An EOQ Model Without Shortages with Uncertain Cost Associated with Some Fuzzy Parameters and Interval Parameters

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.

Economic Order Quantity (EOQ) models without loss of generality for single items and multi-items are presented to choose an order quantity that minimizes its cost per unit time subject to the constraint on the amount of carbon emitted. Here, the proposed model is discussed in an uncertain environment. So, the EOQ model with a fixed cost, holding cost, and purchased cost (or produced cost) has been considered in a fuzzy environment. Also, fixed emitted carbon, holding emitted carbon, and purchased (or produced) emitted carbon are taken in a fuzzy environment with the limitation of total carbon emission per unit production time. Here we considered a fixed cost, holding cost, and purchased cost (or produced cost) as trapezoidal fuzzy numbers. The computational procedure for the defined EOQ model is carried out by using the signed-distance method and expected value technique. Numerical examples are also given to exemplify the proposed model.

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 classical economic order quantity (EOQ) model assumes that items produced are of perfect quality and that the unit cost of production is independent of demand. However, in realistic situations, product quality is never perfect, but is directly affected by the reliability of the production process. In this paper, we consider an EOQ model with imperfect production process and the unit production cost is directly related to process reliability and inversely related to the demand rate. In addition, a numerical example is given to illustrate the developed model. Sensitivity analysis is also performed and discussed.

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 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 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.

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.

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.

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.

In this study, under the carbon cap-and-trade mechanism, the ordering cost presents a stepwise function for ordering quantity, and the optimal economic ordering quantity model aims to explore the manufacturer's total cost minimization in the finite planning horizon, in combination with the actual situation that the product will produce carbon emissions during transportation and storage. The economic order quantity (EOQ) model with stepwise ordering cost is applicable to the decision environment in which goods are utilized by sea, by rail or by air (e.g., the order cost is charged in addition to the basic fixed cost, the importer of raw materials will pay an additional freight related to delivery, such as the rent for the use of container numbers.). A heuristic algorithm is also proposed to analyze the relevant properties of the optimal solution of the model and to solve the optimal order times and quantities of the manufacturer under the constraint of carbon policy.We further compared the optimal order times with the case without carbon constraint and the order times corresponding to the manufacturer's realization of the minimum carbon emission, and obtained the conditions for the manufacturer to achieve low cost and low emission under the carbon policy.Finally, the theoretical results of the model are verified by numerical examples,and the influence of relevant parameters on the inventory strategy of manufacturers is discussed. The results show that under the carbon cap-and-trade policy, there is an optimal ordering strategy that minimizes the total cost of the manufacturer in the finite horizon. When the demand of the manufacturer is under finite horizon and the carbon policy is equal to the specific multiplier of orders, the manufacturer can achieve a win-win result of low cost and low emissions.

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.

The presence of retail businesses in Indonesia has many positive impacts on the community, especially in improving the economy. The existence of buying and selling transactions involving suppliers, retailers, and the community as consumers can play a role in improving the national economy. Retail can be called a bridge for suppliers and consumers to meet their needs. The diversity of consumer needs requires retailers to provide a variety of products from many suppliers. Efforts that need to be made by retail businesses in order to minimize costs incurred are by controlling inventory. To prevent excessive expenditure, the inventory control method used is to apply the Economic Order Quantity (EOQ) model. The EOQ model can provide the optimum total inventory cost by adjusting the frequency of orders placed over a period of time. After obtaining the total inventory cost, the calculation of safety stock, reorder point, and maximum capacity can also be applied so that the inventory costs incurred can be minimal.

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.