EOQ Model with Controllable Lead Time, Setup Cost and Backordering Rate

2011 ◽  
Vol 204-210 ◽  
pp. 464-469 ◽  
Author(s):  
Bo Huang ◽  
Wei Dong Meng ◽  
Yu Yu Li
Keyword(s):  
Lead Time ◽  
Optimal Solution ◽  
General Distribution ◽  
Inventory Level ◽  
Order Quantity ◽  
Setup Cost ◽  
Safety Stock ◽  
Total Cost ◽  
Eoq Model ◽  
Controllable Lead Time

This paper developed an EOQ model, in which the demand follows a general distribution, under the assumption that lead time can be shortened and setup cost can be reduced by added investment, and backorder rate depends on inventory level and price discount in the period of shortage. We proved the existence and uniqueness of optimal solution and proposed an algorithm searching for it. We find that order quantity, safety stock and inventory total cost can be normally reduced by shortening lead time and reducing setup cost, furthermore, backordering parameter and probability of shortage have a great impact on inventory total cost, so an enterprise should do its best to reduce probability of shortage, especially when backordering parameter is small.

scholarly journals SUPPLY LEAD TIME UNCERTAINTY IN A SUSTAINABLE ORDER QUANTITY INVENTORY MODEL

2013 ◽  
Vol 4 (4) ◽  
pp. 15-27 ◽  
Author(s):  
Salvatore Digiesi ◽  
Giorgio Mossa ◽  
Giovanni Mummolo
Keyword(s):  
Inventory Management ◽  
Lead Time ◽  
Expected Value ◽  
Air Pollutant ◽  
Pollutant Emission ◽  
Optimal Order ◽  
Inventory Level ◽  
Order Quantity ◽  
Industrial Case Study ◽  
Safety Stock

Abstract Transport plays a key role in inventory management since it affects logistic costs as well as environmental performance of the supply chain. Expected value and variability of supply lead time depend on the transportation means adopted, and influence the optimal values of order quantity, reorder level, and safety stock to be adopted. Fast transportation means allow reducing expected value of the lead time; they are characterized by the highest costs of externalities (i.e. air pollutant emission, noise, congestion, accidents). On the contrary, slow transportation means require high inventory level due to large order quantity; in this case costs of externalities tend to decrease. The Sustainable Order Quantity (SOQ) [1] allows identifying optimal order quantity, reorder level, safety stock as well as transportation means which minimize the sum of the logistic and environmental costs in case of stochastic variability of product demand. In this paper, the authors propose a new SOQ analytical model considering stochastic variability of supply lead time (LT). A solution procedure is suggested for solving the proposed model. The approach is applied to a real industrial case study in order to evaluate the benefits of applying it if compared with the traditional one.

scholarly journals The EOQ Model for Deteriorating Items with a Conditional Trade Credit Linked to Order Quantity in a Supply Chain System

Mathematics ◽  
2021 ◽  
Vol 9 (18) ◽  
pp. 2311
Author(s):  
Kun-Jen Chung ◽  
Jui-Jung Liao ◽  
Hari Mohan Srivastava ◽  
Shih-Fang Lee ◽  
Shy-Der Lin
Keyword(s):  
Trade Credit ◽  
Analytic Solution ◽  
Optimal Solution ◽  
Optimization Methods ◽  
Deteriorating Items ◽  
Order Quantity ◽  
Supply Chain System ◽  
Total Cost ◽  
Eoq Model ◽  
Total Cost Function

For generality, we observed that some of the optimization methods lack the mathematical rigor and some of them are based on intuitive arguments which result in the solution procedures being questionable from logical viewpoints of a mathematical analysis such as those in the work by Ouyang et al. (2009). They consider an economic order quantity model for deteriorating items with partially permissible delays in payments linked to order quantity. Basically, their inventory models are interesting, however, they ignore explorations of interrelations of functional behaviors (continuity, monotonicity properties, differentiability, et cetera) of the total cost function to locate the optimal solution, so those shortcomings will naturally influence the implementation of their considered inventory model. Consequently, the main purpose of this paper is to provide accurate and reliable mathematical analytic solution procedures for different scenarios that overcome the shortcomings of Ouyang et al.

scholarly journals Impact of defective items on (Q, r, L) inventory model involving controllable setup cost

2004 ◽  
Vol 14 (2) ◽  
pp. 247-258 ◽  
Author(s):  
Bor-Ren Chuang ◽  
Liang-Yuh Ouyang ◽  
Yu-Jen Lin
Keyword(s):  
Normal Distribution ◽  
Lead Time ◽  
Optimal Solution ◽  
Inventory Model ◽  
Decision Variable ◽  
Order Quantity ◽  
Setup Cost ◽  
Defective Items ◽  
Reorder Point

In a recent paper, Ouyang et al. [10] proposed a (Q, r, L) inventory model with defective items in an arrival lot. The purpose of this study is to generalize Ouyang et al.?s [10] model by allowing setup cost (A) as a decision variable in conjunction with order quantity (Q), reorder point (r) and lead time (L). In this study, we first assume that the lead time demand follows a normal distribution, and then relax this assumption by only assuming that the first two moments of the lead time demand are given. For each case, an algorithm procedure of finding the optimal solution is developed.

scholarly journals A Revision on Cost Elements of the EOQ Model

2016 ◽  
Vol 11 (1) ◽  
pp. 5-14 ◽  
Author(s):  
Mehdi Rajabi Asadabadi
Keyword(s):  
Capital Cost ◽  
Decision Makers ◽  
Economic Order Quantity ◽  
New Order ◽  
Order Quantity ◽  
Setup Cost ◽  
Total Cost ◽  
Eoq Model ◽  
Proposed Model ◽  
Holding Cost

AbstractThe overall objective of this paper is to investigate the fundamental cost elements of the traditional EOQ model and develop the model by expiring some of its unrealistic assumptions. Over the last few decades, there have been numerous studies developing the EOQ model, but the basic cost elements of the EOQ model have not been investigated efficiently. On the other hand, the capital cost of buying inventories seems to be important to be investigated separately as well as holding cost and ordering cost in the model. In this paper, the capital cost of the inventory and possible stepwise increases in holding and setup cost are taken into account to make a revised formula to compute the economic order quantity. The proposed model involves explicitly the capital cost of buying the inventories in the EOQ model to ensure the decision makers that their financial concerns are considered in the revised model and the new order quantity results the minimum total cost.

scholarly journals Inventory Level Improvement in Pharmacy Company Using Probabilistic EOQ Model and Two Echelon Inventory: A Case Study

2020 ◽  
Vol 13 (3) ◽  
pp. 229-242
Author(s):  
Desy Anisya Farmaciawaty ◽  
◽  
Mursyid Hasan Basri ◽  
Akbar Adhi Utama ◽  
Fransisca Budyanto Widjaja ◽  
...  
Keyword(s):  
Inventory Management ◽  
Lead Time ◽  
Inventory Level ◽  
Setup Cost ◽  
Inventory Cost ◽  
Decentralized System ◽  
Class A ◽  
Eoq Model ◽  
Holding Cost

Abstract. This research is aimed to maintain the inventory level in a two-echelon pharmacy company. The company is a pharmacy company that has 16 branches that operate in Bandung and the surrounding area. The company has a problem with its high inventory cost. To solve the problem, the authors compare two methods that suit the company condition, i.e., the decentralized system using probabilistic EOQ model and the centralization system using the multi-echelon inventory technique. We analyzed sales data and on-hand inventory data acquired from the company information system to perform the study. We limit the scope to the class A items only. We also assume the lead time, setup cost, and holding cost used in this study with the company's owner's consent. To conclude, using the decentralized system, the company will save 31% of their inventory cost, while using the centralization system with the multi-echelon technique, the company will be able to save 61% of their inventory cost. We recommend the company to refer to its competitive strategy before deciding which model it would be implemented. Keywords: Centralization, Decentralization, Probabilistic Economic Order Quantity (EOQ), Multi-Echelon Inventory, Pharmaceutical Inventory Management

Supply Chain Coordination Under Service Level Constraint and Controllable Lead Time

2016 ◽  
Vol 7 (2) ◽  
pp. 84-106 ◽  
Author(s):  
Prashant Jindal ◽  
Anjana Solanki
Keyword(s):  
Supply Chain ◽  
Cost Reduction ◽  
Lead Time ◽  
Cost Allocation ◽  
Optimal Solution ◽  
Service Level ◽  
Decision Variable ◽  
Allocation Model ◽  
Controllable Lead Time ◽  
Ordering Cost Reduction

This paper investigates the coordination issue in a decentralized supply chain having a vendor and a buyer for a defective product. The authors develop two inventory models with controllable lead time under service level constraint. The first one is propose under decentralized mode based on the Stackelberg model, the other one is propose under centralized mode of the integrated supply chain. Ordering cost reduction is also including as a decision variable along with shipping quantity, lead time and number of shipments. Computational findings using the software Matlab 7.0 are provided to find the optimal solution. The results of numerical examples show that centralized mode is better than that of decentralized mode, and to induce both vendor and buyer for coordination, proposed cost allocation model is effective. The authors also numerically investigate the effects of backorder parameter on the optimal solutions. Benefit of ordering cost reduction in both models is also provided.

A JOINT EOQ MODEL FOR SUPPLIER AND RETAILER WITH DETERIORATING ITEMS

2004 ◽  
Vol 21 (02) ◽  
pp. 163-178 ◽  
Author(s):  
CHINHO LIN ◽  
YIHSU LIN
Keyword(s):  
Necessary Conditions ◽  
Optimal Solution ◽  
Planning Horizon ◽  
Solution Procedure ◽  
Sensitivity Analyses ◽  
Mutual Cooperation ◽  
Total Cost ◽  
Numerical Examples ◽  
Eoq Model ◽  
Sufficient And Necessary Conditions

The paper studies the joint inventory model between supplier and retailer relying on mutual cooperation. Unlike other studies, the deteriorated rate and partial back-ordering are consistent with assumptions for dealing with more general cases. Since it is difficult to solve this problem directly, we derived the sufficient and necessary conditions in the planning horizon, and proposed a procedure to find the optimal solution. Numerical examples and sensitivity analyses are also provided to illustrate the solution procedure. The results reveal that the extensions of the model provide a wider and reasonable situation in practice, and that they also reduce the total cost.

AN EOQ MODEL WITH CONTROLLABLE SELLING RATE

2008 ◽  
Vol 25 (02) ◽  
pp. 151-167 ◽  
Author(s):  
HORNG-JINH CHANG ◽  
PO-YU CHEN
Keyword(s):  
Distribution Function ◽  
Transaction Cost ◽  
Optimal Solution ◽  
Bivariate Distribution ◽  
Inventory Level ◽  
Selling Price ◽  
Eoq Model ◽  
Concrete Form ◽  
Demand Rate ◽  
Classical Economic

According to the marketing principle, a decision maker may control demand rate through selling price and the unit facility cost of promoting transaction. In fact, the upper bound of willing-to-pay price and the transaction cost probably depend upon the subjective judgment of individual consumer in purchasing merchandise. This study therefore attempts to construct a bivariate distribution function to simultaneously incorporate the willing-to-pay price and the transaction cost into the classical economic order quantity (EOQ) model. Through the manipulation of the constructed bivariate distribution function, the demand function faced by the supplier can be expressed as a concrete form. The proposed mathematical model mainly concerns how to determine the initial inventory level for each business cycle, so that the profit per unit time is maximized by means of the selling price and the unit-transaction cost to control the selling rate. Furthermore, the sensitivity analysis of optimal solution is performed and the implication of this extended inventory model is also discussed.

scholarly journals An Algorithm for Solution of an Interval Valued EOQ Model

2012 ◽  
Vol 3 (1) ◽  
pp. 55-64 ◽  
Author(s):  
Susovan CHAKRABORTTY ◽  
Madhumangal PAL ◽  
Prasun Kumar NAYAK
Keyword(s):  
Lead Time ◽  
Solution Procedure ◽  
Lot Size ◽  
Setup Cost ◽  
Single Product ◽  
Interval Numbers ◽  
Eoq Model ◽  
Interval Valued ◽  
Total Average Cost ◽  
Total Average

This paper deals with the problem of determining the economic order quantity (EOQ)in the interval sense. A purchasing inventory model with shortages and lead time, whose carryingcost, shortage cost, setup cost, demand quantity and lead time are considered as interval numbers,instead of real numbers. First, a brief survey of the existing works on comparing and ranking anytwo interval numbers on the real line is presented. A common algorithm for the optimum productionquantity (Economic lot-size) per cycle of a single product (so as to minimize the total average cost) isdeveloped which works well on interval number optimization under consideration. A numerical exampleis presented for better understanding the solution procedure. Finally a sensitive analysis of the optimalsolution with respect to the parameters of the model is examined.

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