A Variant Deterministic Model of Classical EOQ Formula

The classical economic order quantity (EOQ) model assumes not only a constant demand rate but also a fixed unit purchasing cost. In today's time-based competition, the unit cost of a high-tech product declines significantly over its short product life cycle while its demand increases. Therefore, using the classical EOQ formulation for a high-tech product will cause varying magnitudes of error. In addition, the cost of purchases as a percentage of sales is often substantial. Consequently, adding the purchasing strategy into the EOQ model is vital. In this paper, we assume that not only the demand function but also the unit purchase cost is fluctuating with time. We then provide an easy-to-use algorithm to find the optimal replenishment number and schedule. In a numerical example, we show that the total cost obtained by our proposed model is 32.4% less expensive than that obtained by the classical EOQ model.

EES-EOQ model with uncertain acquisition quantity and market demand in dedicated or combined remanufacturing systems

Deterministic Economic Order Quantity (EOQ) models have been studied intensively in the literature, where the demand process is described by an ordinary differential equation, and the objective is to obtain an EOQ, which minimizes the total cost per unit time. The total cost per unit time consists of a “discrete” part, the setup cost, which is incurred at the time of ordering, and a “continuous” part, the holding cost, which is continuously accumulated over time. Quite formally, such deterministic EOQ models can be viewed as fluid approximations to the corresponding stochastic EOQ models, where the demand process is taken as a stochastic jump process. Suppose now an EOQ is obtained from a deterministic model. The question is how well does this quantity work in the corresponding stochastic model. In the present paper we justify a translation of EOQs obtained from deterministic models, under which the resulting order quantities are asymptotically optimal for the stochastic models, by showing that the difference between the performance measures and the optimal values converges to zero with respect to a scaling parameter. Moreover, we provide an estimate for the rate of convergence. The same issue regarding specific Economic Production Quantity (EPQ) models is studied, too.

Perfect quality of batches is an assumption in the classic economic order quantity (EOQ) model (of inventory management); however, in practice some disruptions may occur in a supply chain. This paper presents an EOQ model with random disruption and partial backorders. So, when shortage occurs (due to quality problems or normal shortages), some customers are willing to wait for delivery until the next period. There is a finite probability that batches may be defective so an ‘all or none’ policy is used after inspection of batches. The optimal inventory cost and the corresponding decision variables are studied. A solution method is proposed to optimise the inventory cost, and then two numerical examples and a sensitivity analysis are provided to illustrate the results.

A carbon-constrained EOQ model with uncertain demand for remanufactured products

The purpose of this research is to determine and analyze the minimum order quantities and the supply cost through Economic Order Quantity (EOQ) Model without Stock Out, EOQ Model with Buffer Stock, and Robust Optimization. EOQ model without Stock Out is an inventory model with a fixed number of requests and a fixed period of demand so the goods are considered always available or there is no stock out. Whereas EOQ Model with Buffer Stock is an inventory model with uncertainty demand during the lead time that described with a uniform density function. Another model is Robust Optimization Model that is used for cases with uncertainty demand. The results showed that the minimum order quantities through EOQ Model without Stock Out and EOQ Model with Buffer Stock was almost the same value but the cost was more minimum with the EOQ Model with Buffer Stock. Whereas, through the Robust Optimization Model there are different minimum order quantities for each period with a minimum supply cost compared to the two previous models. This occurs in both types of Spuit, namely Spuit Terumo 3 mL and Spuit Terumo 5 mL.

We analyze the impact of pandemics disruptions on the decision related to supply chain management. Two models are developed and a closed-form solution is obtained for the optimal order size. In our first model, we consider the classical EOQ (Economic Order Quantity) model with Bernoulli supply having a disruption probability related to the pandemic situation. In our second model, we consider the classical EOQ (Economic Order Quantity) model with Binomial supply under pandemic situation. At last, we suggest ideas for future research.

Inventory management is crucial for companies to minimize unnecessary costs associated with overstocking or understocking items. Utilizing the economic order quantity (EOQ) to minimize total costs is a key decision in inventory management, particularly in achieving a sustainable supply chain. The classical EOQ formula is rarely applicable in practice. For example, suppliers may enforce a minimum order quantity (MOQ) that is much larger than the EOQ. Some conditions such as imperfect quality and growing items represent variants of EOQ. Moreover, some requirements, such as the reduction of CO2 emissions, can alter the formula. Moreover, disruptions in the supply chain, such as COVID-19, can affect the formula. This study investigates which requirements must be considered during the calculation of the EOQ. Based on a literature review, 18 requirements that could alter the EOQ formula were identified. The level of coverage for these requirements has been tracked in the literature. Research gaps were presented to be investigated in future research. The analysis revealed that, despite their importance, at least 11 requirements have seldom been explored in the literature. Among these, topics such as EOQ in Industry 4.0, practical EOQ, and resilient EOQ have been identified as promising areas for future research.

Inventory control management remains a cornerstone of operational efficiency in modern supply chain systems. This study explores the Economic Order Quantity (EOQ) model, a foundational inventory control technique, by comparing its application under two distinct demand scenarios: constant and variable demand rates. This research highlights how demand variability influences optimal order quantities, total inventory costs, and decision-making processes through a detailed theoretical framework, mathematical analysis, and practical implications. From recent literature in operations research and supply chain management, the article provides insights into the adaptability of the EOQ model across diverse demand conditions, offering a comprehensive guide for practitioners and researchers alike.

Note: An application of the EOQ model with nonlinear holding cost to inventory management of perishables

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)

In the manufacturing industry, optimal raw material inventory management is crucial for smooth production and cost efficiency. PT SSI faces problems in managing insert frames, which causes high ordering and storage costs. This study analyzes the application of the Economic Order Quantity (EOQ) method to determine the optimal order quantity and reduce total inventory costs. With a descriptive quantitative approach, data were collected through interviews, historical analysis of ordering and inventory costs, and calculations of EOQ and Total Inventory Cost (TIC). The results showed that the EOQ method reduced the frequency of orders from 48 to 24 times per year with an optimal order quantity of 63,155 units. Total inventory costs were also reduced from Rp 279,412,534 to Rp 230,256,690 per year, proving that the EOQ method is more efficient. The novelty of this research is the combination of EOQ with specific variables of the semiconductor industry. Further research is recommended to explore demand uncertainty and the integration of EOQ with artificial intelligence and ERP systems to improve inventory management accuracy. Keywords: Economic Order Quantity (EOQ), Inventory Control, Operational Efficiency, Optimal Order Quantity, Total Inventory Cost

The economic order quantity (EOQ) model has become an important instrument in inventory management to minimize costs by balancing ordering and holding costs. This study examines the alignment of the EOQ model with the principles of Maqasid Shari’a, including hifdzul din (protecting religion), hifdzul nafs (protecting the soul), hifdzul aql (protecting reason), hifdzul nasl (protecting descendants), and hifdzul maal (protecting property) and its relevance in the context of Islamic business. Qualitative data were collected through a literature review with a content analysis approach, then analyzed thematically to identify the relationship between EOQ characteristics and Maqasid Shari’a dimensions. The results of the study indicate that the EOQ model is in line with the five principles of Maqasid Shari’a, which include: 1) Hifdzul din: 2) Hifdzul nafs: 3) Hifdzul aql: 4) Hifdzul nasl: 5) Hifdzul maal: This study concludes that by integrating the EOQ model with Maqasid Shari’a, maslahah (common good) will be achieved in the form of economic efficiency and strengthening the ethical and social dimensions in business. The implications will encourage increased transparency, waste reduction, and environmental sustainability. These findings can be a conceptual basis for developing a holistic inventory management model following Islamic economics principles.

In this note, I amend Goyal's model by considering the difference between unit price and unit cost. I then establish an easy analytical closed-form solution to the problem. The theoretical results obtained here reveal the following two managerial phenomena. (1) In certain cases, the economic replenishment interval and order quantity decreases under the permissible delay in payments, which contradicts to Goyal's conclusion. It makes economic sense for some customers to order less quantity (or shorten the replenishment time interval) and to take the benefits of the permissible delay more frequently. (2) If a supplier wants to reduce his/her large level of inventory, then he/she should charge an excessive interest rate on his/her customer's outstanding amount after the credit term expires. Consequently, his/her customers will order to buy more quantity than the classical economic order quantity. As a matter of fact, these two managerial phenomena have been demonstrated in the decision making of using credit cards. For example, most credit card companies provide card holders 25 days of grace period, and charge 18–20% interest on the amount past due (ie, the second phenomenon). However, for a well-established credit card holder, he/she will take the benefit of 25 days of grace period constantly, but will not spend over his/her limit and face an excessive finance charge (ie, the first phenomenon).

Inventory control policies for new-product items are highly perceptive to different marketing policies especially for innovation effects at the earlier stage of the product life cycle but unfortunately classical economic order quantity (EOQ) model do not recognises the innovation driven demand model. In this paper, a time dependent innovation driven demand model has been introduced in the basic EOQ model to calculate the different optimal policies. The proposed model acknowledged relationship between the innovation coefficient and the optimal policies. Four hypotheses were framed in this paper based on the numerical exercise that could explain the impact of dynamic pattern of the innovation coefficient on different optimal policies.