An economic order quantity model under constant purchasing price increments

Inventory management and transportation have been the principal areas of focus in industrial engineering and management for a long time. Inventory management attracts considerable attention in logistics and supply chain management today because new supply chain models have become more integrative and complex. New market forces have introduced many complex elements which affect the performance of the supply chain in general and inventory level in particular. Inventory decisions are high risk and high impact for supply chain management. Hence, this paper compiles all the derivations of classical deterministic lot size economic order quantity models and proposes a new method to verify the formula. Keyword: Inventory Management, Supply Chain Management (SCM), Economic Order Quantity (EOQ) I. INTRODUCTION At the very basic level any firm faces two main decisions concerning the management of inventory: When should new stock be ordered and in what quantities? With regard to the order quantity, that minimizes inventory related costs. The classical EOQ (economic order quantity) model remains the basic inventory model even when it is not applicable in real life business situations in most cases. In inventory related literature, the answer to the question of when to order is given with reference to the ROP (reorder point), and the point at which the replenishment order should be initiated so that the facility receives the inventory in time to maintain its target level of service. In the static and deterministic model, the ROP is the simple multiplication of the number of lead days and the daily demand. It means that every time the inventory falls to the ROP level, an order must be initiated. And the order quantity is given by the EOQ model which is based on cost minimization. Figure-1:~ A simple inventory model based on fixed demand and fixed lead time (1). The EOQ is the balance between order and holding costs attached with the inventory. The order cost is made up of fixed and variable costs, whereas the holding cost consist of costs of maintenance. The formula is: Q = √ (2CoD/Cc) Q is the order quantity per order, D is the demand per year Co is the fixed cost which the warehouse incurs every time it places an order Cc is the inventory carrying or holding cost per unit per year, and Notice that it highlights two important insights regarding the EOQ model. These are: 1. Optimum order size is a balance between the holding cost and the fixed order cost. 2. Total inventory cost is related with order size, but the relationship is not significant.

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.

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)

Jona Shop is located in Indonesia, Jakarta is currently having a problem. The problem is the shop’s owner thinks that the inventory costs are too big especially for a powdered drink which brand is “Nutrisari”. The author finishes an EOQ (Economic Order Quantity) model for minimize the inventory cost. EOQ model is an old model but a valid model which still used now. Even EOQ model is an old model, many researchers used EOQ model to minimize inventory cost until 50% or more than 50%. But the EOQ model has some assumptions and Jona Shop fulfilled all the assumptions in the EOQ model. The assumptions of EOQ model are demand is known and constant, the lead time is constant and known, only one product can be estimated, every order is accepted in one-time delivery and can be used right away, there is no backorder because run out stock, no discount, and the holding cost per year and the ordering cost per year are constant. The result of the EOQ model can save up to almost 90%.

The purpose of this research is to see whether an Economic Order Quantity model can be used to reduce cost of inventory significantly in PT PQR, manufacturer of spring and sponge mattresses in Pekanbaru, Indonesia. The research was conducted on three main materials required in producing spring and sponge mattresses. Using Economic Order Quantity (EOQ) model to analyze historical demand on main materials, it is proven that with EOQ model the company can save by more than 45% from procuring and inventory costs of those materials. The research continues to forecast the sales demand to get the annual requirement of materials needed in 2014 and calculate the EOQ model again. The results show that, comparing with traditional practice done by company, EOQ model can reduce costs up to 118 million rupiah per year.

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.

The effective supply chain scheduling is a crucial task in business management which can be determined by developing the optimum schedules. Here, this paper develops the optimum schedules using an EOQ model with dynamic demand pattern because in this era of globalization and dynamic environment the Economic Order Quantity (EOQ) model loses its importance when it is based upon the constant demand pattern. Therefore, it becomes indispensable to develop the EOQ model under an environment of dynamic demand pattern. Here, the dynamic demand pattern includes the relevant parameters which varies with time. The effects of such parameters are necessary to incorporate in determining the optimum schedules and hence the optimum inventory levels. Also, to establish a product in the market and to increase its customer base one can take the help of promotional efforts in the form of trade credit financing. This paper discusses the optimum scheduling for a part of supply chain system using an EOQ model where the demand is dynamic varies with time and one of the promotional effort in the form of a two-stage trade credit is considered. The applicability of the model can be well understood through the sensitivity analysis of the parameters and its managerial implications.

Previous studies on the issue of imperfect quality inventory assumed the direct cost of the product was irrelevant and the screening processes were perfect. However, in practice, the purchase price is some function of the quantity purchased and the inspection testing may fail to be perfect due to Type 1 and Type 2 errors. Thus, this paper proposes a cost-minimizing Economic Order Quantity (EOQ) model that incorporates imperfect production quality, inspection errors (including Type 1 and 2), shortages backordered, and quantity discounts. It is assumed that production, in which 100% screening processes are performed with possible inspection errors, is received with defective quality items and the supplier offers all-unit quantity discounts to the buyer. An algorithm is developed to determine the optimal lot size, shortages and purchase price. Three numerical examples are provided to illustrate the proposed model and algorithm. Numerical computations show that the algorithm is intuitively simple and efficient. Managerial insights are also drawn. Key words: Inventory, quantity discounts, imperfect quality, screening errors, shortage back-ordering.

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.

The rise of consumer rights has caused businesses to focus increasingly on product quality. The inability of businesses to identify defective items before selling them results in higher return costs, decreased sales revenue, damaged reputations, and decreased competitiveness. This study examines the economic order quantity (EOQ) model in which the retailer discovers defective goods among received products. Although retailers conduct quality inspections, the inspection process is imperfect. We assume that Type I and Type II inspection errors occur during product quality inspection and that the market demand rate is sensitive to Type II inspection errors. To improve inspection, the retailer invests capital to decrease Type II inspection errors. This study investigates the optimal order quantity and the power of the test to maximize total profit per unit time. Mathematical analysis is used to show the optimal solution exists. An algorithm is then developed to calculate the optimal solution. Finally, numerical examples demonstrate the solution process and sensitivity analysis with respect to major parameters is carried out.

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

The economic order quantity model with compounding

The economic order quantity (EOQ) model is usually not paid attention to make the model more realistic. The realistic EOQ model can bring a significant change while evaluating the profit and loss of any organisation. In this paper a mathematical model has been developed for obtaining the EOQ in which the demand of the product is assumed to follow an innovative imitative behaviour as proposed by Bass (1969). The theory of innovation-diffusion has been incorporated in this model. To make the model more realistic an attempt has been made to solve the model in light of fuzzy set theory under the trapezoidal membership function. The coefficient of innovation, the coefficient of imitation and the inventory carrying cost is assumed to be fuzzy numbers with trapezoidal membership function. By the median rule of defuzzification, total cost formula has been derived in the fuzzy sense in order to obtain the optimal order quantity. The effectiveness of this model is illustrated with a numerical example and sensitivity analysis of the optimal solution with respect to different parameters of the system is performed.

A standard mathematical model for inventory management is known as the Economic Order Quantity (EOQ) model. In this communication the EOQ model is extended to include the possibility of determining how much, if any, excess stock should be sold at the beginning of a decision period. The new model is of practical importance for situations in which a formal inventory management system is to be instituted while substantial inventories exist or when changes in demand, ordering cost, or carrying and interest charges require recomputation of the economic order quantity.

In the context of inventory management, this review presentation offers a thorough overview of several Economic Order Quantity (EOQ) models and their real-world uses. It explores the fundamental EOQ model and broadens to incorporate models that account for perishable items, quantity discounts, and scarcity prices. The talk also looks at the many sectors in which these models are used to optimize order amounts, save costs, and improve operational efficiency. Businesses may improve their inventory control strategies, realize considerable cost savings, and increase performance by making educated decisions based on a thorough grasp of the various EOQ models and their practical implementations.