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

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.

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

International Journal of Operations Research and Information Systems ◽

10.4018/ijoris.2017100104 ◽

2017 ◽

Vol 8 (4) ◽

pp. 59-75 ◽

Cited By ~ 3

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.

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Optimal Price and Lot Size for an EOQ Model with Full Backordering under Power Price and Time Dependent Demand

Mathematics ◽

10.3390/math9161848 ◽

2021 ◽

Vol 9 (16) ◽

pp. 1848

Author(s):

Luis A. San-José ◽

Joaquín Sicilia ◽

Manuel González-de-la-Rosa ◽

Jaime Febles-Acosta

Keyword(s):

Lot Sizing ◽

Optimal Solution ◽

Selling Price ◽

Inventory Problem ◽

Lot Size ◽

Power Functions ◽

Eoq Model ◽

Demand Rate ◽

Parameter Values ◽

Dependent Demand

In this paper, we address an inventory system where the demand rate multiplicatively combines the effects of time and selling price. It is assumed that the demand rate is the product of two power functions, one depending on the selling price and the other on the time elapsed since the last inventory replenishment. Shortages are allowed and fully backlogged. The aim is to obtain the lot sizing, the inventory cycle and the unit selling price that maximize the profit per unit time. To achieve this, two efficient algorithms are proposed to obtain the optimal solution to the inventory problem for all possible parameter values of the system. We solve several numerical examples to illustrate the theoretical results and the solution methodology. We also develop a numerical sensitivity analysis of the optimal inventory policy and the maximum profit with respect to the parameters of the demand function.

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

Mathematical Problems in Engineering ◽

10.1155/2014/962128 ◽

2014 ◽

Vol 2014 ◽

pp. 1-14 ◽

Cited By ~ 1

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.

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Retailer’s optimal ordering policies for EOQ model with imperfective items under a temporary discount

Yugoslav journal of operations research ◽

10.2298/yjor140615011l ◽

2016 ◽

Vol 26 (2) ◽

pp. 219-240

Author(s):

Wen Lin ◽

Horng Chang

Keyword(s):

Economic Order Quantity ◽

Order Quantity ◽

Objective Functions ◽

Inventory Models ◽

Screening Process ◽

Numerical Examples ◽

Closed Form Solutions ◽

Eoq Model ◽

Optimal Ordering ◽

Special Order

In this article, we study inventory models to determine the optimal special order and maximum saving cost of imperfective items when the supplier offers a temporary discount. The received items are not all perfect and the defectives can be screened out by the end of 100% screening process. Three models are considered according to the special order occurs at regular replenishment time, non-regular replenishment time, and screening time of economic order quantity cycle. Each model has two sub-cases to be discussed. In temporary discount problems, in general, there are integer operators in objective functions. We suggest theorems to find the closed-form solutions to these kinds of problems. Furthermore, numerical examples and sensitivity analysis are given to illustrate the results of the proposed properties and theorems.

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Inventory Models with Defective Units and Sub-Lot Inspection

Mathematics ◽

10.3390/math8061038 ◽

2020 ◽

Vol 8 (6) ◽

pp. 1038

Author(s):

Han-Wen Tuan ◽

Gino K. Yang ◽

Kuo-Chen Hung

Keyword(s):

Lower Bound ◽

Optimal Solution ◽

Upper Bounds ◽

Interior Solution ◽

Order Quantity ◽

Inventory Models ◽

Defective Items ◽

Numerical Examples ◽

Counter Example ◽

Analytical Foundation

Inventory models must consider the probability of sub-optimal manufacturing and careless shipping to prevent the delivery of defective products to retailers. Retailers seeking to preserve a reputation of quality must also perform inspections of all items prior to sale. Inventory models that include sub-lot sampling inspections provide reasonable conditions by which to establish a lower bound and a pair of upper bounds in terms of order quantity. This should make it possible to determine the conditions of an optimal solution, which includes a unique interior solution to the problem of an order quantity satisfying the first partial derivative. The approach proposed in this paper can be used to solve the boundary. These study findings provide the analytical foundation for an inventory model that accounts for defective items and sub-lot sampling inspections. The numerical examples presented in a previous paper are used to demonstrate the derivation of an optimal solution. A counter-example is constructed to illustrate how existing iterative methods do not necessarily converge to the optimal solution.

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AN EOQ MODEL WITH CONTROLLABLE SELLING RATE

Asia Pacific Journal of Operational Research ◽

10.1142/s0217595908001687 ◽

2008 ◽

Vol 25 (02) ◽

pp. 151-167 ◽

Cited By ~ 4

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.

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An EOQ model for rebate value and selling-price-dependent demand rate with shortages

International Journal of Mathematics in Operational Research ◽

10.1504/ijmor.2011.037315 ◽

2011 ◽

Vol 3 (1) ◽

pp. 99 ◽

Cited By ~ 3

Author(s):

M. Valliathal ◽

R. Uthayakumar

Keyword(s):

Selling Price ◽

Eoq Model ◽

Demand Rate ◽

Dependent Demand Rate ◽

Dependent Demand

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On Optimal Inventory Model for Obsolescence Perishable Products under Unpermitted-Stockout

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.201-203.1292 ◽

2011 ◽

Vol 201-203 ◽

pp. 1292-1295

Author(s):

Xiao Liang Xie

Keyword(s):

Optimal Solution ◽

Inventory Model ◽

Economic Order Quantity ◽

Inventory Level ◽

Order Quantity ◽

Short Life ◽

Numerical Examples ◽

Fast Change ◽

Demand Rate ◽

Long Life

With the advancement of science and technology and the fast change of buyer requirements, the short-life products have been shortened at large, some formerly long-life products gradually turn to value deterioration products. The ratio of value deterioration products to modern products is getting higher and higher. This paper develops a deterministic economic order quantity EOQ inventory model, where the demand rate depends on the on-hand inventory when inventory level exceeds certain quantity , otherwise the demand rate is constant. The effects of obsolescence are taken into account, for it is related to the demand rate. The results are discussed through two numerical examples. A sensitivity analysis of the optimal solution with respect to parameters of the system is carried out.

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Optimal Pricing and Ordering Policy for Deteriorating Items with Stock-and-Price Dependent Demand and Presale Rebate

Scientific Programming ◽

10.1155/2016/1507285 ◽

2016 ◽

Vol 2016 ◽

pp. 1-7

Author(s):

Lianxia Zhao ◽

Jianxin You

Keyword(s):

Sensitivity Analysis ◽

Deteriorating Items ◽

Time Dependent ◽

Optimal Pricing ◽

Selling Price ◽

Effective Algorithm ◽

Numerical Examples ◽

Ordering Policy ◽

Demand Rate ◽

Dependent Demand

This paper considers an EOQ inventory model with presale policy for deteriorating items, in which the demand rate depends on both on-hand inventory and selling price. Under the assumption that all the presale orders are fully backlogged with waiting-time dependent rebate, this study develops several propositions and derives optimal pricing and ordering policy by designing an effective algorithm. Two numerical examples are also given to illustrate the effectiveness of the algorithm. Finally, the sensitivity analysis of the main parameters is provided.

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