A simple derivation of the optimal solution for the EOQ model for deteriorating items with planned backorders

2021 ◽  
Vol 89 ◽  
pp. 1373-1381 ◽  
Author(s):  
Cenk Çalışkan
Keyword(s):  
Optimal Solution ◽  
Deteriorating Items ◽  
Simple Derivation ◽  
Eoq Model

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 An EOQ model for deteriorating items under supplier credits when demand is stock dependent

2010 ◽  
Vol 20 (1) ◽  
pp. 145-156
Author(s):  
Nita Shah ◽  
Poonam Mishra
Keyword(s):  
Sensitivity Analysis ◽  
Optimal Solution ◽  
Deteriorating Items ◽  
Critical Parameters ◽  
Eoq Model ◽  
Constant Rate ◽  
Cash Discount

In many circumstances retailer is not able to settle the account as soon as items are received. In that scenario supplier can offer two promotional schemes namely cash discount and /or a permissible delay to the customer. In this study, an EOQ model is developed when units in inventory deteriorate at a constant rate and demand is stock dependent. The salvage value is associated to deteriorated units. An algorithm is given to find the optimal solution. The sensitivity analysis is carried out to analyze the effect of critical parameters on optimal solution.

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 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.

An EOQ model with deteriorating items and self-selection constraints

2020 ◽  
Vol 14 (6) ◽  
pp. 1491-1518
Author(s):  
Mehmet Önal ◽  
O. Erhun Kundakcioglu ◽  
Smita Jain
Keyword(s):  
Deteriorating Items ◽  
Eoq Model ◽  
Self Selection

scholarly journals EOQ model for deteriorating items with exponential demand rate and shortages

2013 ◽  
Vol 1 (2) ◽  
pp. 67-76 ◽  
Author(s):  
H.S. Shukla ◽  
Vivek Shukla ◽  
Sushil Kumar Yadava
Keyword(s):  
Deteriorating Items ◽  
Eoq Model ◽  
Demand Rate

scholarly journals Optimizing preservation strategies for deteriorating items with time-varying holding cost and stock-dependent demand

2020 ◽  
Vol 30 (2) ◽  
pp. 237-250
Author(s):  
Aditi Khanna ◽  
P Priyamvada ◽  
Chandra Jaggi
Keyword(s):  
Optimal Solution ◽  
Optimal Investment ◽  
Deteriorating Items ◽  
Time Varying ◽  
Preservation Technology ◽  
Special Cases ◽  
Stock Dependent Demand ◽  
Managerial Implications ◽  
Holding Cost ◽  
Dependent Demand

Organizations are keen on rethinking and optimizing their existing inventory strategies so as to attain profitability. The phenomenon of deterioration is a common phenomenon while managing any inventory system. However, it could become a major challenge for the business if not dealt carefully. An investment in preservation technology is by far the most inuential move towards dealing with deterioration proficiently. Additionally, it is noticed that the demand pattern of many products is reliant on its availability and usability. Thus, considering demand of the product to be ?stock-dependent" is a more practical approach. Further, in case of deteriorating items, it is observed that the longer an item stays in the system the higher is its holding cost. Therefore, the model assumes the holding cost to be time varying. Hence, the proposed framework aims to develop an inventory model for deteriorating items with stock-dependent demand and time-varying holding cost under an investment in preservation technology. The objective is to determine the optimal investment in preservation technology and the optimal cycle length so as to minimize the total cost. Numerical example with various special cases have been discussed which signifies the effect of preservation technology investment in controlling the loss due to deterioration. Finally, the effect of key model features on the optimal solution is studied through sensitivity analysis which provides some important managerial implications.

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