scholarly journals A Fuzzy EPQ Model for Non-Instantaneous Deteriorating Items where Production Depends on Demand which is Proportional to Population, Selling Price as well as Advertisement

2019 ◽  
Vol 10 (5) ◽  
pp. 1679 ◽  
Author(s):  
Abhishek Kanti Biswas ◽  
Sahidul Islam
Keyword(s):  
Optimal Solution ◽  
Inventory Level ◽  
Selling Price ◽  
Distance Method ◽  
Defective Items ◽  
Holding Cost ◽  
Epq Model ◽  
Optimal Inventory Level ◽  
Cost Parameters ◽  
Total Average

The inventory system has been drawing more intrigue because this system deals with the decision that minimizes the total average cost or maximizes the total average profit. For any farm, the demand for any items depends upon population, selling price and frequency of advertisement etc. Most of the model, it is assumed that deterioration of any item in inventory starts from the beginning of their production. But in reality, many goods are maintaining their good quality or original condition for some time. So, price discount is availed for defective items. Our target is to calculate the total optimal cost and the optimal inventory level for this inventory model in a crisp and fuzzy environment. Here Holding cost taken as constant and no-shortages are allowed. The cost parameters are considered as Triangular Fuzzy Numbers and to defuzzify the model Signed Distance Method is applied. A numerical example of the optimal solution is given to clarify the model. The changes of different parameters effect on the optimal total cost are presented and sensitivity analysis is given.JEL Classification: C44, Y80, C61Mathematics Subject Classification: 90B05

scholarly journals Multi-objective economic production quantity model for fully backlogged problem where demand depend on some conditions and permissible delay in payment

2019 ◽  
Vol 10 (3) ◽  
pp. 1106
Author(s):  
Abhishek Kanti Biswas ◽  
Sahidul Islam
Keyword(s):  
Selling Price ◽  
Defective Items ◽  
Multi Objective ◽  
Economic Production ◽  
Permissible Delay In Payment ◽  
Holding Cost ◽  
Epq Model ◽  
Production Quantity ◽  
Nearest Interval Approximation ◽  
The Cost

For any business, inventory system takes a monumental part. Keep this aspect in mind, we formulate multi-objective displayed EPQ model consider with non-instantaneous deteriorating things where production depends on demand and variable demand pattern depends on display self-space, selling price and frequency of advertisement of the item. The customers are more attracted to buy an item by observing self-space, selling price and advertisement. Imperfect materials are now and again come back to providers for a discount or credit. Here price discount is available for deteriorated and defective items. Holding cost varies with time where shortages are allowed and fully backlogged. Fuzzy environment touches the reality instead of the crisp environment. So, we assumed the cost components as Triangular Fuzzy Numbers and Nearest Interval Approximation Method is used to defuzzify the model. Finally, numerical examples as well as  sketches are given to illustrate the model.

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 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.

scholarly journals Inventory Model with Demand Dependent on Unit Price under Fuzzy Parameters and Decision Variables

2019 ◽  
Vol 8 (3) ◽  
pp. 784-788
Keyword(s):  
Numerical Solutions ◽  
Unit Cost ◽  
Optimal Solution ◽  
Unit Price ◽  
Lot Size ◽  
Setup Cost ◽  
Eoq Model ◽  
Decision Variables ◽  
Holding Cost ◽  
Cost Parameters

An EOQ model with demand dependent on unit price is considered and a new approach of finding optimal demand value is done from the optimal unit cost price after defuzzification. Here the cost parameters like setup cost, holding cost and shortage cost and also the decision variables like unit price, lot size and the maximum inventory are taken under fuzzy environment. Triangular fuzzy numbers are used to fuzzify these input parameters and unknown variables. For the proposed model an optimal solution has been determined using Karush Kuhn-Tucker conditions method. Graded Mean Integration (GMI) method is used for defuzzification. Numerical solutions are obtained and sensitivity analysis is done for the chosen model

scholarly journals An Inventory Model for Imperfect Quality Products with Rework, Distinct Holding Costs, and Nonlinear Demand Dependent on Price

Mathematics ◽  
2021 ◽  
Vol 9 (12) ◽  
pp. 1362
Author(s):  
Leopoldo Eduardo Cárdenas-Barrón ◽  
María José Lea Plaza-Makowsky ◽  
María Alejandra Sevilla-Roca ◽  
José María Núñez-Baumert ◽  
Buddhadev Mandal
Keyword(s):  
Optimal Solution ◽  
Inventory Model ◽  
Inventory System ◽  
Inventory Level ◽  
Selling Price ◽  
Lot Size ◽  
Inventory Models ◽  
Holding Costs ◽  
Imperfect Items ◽  
The Moment

Traditionally, the inventory models available in the literature assume that all articles in the purchased lot are perfect and the demand is constant. However, there are many causes that provoke the presence of defective goods and the demand is dependent on some factors. In this direction, this paper develops an economic order quantity (EOQ) inventory model for imperfect and perfect quality items, taking into account that the imperfect ones are sent as a single lot to a repair shop for reworking. After reparation, the items return to the inventory system and are inspected again. Depending on the moment at which the reworked lot arrives to the inventory system, two scenarios can occur: Case 1: The reworked lot enters when there still exists inventory; and Case 2: The reworked lot comes into when the inventory level is zero. Furthermore, it is considered that the holding costs of perfect and imperfect items are distinct. The demand of the products is nonlinear and dependent on price, which follows a polynomial function. The main goal is to optimize jointly the lot size and the selling price such that the expected total profit per unit of time is maximized. Some theoretic results are derived and algorithms are developed for determining the optimal solution for each modeled case. It is worth mentioning that the proposed inventory model is a general model due to the fact that this contains some published inventory models as particular cases. With the aim to illustrate the use of the proposed inventory model, some numerical examples are solved.

Imprecise Inventory Model for Items With Imperfect Quality Subject to Learning Effects Having Shortages

2018 ◽  
pp. 284-304
Author(s):  
Sumana Saha ◽  
Tripti Chakrabarti
Keyword(s):  
Optimal Solution ◽  
Inventory Model ◽  
Extension Principle ◽  
Market Demand ◽  
Screening Process ◽  
Defective Items ◽  
Inventory Costs ◽  
Eoq Model ◽  
Proposed Model ◽  
Holding Cost

The fundamental assumption of an economic order quantity (EOQ) model is that 100% of items in an ordered lot are perfect. This assumption is not always pertinent for production processes because of process deterioration or other factors. This paper develops an EOQ model for that each ordered lot contains some defective items and shortages backordered. Here, an inventory model is developed to deal the impreciseness present in market demand. It is assumed that the received items are not of perfect quality and after screening, imperfect items are withdrawn from inventory and sold at discounted price. However, in practice, errors occur in screening test. So, the screening process fails to be perfect. Due to acquaintance with handling methodology and system, holding cost and ordering cost are gradually decreases from one shipment to another. So, learning effect is incorporated on holding cost, ordering cost and number of defective items present in each lot. Due to impreciseness in market demand and in different inventory costs, profit expression is fuzzy in nature. To fuzzify the profit expression, Extension Principle is used and for defuzzification Signed distance method is applied. Finally, the feasibility of proposed model and the effect of learning on optimal solution are shown through numerical example.

scholarly journals Multi objective fuzzy inventory model with deterioration, price and time dependent demand and time dependent holding cost

2020 ◽  
Vol 11 (3) ◽  
pp. 928
Author(s):  
Satya Kumar Das ◽  
Sahidul Islam
Keyword(s):  
Graphical Representation ◽  
Fuzzy Programming ◽  
Inventory Model ◽  
Time Dependent ◽  
Selling Price ◽  
Multi Objective ◽  
Holding Cost ◽  
Fuzzy Inventory ◽  
Cost Parameters ◽  
Dependent Demand

In this paper, we have formulated an inventory model with time dependent holding cost, selling price as well as time dependent demand. Multi-item inventory model has been considered under limitation on storage space. Due to uncertainty all the require cost parameters are taken as generalized trapezoidal fuzzy number. Our proposed multi-objective inventory model has been solved by using fuzzy programming techniques which are FNLP, FAGP, WFNLP and WFAGP methods. A numerical example is provided to demonstrate the application of the model. Finally to illustrate the model and sensitivity analysis and graphical representation have been shown. 

scholarly journals A reverse logistics inventory model with multiple production and remanufacturing batches under fuzzy environment

2021 ◽  
Author(s):  
Swati Sharma ◽  
S. R. Singh ◽  
Mohit Kumar
Keyword(s):  
Reverse Logistics ◽  
Optimal Solution ◽  
Inventory Model ◽  
Setup Cost ◽  
Distance Method ◽  
Total Cost ◽  
Multiple Production ◽  
Fuzzy Environment ◽  
Cost Parameters ◽  
The Impact

In the last few years, inventory modeling with reverse logistics has received more attention from both the academic world and industries. Most of the existing works in the literature believed that newly produced products and remanufactured products have the same quality. However, in many industries, customers do not consider remanufactured products as good as new ones. Therefore, this study develops a reverse logistics inventory model with multiple production and remanufacturing batches (cycles) under the fuzzy environment where the remanufactured products are of subordinate quality as compared to the newly produced products. As the precise estimation of inventory cost parameters such as holding cost, setup cost, etc. becomes often difficult; so these cost parameters are represented as triangular fuzzy numbers. Used products are purchased, screened and then suitable products are remanufactured. The production and remanufacturing rates are demand dependent. The main goal of this study is to obtain the optimal production and remanufacturing policy that minimizes the total cost per unit time of the proposed inventory system. The signed distance method is employed to defuzzify the total cost function. A numerical example is presented to demonstrate the developed model. Finally, sensitivity analysis is executed to study the impact of key parameters on the optimal solution.

scholarly journals A Sustainable Inventory Model with Imperfect Products, Deterioration, and Controllable Emissions

Mathematics ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 2049
Author(s):  
Abu Hashan Md Mashud ◽  
Dipa Roy ◽  
Yosef Daryanto ◽  
Mohd Helmi Ali
Keyword(s):  
Product Quality ◽  
Co2 Reduction ◽  
Green Technology ◽  
Selling Price ◽  
Defective Items ◽  
Technology Investment ◽  
Deterioration Rate ◽  
Preservation Technology ◽  
Holding Cost ◽  
Carbon Dioxide Co2

Maintaining product quality and environmental performance are emerging concerns in modern competitive and transparent businesses. Many retailers separate perfect products from imperfect ones to ensure product quality and endeavor to achieve carbon dioxide (CO2) reduction through green technology investments and sustainable inventory planning. Product deterioration often badly hampers the retailing business; hence, suitable preservation technologies are used. In this study, we examined the optimization model of the selling price, investment, and replenishment planning to maximize the total profit. The proposed model considered the effect of a greater deterioration rate and discount price of imperfect products. Due to the high uncertainty in demand, a realistic holding cost was deliberated with a variable and constant part. Every time the retailer transports purchased items, greenhouse gases (GHGs), including CO2, are produced. Government regulations on CO2 minimization and customer awareness for greener products stimulate retailers to invest in energy-efficient green technology. This study simultaneously showed a harmonious relationship among the attributes of preservation technology, green technology investment, and discounts on defective items. Theoretical derivations were performed with numerical analysis.

Supply Chain Model with Two Storage Facility for Stock Dependent Demand Incorporating Learning and Inflationary Effect under Crisp and Fuzzy Environment

2017 ◽  
Vol 6 (2) ◽  
pp. 82-109 ◽  
Author(s):  
Chaman Singh ◽  
Shiv R. Singh
Keyword(s):  
Supply Chain ◽  
Inventory Level ◽  
Chain Model ◽  
Selling Price ◽  
Purchasing Cost ◽  
Supply Chain Model ◽  
Stock Dependent Demand ◽  
Demand Rate ◽  
Cost Parameters ◽  
Dependent Demand

In this paper, a supply chain model with power form stock-dependent demand rate is developed, incorporating the effect of learning and inflationary environment. In order to bring their research closer to reality, all the cost parameters involved in the model are considered fuzzy in nature. The demand rate is assumed to be a polynomial form of current inventory level in Own-warehouse. To display the items, retailer has one warehouse of finite capacity, treated as own warehouse (OW) and may hire another warehouse of large capacity, treated as rented warehouse (RW) to storage the excess inventory. Learning effect is incorporated on retailer's selling price, purchasing cost, part of holding cost, deterioration cost and ordering cost. Proposed model is illustrated with some numerical example along with sensitivity analysis of parameters.

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