Classical Economic Order Quantity Model Research Articles

A vendor-buyer supply chain model with stochastic lead times and screening errors

Inventory management and coordination among different echelons are some of the primary factors for the success of any supply chain. The classical economic order quantity (EOQ) model endeavours to achieve optimisation in the field of inventory management across supply chains. Most of the literature on supply chains ignores the role of quality, human factors and variability in lead-time-demand, while trying to improve its performance. The objective of this paper is to study the combined effect of defective items, inspection errors and stochastic lead time demand on the optimal cost of a two level (vendor-buyer) supply chain. A simple solution procedure along with a numerical example is presented to determine the optimal solution to this model. A sensitivity analysis is carried out to illustrate the significance of different parameters. Finally, a discussion on management insights is presented to complement the model and results.

Joint replenishment model for multiple products with substitution

We extend the classical economic order quantity model to address the joint replenishment of multiple products under substitution. The proposed model optimizes ordering quantities for each product under substitution effects with the objective of minimizing the total cost associated with the setup, holding, and shortage of products, while partially meeting demand. First, the special case of three substitutable products is examined in detail. Then, a nonlinear mathematical programming formulation is presented as a general-purpose solution approach for any number of substitutable products. The convexity of the model is discussed. We find that the objective function to be convex in the important special case of products having equal unit holding costs, which typically holds for substitutable products in practice. Sensitivity analysis is conducted in order to determine the impact of cost parameters variations on the ordering policy. We focus on identifying conditions that favor substitution among products. We find that allowing substitution among products is an effective vehicle for cost cutting in supply chain settings involving high fixed costs, low holding costs, and low shortage costs.

An EOQ model with random disruption and partial backordering

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.

Dynamic and stochastic behavior of coefficient of demand uncertainty incorporated with EOQ variables: An application in finished-goods inventory from General Motors׳ dealerships

The objective of this paper is to investigate finished-goods inventory in the U.S. automobile industry using an econometric method known as the variable mean response (VMR) estimation. The research uses the classical economic order quantity (EOQ) model as a starting point. Different from the usual form of the model, here we relax certain assumptions inherent to the EOQ and treat demand as uncertain rather than deterministic. In this research, eight models are developed and applied empirically. The results of the proposed models and methodology provide inventory decision-makers with different managerial implications and strategic improvements. Overall, the empirical results demonstrate many avenues for considering new inventory policies.

An EOQ model with backlogging

This paper deals with a new approach of linguistic dichotomous fuzzy variables for a classical backordered EOQ (Economic Order Quantity) model with PE (Promotional Effort) and selling price dependent demand rate. In practice, we have observed that the demand rate during a shortage period decreases with time. Based on these assumptions, we have developed a cost minimization problem (a crisp model) by trading off setup cost, inventory cost, backordering cost and cost for promotional effort. Then, we have studied a fuzzy model by considering the coefficient vectors as pentagon fuzzy numbers associated with some co-ordinates. Defuzzification is made with the help of the center-of-gravity method followed by a ranking index and the Euclidean distance of the objective function. Considering a numerical example, phi- (φ-)coefficients have been computed for each method and a decision is made according to the natural characteristics of the decision variables. Finally, conclusions are drawn, explaining the justification of the model.

An Alternative Fuzzy EOQ Model with Backlogging for Selling Price and Promotional Effort Sensitive Demand

This paper deals with a classical Economic Order Quantity model with backlogging and the demand of end customers is dependent on promotional effort and selling price simultaneously. The order quantity and shortage quantities are functionally related to promotional effort (PE), unit selling price and time alone. At first, a crisp solution is made. Then, a general fuzzy optimal and intuitionistic fuzzy optimal policy have been discussed, considering selling price and PE as fuzzy number and fuzzy variable respectively. Finally, a graphical illustration, numerical examples with sensitivity analysis and conclusion are made for justification of the model.

역주문을 고려한 공정-저장조 망구조의 최적설계

Product shortage which causes backordering and/or lost sales cost is very popular in chemical industries, especially in commodity polymer business. This study deals with backordering cost in the supply chain optimization model under the framework of process-inventory network. Classical economic order quantity model with backordering cost suggested optimal time delay and lot size of the final product delivery. Backordering can be compensated by advancing production/transportation of it or purchasing substitute product from third party as well as product delivery delay in supply chain network. Optimal solutions considering all means to recover shortage are more complicated than the classical one. We found three different solutions depending on parametric range and variable bounds. Optimal capacity of production/transportation processes associated with the product in backordering can be different from that when the product is not in backordering. The product shipping cycle time computed in this study was smaller than that optimized by the classical EOQ model.

An economic order quantity model for deteriorating item in a purchasing system with multiple prepayments

In the classic economic order quantity model the purchasing cost of an order should be paid at the time of its receipt. Sometimes, retailers ask purchasers to pay all or a fraction of the purchasing cost in advance and sometimes allow them to divide the prepayment into several equal-sized parts. In this paper, economic order quantity model for a deteriorating product with and without shortage under consecutive prepayments are developed. Numerical examples illustrate the proposed models and solution method and sensitivity analysis provides some managerial insights for managers.

An EOQ model with partial backordering and advance payments for an evaporating item

In the classic Economic Order Quantity model the purchasing cost of an order is paid at the time of its receipt. In some cases retailers ask purchasers to pay all or a fraction of the purchasing cost in advance and may allow them to divide the prepayment into several equal-sized parts. In this paper, an economic order quantity model for an evaporating item with partial backordering and partial consecutive prepayments is developed with a real case study of a gasoline station. Real numerical examples illustrate the proposed model and the solution method.

An Economic Order Quantity model with partial backordering and all-units discount

The classic Economic Order Quantity model assumes that the unit purchasing cost is not based on the order quantity. In practice, a supplier may offer purchasers an all-units discount. We develop a model and solution procedure for the EOQ with all-unit discounts and partial backordering at a constant rate. We show, and illustrate with a numerical example, how that model can be used to find the solution for the EOQ with discount and full backordering. A multi-factor experiment is used to gain insights into the improvement in performance of the proposed procedure relative to using the basic EOQ or the EOQ with full backordering and to identify the model parameters that have the greatest impact on the model׳s performance.

Joint replenishment model with substitution

When products are coupled to the same cycle, the joint replenishment model (JRM) is used to determine optimal inventory levels, where the amount to order (for each item) is designed to minimize the joint holding and ordering costs based on a given demand. JRM studies assume that there is no substitution between items. However, this assumption is unrealistic in some settings where substitution cannot be ignored. This paper combines the separate works on substitution and joint replenishment and proposes a solution procedure for solving the joint replenishment model with substitution (JRMS) for two products within the framework of the classical economic order quantity model. We determine the optimal order quantities for each product taking into consideration substitution between them so that demand is partially met and the total cost associated with the delivery, holding, and shortage of the products is minimized. We also provide an extensive scenario analysis and draw insights. In particular, we shed some light on the role of substitution in reducing the fixed cost. We show that JRMS can result in substantial cost savings compared to the ordinary JRM.

Optimal Design of Generalized Batch‐Storage Network Considering Shortage Costs

Product shortages, which cause backlogging and/or lost sales costs commonly occur in the chemical industries, especially in the commodity polymer business. Shortage costs in a supply chain optimization model are studied under the framework of a generalized batch‐storage network. A classical economic order quantity model with backlogging costs suggested an optimal time delay and final product delivery lot size. A product shortage can be mitigated by advancing production/transportation or by purchasing a substitute product from a third party as well as by a product delivery delay in the supply chain network. Optimal solutions that consider all means for recovering shortage are more complicated than the classical case. Four solutions are identified depending on the parametric range and variable bounds. The optimal capacity for production/transportation processes associated with a product in shortage can differ from that of a product not in shortage. An illustrative example is presented in support of the analytical results. © 2013 American Institute of Chemical Engineers AIChE J, 59: 2454–2470, 2013

An economic order quantity model with a known price increase and partial backordering

A constant unit purchase cost is one of the main assumptions in the classic Economic Order Quantity model. In practice, suppliers sometimes face a known price increase. In this paper, we develop EOQ models with a known price increase and partial backordering under two different assumptions about when the increase will occur. We prove the concavity of the extra profit functions for both scenarios if a special order is placed just before the price increases. A solution method is proposed and numerical examples are presented.

Optimal Inventory Policy of Production Management: A Present Value Framework

The classical economic production quantity (EPQ) assumes that the replenishments are instantaneous. As a manager of a factory, there is a problem must be taken into consideration. If the establishment buys all of the raw materials at the beginning, the stock-holding cost for the raw materials should be counted into the relevant costs. So the main purpose of this paper will add the raw materials stock-holding cost to the EPQ model and take the time value of money into consideration. Therefore, we will calculate the present value and compare the difference between take and does not take the time value of money into consideration. From these procedures of calculating, we found some interesting results: 1) the present value of total stock-holding cost of raw materials plus products from the beginning to time t is the same as the stock-holding cost of classical economic order quantity (EOQ) model; 2) the present value of total relevant cost is independent of the production rate (if the production rate is greater than the demand rate); 3) the optimal cycle time of total relevant cost not taking the time value into consideration is the same the optimal cycle time of classical EOQ model; 4) the purchasing cost per unit time is irrelevant to time.

Optimal Lot Sizing with NPV Approach for Inventory Systems with Constant Demand

This paper presents two new economic order quantity (EOQ) formulations supplemented with net present value (NPV) approach. While NPV approach is broadly accepted as the most realistic framework in modelling inventory systems, the literature possesses rather contradicting results on the application. In this paper, we introduce a NPV based EOQ model for an inventory system with constant demand, under fixed ordering cost and linear holding and penalty cost assumptions. For this particular problem, Gurnani (1983) is the first to provide some results on NVP approach. His study is criticized by Kim and Chung (1985) afterwards. In this study, we show that the earlier works of Gurnani, and Kim and Chung are both flawed, and we provide the optimal formulations for both cost minimization and profit maximization objectives. Through an extensive numerical study, we demonstrate that classical EOQ model may lead to sub-optimal solutions without an embedded cash flow analysis. Meanwhile, we also show how EOQ models proposed by Gurnani and Kim and Chung deviate from optimality.

Analysis of purchasing activity with discounted cash flow inventory models

The classical economic order quantity model has two types of costs: ordering and inventory holding costs. In this paper we try to investigate the effect of purchasing activity on cash flow of a firm. In the examinations we use a cash flow identity similar to that of in inventory modeling. In our approach we analyze the purchasing and ordering process with discounted costs. The cost function of the model consists of linear cash holding, linear opportunity cost of spending cash, and linear interest costs. We show the optimal solution of the proposed model. The optimal solutions will be presented by numerical examples.

A Variant Deterministic Model of Classical EOQ Formula

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.

An economic order quantity model with multiple partial prepayments and partial backordering

The classic Economic Order Quantity model assumes that an order is paid for at the time of its receipt. In practice, suppliers may require purchasers to pay a fraction of the order’s cost in advance and sometimes allow them to divide the prepayment into multiple equal-sized parts to be paid during a fixed lead time. In this paper, an EOQ model with multiple prepayments under three different conditions: (a) no shortage, (b) full backordering and (c) partial backordering, are developed. Numerical examples illustrate the proposed models and solution method.

Including sustainability criteria into inventory models

Research on sustainability performance has considerably enriched operations management literature in recent years. However, work with quantitative models is still scarce. This paper contributes by revisiting classical inventory methods taking sustainability concerns into account. We believe that reducing all aspects of sustainable development to a single objective is not desirable. We thus reformulate the classical economic order quantity model as a multiobjective problem. We refer to this model as the sustainable order quantity model. Then, a multi-echelon extension of the sustainable order quantity model is studied. For both models, the set of efficient solutions (Pareto optimal solutions) is analytically characterized. These results are used to provide some insights about the effectiveness of different regulatory policies to control carbon emissions. We also use an interactive procedure that allows the decision maker to quickly identify the best option among these solutions. The proposed interactive procedure is a new combination of multi-criteria decision analysis techniques.

An economic order quantity model with partial backordering and a special sale price

A constant unit purchase cost is one of the main assumptions in the classic economic order quantity model. In practice, suppliers sometimes offer special sale prices to stimulate sales or decrease inventories of certain items. In this paper we develop an EOQ model with a special sale price and partial backordering. We prove the convexity of the cost-reduction function if a special order is placed at the special sale price. A solution method is proposed and numerical examples are presented.