EOQ Model with Stock-Level Dependent Demand and Different Holding Cost Functions

2017 ◽  
Vol 8 (4) ◽  
pp. 59-75 ◽  
Author(s):  
H.S. Shukla ◽  
R.P. Tripathi ◽  
Neha Sang
Keyword(s):  
Order Approximation ◽  
Optimal Solution ◽  
Optimal Order ◽  
Order Quantity ◽  
Inventory Cost ◽  
Stock Level ◽  
Numerical Examples ◽  
Eoq Model ◽  
Holding Cost ◽  
Dependent Demand

This paper presents EOQ (Economic Order Quantity) model with stock- level dependent demand and different types of holding cost function. We show that the total relevant inventory cost per unit time is convex with respect to cycle time. Mathematical models are established to determine optimal order quantity and total relevant inventory cost. Numerical examples are provided for two different models i.e. (i): Instantaneous replenishment with inventory dependent holding cost and (ii) Instantaneous replenishment with quadratic time dependent carrying cost. Numerical examples are provided to illustrate the proposed model. Sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out. The second order approximation is used for finding closed form optimal solution. Mathematica 5.2 software is used to find numerical results.

scholarly journals Inventory models with stock - and price-dependent demand for deteriotating items based on limited space

2022 ◽  
Vol 12 (1) ◽  
pp. 0-0
Keyword(s):  
Optimal Solution ◽  
Selling Price ◽  
Order Quantity ◽  
Inventory Models ◽  
Stock Level ◽  
Numerical Examples ◽  
Eoq Model ◽  
Eoq Models ◽  
Demand Rate ◽  
Dependent Demand

This paper deals with the problem of determining the optimal selling price and order quantity simultaneously under EOQ model for deteriorating items. It is assumed that the demand rate depends not only on the on-display stock level but also the selling price per unit, as well as the amount of shelf/display space is limited. We formulate two types of mathematical models to manifest the extended EOQ models for maximizing profits and derive the algorithms to find the optimal solution. Numerical examples are presented to illustrate the models developed and sensitivity analysis is reported.

scholarly journals Inventory models with stock- and price-dependent demand for deteriorating items based on limited shelf space

2010 ◽  
Vol 20 (1) ◽  
pp. 55-69 ◽  
Author(s):  
Chun-Tao Chang ◽  
Yi-Ju Chen ◽  
Tzong-Ru Tsai ◽  
Wu Shuo-Jye
Keyword(s):  
Optimal Solution ◽  
Deteriorating Items ◽  
Selling Price ◽  
Order Quantity ◽  
Shelf Space ◽  
Stock Level ◽  
Eoq Model ◽  
Eoq Models ◽  
Demand Rate ◽  
Dependent Demand

This paper deals with the problem of determining the optimal selling price and order quantity simultaneously under EOQ model for deteriorating items. It is assumed that the demand rate depends not only on the on-display stock level but also the selling price per unit, as well as the amount of shelf/display space is limited. We formulate two types of mathematical models to manifest the extended EOQ models for maximizing profits and derive the algorithms to find the optimal solution. Numerical examples are presented to illustrate the models developed and sensitivity analysis is reported.

scholarly journals Replenishment Model with Entropic Order Quantity for Deteriorating Items under Inflation

2021 ◽  
pp. 34-47
Author(s):  
P. K. Tripathy ◽  
Anima Bag
Keyword(s):  
Cost Minimization ◽  
Optimal Solution ◽  
Deteriorating Items ◽  
Optimal Order ◽  
Selling Price ◽  
Order Quantity ◽  
Total Cost ◽  
Purchase Cost ◽  
Holding Cost ◽  
Special Approach

The purpose of the current paper is to determine an optimal order quantity so as to minimize the total cost of the inventory system of a business enterprise. The model is developed for deteriorating items with stock and selling price dependent demand under inflation without permitting shortage. Optimal solution is achieved by cost minimization strategy considering replenishment cost, purchase cost, holding cost and deterioration cost with a special approach to entropy cost for bulk size purchasing units. The effectiveness of the proposed model has been avowed through empirical investigation. Sensitivity analysis has been accomplished to deduce managerial insights. Findings suggest that an increased inflationary effect results in increment in the system total cost. The paper can be extended by allowing shortage. The model can be utilized in the business firms dealing with bulk purchasing units of electric equipments, semiconductor devices, photographic films and many more.

The Comparative Study of EOQ Newsboy and Silver-Meal Method for SMEs Business

2014 ◽  
Vol 1044-1045 ◽  
pp. 1807-1811
Author(s):  
Lakkana Ruekkasaem
Keyword(s):  
Optimal Order ◽  
Order Quantity ◽  
Inventory Cost ◽  
Eoq Model ◽  
Proper Number ◽  
Newsboy Model ◽  
Optimal Order Quantity ◽  
The Comparative Study ◽  
Ordering Quantity

This study was conducted to determine an appropriate model to be used so that a cleanroom equipment company will be able to order a proper number of various types of products to serve the demand of customers at different periods of time. The case study had high inventory cost due to the fact that it could not order goods accordingly. The research compared the efficiency of Economic Ordering Quantity (EOQ), Newsboy Model and Silver-Meal Method to find the optimal order quantity model for this company. The results of the study indicated that the EOQ model (in case allowing for some inventory shortage) obtained the least inventory cost.

scholarly journals An EOQ model with stock dependent demand and imperfect quality items

2010 ◽  
Vol 20 (2) ◽  
pp. 237-247 ◽  
Author(s):  
Shibaji Panda
Keyword(s):  
Optimal Order ◽  
Optimal Solutions ◽  
Order Quantity ◽  
Screening Process ◽  
Imperfect Quality ◽  
Eoq Model ◽  
Total Profit ◽  
Approximate Optimal Solutions ◽  
Single Batch ◽  
Dependent Demand

This paper deals with an economic order quantity model where demand is stock dependent. Items received are not of perfect quality and each lot received contains percentage defective imperfect quality items, which follow a probability distribution. Two cases are considered. 1) Imperfect quality items are held in stock and sold in a single batch after a 100 percent screening process. 2) A hundred percent screening process is performed but the imperfect quality items are sold as soon as they are detected. Approximate optimal solutions are derived in both cases. A numerical example is provided in order to illustrate the development of the model. Sensitivity analysis is also presented, indicating the effects of percentage imperfect quality items on the optimal order quantity and total profit.

scholarly journals Optimal order policy for deteriorating items in response to temporary price discount linked to order quantity

2009 ◽  
Vol 40 (4) ◽  
pp. 383-400 ◽  
Author(s):  
Liang-Yuh Ouyang ◽  
Chih-Te Yang ◽  
Hsiu-Feng Yen
Keyword(s):  
Cost Saving ◽  
Optimal Solution ◽  
Deteriorating Items ◽  
Optimal Order ◽  
Market Demand ◽  
Order Quantity ◽  
Price Discount ◽  
Total Cost ◽  
Holding Cost ◽  
Special Order

This paper investigates the possible effects of a temporary price discount offered by a supplier on a retailer's replenishment policy for deteriorating items, whereby the price discount rate depends on the order quantity. The purpose of this study is to develop a decision process for retailers to assist in determining whether to adopt a regular or special order policy. Furthermore, the optimal quantity of a special order policy for a selected case is determined by maximizing the total cost saving between special and regular orders for the duration of the depletion time. This research establishes an algorithm to determine the optimal solution and utilizes several numerical examples to illustrate the theoretical results and subsequently conducts a sensitivity analysis of the optimal solution with respect to the main parameters. Finally, the results reveal that (1) the optimal special order quantity is determined by trading off the benefits of the price discount against the additional holding cost, (2) the retailer benefits in terms of total cost saving if the remnant inventory is as low as possible when adopting a special order policy, (3) for the retailer it is preferable to adopt the special order policy if the unit purchase cost, market demand rate and/or ordering cost increase, and (4) the retailer will order a lower quantity and the total cost saving will decrease when either the holding cost rate or deterioration rate is high. Thus, this study provides the basis for enterprises to make inventory decisions.

scholarly journals Bartering: Price-Setting Newsvendor Problem with Barter Exchange

2021 ◽  
Vol 13 (12) ◽  
pp. 6684
Author(s):  
Milena Bieniek
Keyword(s):  
Demand Function ◽  
Social Economic ◽  
Optimal Solution ◽  
Newsvendor Problem ◽  
Optimal Order ◽  
Price Setting ◽  
Order Quantity ◽  
Economic Uncertainty ◽  
Optimal Price ◽  
Dependent Demand

Barter exchange is a system of swapping goods or services for other goods or services in a moneyless and direct manner. Barter has become an effective model of a circular economy because it reduces the consumption impact. Bartering maximizes the utility of assets and existing resources, and can unleash the unspent social, economic, and environmental value of underutilized assets. The present article analyzes the price-setting newsvendor problem with a barter exchange option. The retailer facing a stochastic price-dependent demand sells a product on the market and, additionally, needs another product for its own purposes. Therefore, first, the retailer trades the unsold product for the product it needs by means of barter, and next disposes of the unsold product at a discounted price at the end of the selling season. The retailer’s optimal order quantity and optimal price are derived assuming additive uncertainty in demand. This type of demand function has special characteristics, for example, the actual demand may attain negative values in times of economic uncertainty. The possibility of negative demand realizations is taken into consideration in the study. It proves that, in certain cases, the optimal solution belongs to the set of high barter prices which implies that the actual demand may be negative.

scholarly journals EOQ Model for Deteriorating Items with Stock-Level-Dependent Demand Rate and Order-Quantity-Dependent Trade Credit

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Jie Min ◽  
Jian Ou ◽  
Yuan-Guang Zhong ◽  
Xin-Bao Liu
Keyword(s):  
Trade Credit ◽  
Sufficient Conditions ◽  
Optimal Solution ◽  
Deteriorating Items ◽  
Order Quantity ◽  
Eoq Model ◽  
Demand Rate ◽  
Delay In Payments ◽  
Dependent Demand Rate ◽  
Dependent Demand

This paper develops a generalized inventory model for exponentially deteriorating items with current-stock-dependent demand rate and permissible delay in payments. In the model, the payment for the item must be made immediately if the order quantity is less than the predetermined quantity; otherwise, a fixed trade credit period is permitted. The maximization of the average profit per unit of time is taken as the inventory system’s objective. The necessary and sufficient conditions and some properties of the optimal solution to the model are developed. Simple solution procedures are proposed to efficiently determine the optimal ordering policies of the considered problem. Numerical example is also presented to illustrate the solution procedures obtained.

scholarly journals Deterministic inventory model for items with Time varying demand, weibull distribution deterioration and shortages

2002 ◽  
Vol 12 (1) ◽  
pp. 61-72 ◽  
Author(s):  
Kun-Shan Wu
Keyword(s):  
Weibull Distribution ◽  
Optimal Solution ◽  
Inventory Model ◽  
Time Varying ◽  
Numerical Examples ◽  
System Parameters ◽  
Eoq Model ◽  
Holding Cost ◽  
Varying Demand ◽  
Weibull Distribution Deterioration

In this paper, an EOQ inventory model is depleted not only by time varying demand but also by Weibull distribution deterioration, in which the inventory is permitted to start with shortages and end without shortages. A theory is developed to obtain the optimal solution of the problem; it is then illustrated with the aid of several numerical examples. Moreover, we also assume that the holding cost is a continuous, non-negative and non-decreasing function of time in order to extend the EOQ model. Finally, sensitivity of the optimal solution to changes in the values of different system parameters is also studied.

scholarly journals Optimal order quantity considering carbon emission costs, defective items, and partial backorder

2021 ◽  
Vol 9 (2) ◽  
pp. 307-316 ◽  
Author(s):  
Yosef Daryanto ◽  
Bellachintya Reira Christata
Keyword(s):  
Optimal Order ◽  
Selling Price ◽  
Low Carbon ◽  
Order Quantity ◽  
Affecting Factors ◽  
Data Set ◽  
Defective Items ◽  
Eoq Model ◽  
Demand Rates ◽  
Holding Cost

To respond to the adoption of carbon pricing regulations, researchers and industry are developing low carbon inventory models that can meet emission reduction targets while maintaining company profits. The challenge is getting tougher when the company is still facing problems related to imperfect product quality. This research solves this problem by developing an economic order quantity (EOQ) model by considering several sources of carbon emissions, as well as the influence of the defective rates, different demand rates, selling price and holding cost for defective products, and shortages backorder. The objective function of the formulated mathematical model is to minimize the total costs which include the emission costs. A numerical example is developed to illustrate the model based on the previous data set. Sensitivity analysis is also carried out to validate the model and to learn more about the system characteristics. The total emissions are calculated and the affecting factors are identified.

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