Adaptation of the Economic Order Quantity (EOQ) Model in the Perspective of Maqasid Shari’a

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)

The Economic Order Quantity (EOQ) model, proposed by Harris in 1913, is one of the most studied models for the inventory management. The model aims at identifying the optimal lot size minimizing the total inventory costs, typically only holding and ordering costs. Many researchers extended this model trying to adapt it to real-life situation by providing new mathematical models. The increasing attention paid to sustainable manufacturing led, in the last years, to include the external costs of logistics in the EOQ model. Starting from a literature review on the inventory management models, this chapter defines the new Sustainable Order Quantity (SOQ) model. In the model, the loss factor parameter quantifies the loss in energy per unitary load transported and unitary distance covered, univocally identifying the various transport means. The optimal order quantity is derived minimizing a logistic cost function that considers both economic and social-environmental costs. The model allows determining at the same time the reorder level, the safety stock as well as the optimal transport means.

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.

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.

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 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 static EOQ (economic ordering quantity) model for manufacturing/remanufacturing hybrid system was improved from the point of view of time-value of system costs, and further considered the effect of time-value of money in inventory management of the hybrid system. A modified dynamic EOQ model based on time-value of system costs was proposed for a hybrid system. The main purpose of the dynamic EOQ model was to study how to determine optimal ordering quantity of the hybrid manufacturing/remanufacturing system. A numerical comparison analysis between the different models was given to illustrate the difference of the average cost and the optical ordering quantity. The results shown the modified EOQ model was often considered a more correct way in the hybrid manufacturing/remanufacturing system. The sensitivity analysis was also made to investigate the effects of main parameters on the modified EOQ model.

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 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.

Inventory management in reverse logistics is more complex than that in conventional logistics because of uncontrollable factors such as inventory levels increasing from reverse logistics, greater-than-expected disposal, and balance of supply and demand with changing market trends. This paper proposes a new economic order quantity (EOQ) model for reuse and recycling by expanding the EOQ model proposed by Dobos and Richter, 2004. The proposed model introduces a sequentially accumulated marginal reuse rate as a parameter in considering the balance of product demand and supply. The marginal reuse rate is calculated by using data on production distribution and disposal distribution of products for every discretized period. This model considers the sequence among recovery options: reuse, recycle and disposal. Parts are reused after having been inspected to determine whether they are reusable or not. Remaining nonreusable parts are recycled and any remaining nonrecycled parts disposed of. The extended EOQ model is applied to a case study using different scenarios for length of use and multiple generations of products. Results of computer experiments confirmed the effectiveness of the proposed method.

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

This dissertation is on inventory management and supply chain coordination mechanisms within an economic order quantity framework. Specifically, this research focuses on modeling optimal order policies and coordination mechanisms for a supply chain involving items which experience probabilistic failure during storage. These items are common types of manufactured items which, nonetheless, require specialized order policy considerations due to their unique characteristics. We first develop the solution for the buyer's problem through the use of an economic order quantity (EOQ) model incorporating item failure. We then proceed to model the manufacturer's problem through the use of an economic production quantity (EPQ) model. Finally, we consider mechanisms to promote mutually-beneficial cooperation between the supplier and n buyers in service of coordinating the entire supply chain. While prior research has focused on items which can be repaired or sold at a discount upon failure, such models are inappropriate for systems where repair costs exceed or are equivalent to item costs and imperfect items are unacceptable. Examples of industries featuring these inventory conditions include the medical, defense, and electronics industries where defective items are largely useless. First, our EOQ model considers a buyer-supplier relationship featuring delivery and stocking of items which experience probabilistic failure in storage. Thereafter, our EPQ model considers in-house production of such items. Collectively, our EOQ and EPQ models provide methods for developing optimal order policies necessary to achieve practicable supply chain coordination. In order to validate the necessity of the developed models, we include an empirical analysis of item reliability for some common mechanical components used in the defense industry, thereby identifying items which fail in the manner modeled in this dissertation. Having considered optimal order policies for both buyers and suppliers, we next develop an optimal solution for a coordinated supply chain. The proposed solution allows the manufacturer to coordinate a supply chain consisting of n buyers in order to achieve a common replenishment time. Through this optimization framework, we minimize total system-wide costs and derive the cost savings associated with our coordinated solution. Numerical examples are then used to demonstrate the magnitude of cost savings achievable through our coordination framework. We conclude by proposing several mechanisms for leveraging the resulting cost savings to induce mutually-beneficial cooperation between the supplier and multiple buyers. Given the lack of buyer-supplier cooperation noted in empirical research related to supply chain coordination, our identification of specific mechanisms useful for inducing mutually-beneficial cooperation between buyers and suppliers represents an important practical contribution to the supply chain coordination literature. These models are accompanied by a thorough overview and discussion of economic order quantity theory, optimal order policies, and supply chain coordination mechanisms.