demand-dependent unit production cost and imperfect production processes. We formulate this inventory decision problem as a geometric program (GP) and solve it to obtain closed-form optimal solutions. An illustrative example is provided to demonstrate the point that GP has potential as a valuable analytical tool for studying a certain class of inventory control problems. We also discuss the aspect of sensitivity analysis based on the GP approach.