scholarly journals A profit jump inventory model for imperfect quality items with receiving reparative batch and order overlapping in dense fuzzy environment

2021 ◽  
Vol 55 (2) ◽  
pp. 723-744
Author(s):  
Sujit Kumar De ◽  
Gour Chandra Mahata
Keyword(s):  
Deterministic Model ◽  
Classical Method ◽  
Profit Maximization ◽  
Extensive Study ◽  
Inventory Model ◽  
Purchasing Cost ◽  
Imperfect Quality ◽  
Holding Costs ◽  
Fuzzy Environment ◽  
Imperfect Items

This paper presents an economic order quantity (EOQ) inventory model for imperfect quality items with receiving a reparative batch and order overlapping in a dense fuzzy environment Here, the imperfect items are identified by screening and are divided into either scrap or reworkable items. The reworkable items are kept in store until the next items are received. Afterwards, the items are returned to the supplier to be reworked. Also, discount on the purchasing cost is employed as an offer of cooperation from a supplier to a buyer to compensate for all additional holding costs incurred to the buyer. The rework process is error free. An order overlapping scheme is employed so that the vendor is allowed to use the previous shipment to meet the demand by the inspection period. However, we assume the total monthly demand quantity as the dense fuzzy number because of learning effect. Moreover, first of all a profit maximization deterministic model is developed and solve by classical method. Fuzzifying the final optimized function via dense fuzzy demand quantity we have employed extended ranking index rule for its defuzzification. During the process of defuzzification we make an extensive study on the paradoxical unit square of the left and right deviations of dense fuzzy numbers. A comparative study is made after splitting the model into general fuzzy and dense fuzzy environment. Finally numerical and graphical illustrations and sensitivity analysis have been made for its global justifications.

scholarly journals A Fuzzy Inventory Model Considering Imperfect Quality Items with Receiving Reparative Batch and Order

2020 ◽  
Vol 5 (10) ◽  
pp. 1179-1185
Author(s):  
Hesamoddin Tahami ◽  
Hengameh Fakhravar
Keyword(s):  
Fuzzy Model ◽  
Inventory Model ◽  
Purchasing Cost ◽  
Imperfect Quality ◽  
Holding Costs ◽  
Fuzzy Environment ◽  
Imperfect Items ◽  
Triangular Numbers ◽  
Order Scheme ◽  
Fuzzy Inventory

This paper presents an inventory model for imperfect quality items with receiving a reparative batch and order overlapping in a fuzzy environment by employing fuzzy triangular numbers. It is assumed that the imperfect items identified by Screening are divided into either scrap or reworkable items. The reworkable items are kept in store until the next items are received. Afterward, the items are returned to the supplier to be reworked. Also, a discount on the purchasing cost is employed as an offer of cooperation from a supplier to a buyer to compensate for all additional holding costs incurred to the buyer. The rework process is error-free. An overlapping order scheme is employed so that the vendor is allowed to use the previous shipment to meet the demand by the inspection period. In the fuzzy model, the graded mean integration method is taken to defuzzify the model and determine its approximation of a profit function and optimal policy. In doing so, numerical examples are rendered to represent the model behavior, and, eventually, the sensitivity analysis is presented.

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.

A TWO-WAREHOUSE INVENTORY MODEL FOR ITEMS WITH IMPERFECT QUALITY AND QUANTITY DISCOUNTS

2011 ◽  
Vol 28 (02) ◽  
pp. 147-161 ◽  
Author(s):  
TIEN-YU LIN
Keyword(s):  
Inventory Model ◽  
The Other ◽  
Quantity Discounts ◽  
Storage Space ◽  
Lot Size ◽  
Numerical Examples ◽  
Purchasing Cost ◽  
Imperfect Quality ◽  
Lot Sizes

In this paper, a two-warehouse inventory model for items with imperfect quality and all-unit quantity discounts was developed. In practice, the supplier usually offers quantity discounts to encourage the retailer ordering larger lot sizes and thus, extra storage space is needed for the retailer. Two levels of storages, owned-warehouse and rented warehouse, are considered in this study to store bulk quantities. We develop two algorithms to determine the optimal lot size and purchasing cost: one is based on the work of Render et al. (2003) and the other is similar to the method proposed by Goyal (1995). Two numerical examples are provided for illustration, in which we show that our algorithms require fewer iterations than that of the modified procedures based on the work of Render et al. (2003).

scholarly journals Optimal Buyer’s Replenishment Policy in the Integrated Inventory Model for Imperfect Items

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Lu Yueli ◽  
Mo Jiangtao ◽  
Wei Yucheng
Keyword(s):  
Inventory Model ◽  
Computational Method ◽  
Imperfect Quality ◽  
Imperfect Items ◽  
Unrealistic Assumption ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Classical Economic ◽  
The Cost ◽  
Optimal Ordering

In the classical economic order quantity (EOQ) models, a common unrealistic assumption is that all the items received are of good quality. However, in realistic environment, a received shipment usually contains a fraction of imperfect quality items. These imperfect items may be scrapped, reworked at a cost, or salvaged at a discounted price. While the percentage of imperfect items is random, the optimal ordering cycle is rarely considered in current literatures. This paper revisits the model (Maddah and Jaber, 2008) and extends it by assuming that the ordering cycle is determined by the demand rate, delivery quantity per shipment, and the mathematical expectation of the defective rate. The possibility of stockout or residue in the end of a cycle will be considered, and the loss of stockout and the salvage of the residue are counted into the cost. Besides, we consider consolidating the shipments of imperfect items over multiple deliveries. Thus, an integrated vendor-buyer inventory model for imperfect quality items with equal-size shipment policy is established to derive the optimal ordering cycle, ordering quantity, and number of deliveries. The computational method of the optimal delivery quantity per shipment and number of deliveries is given through theoretical results. Finally, sensitivity of main parameters is analyzed through simulation experiments and shown by some figures.

scholarly journals Fuzzy stochastic inventory model for deteriorating item

2017 ◽  
Vol 27 (1) ◽  
pp. 91-97 ◽  
Author(s):  
Rahul Waliv ◽  
Hemant Umap
Keyword(s):  
Linear Programming ◽  
Programming Problem ◽  
Profit Maximization ◽  
Inventory Model ◽  
Fuzzy Linear Programming ◽  
Programming Technique ◽  
Purchasing Cost ◽  
Stochastic Inventory ◽  
Stochastic Inventory Model ◽  
Fuzzy Stochastic Programming

A multi item profit maximization inventory model is developed in fuzzy stochastic environment. Demand is taken as Stock dependent demand. Available storage space is assumed to be imprecise and vague in nature. Impreciseness has been expressed by linear membership function. Purchasing cost and investment constraint are considered to be random and their randomness is expressed by normal distribution. The model has been formulated as a fuzzy stochastic programming problem and reduced to corresponding equivalent fuzzy linear programming problem. The model has been solved by using fuzzy linear programming technique and illustrated numerically.

scholarly journals Multi-item fuzzy inventory problem with space constraint via geometric programming method

2006 ◽  
Vol 16 (1) ◽  
pp. 55-66 ◽  
Author(s):  
Kumar Mandal ◽  
Kumar Roy ◽  
Manoranjan Maiti
Keyword(s):  
Space Constraint ◽  
Geometric Programming ◽  
Profit Maximization ◽  
Inventory Model ◽  
Programming Method ◽  
Unit Price ◽  
Selling Price ◽  
Inventory Problem ◽  
Set Up ◽  
Fuzzy Inventory

In this paper, a multi-item inventory model with space constraint is developed in both crisp and fuzzy environment. A profit maximization inventory model is proposed here to determine the optimal values of demands and order levels of a product. Selling price and unit price are assumed to be demand-dependent and holding and set-up costs sock dependent. Total profit and warehouse space are considered to be vague and imprecise. The impreciseness in the above objective and constraint goals has been expressed by fuzzy linear membership functions. The problem is then solved using modified geometric programming method. Sensitivity analysis is also presented here.

scholarly journals Inventory model of deteriorating items with two-warehouse and stock dependent demand using genetic algorithm in fuzzy environment

2012 ◽  
Vol 22 (1) ◽  
pp. 51-78 ◽  
Author(s):  
Dharmendra Yadav ◽  
S.R. Singh ◽  
Rachna Kumari
Keyword(s):  
Genetic Algorithm ◽  
Inventory Model ◽  
Deteriorating Items ◽  
Market Place ◽  
Time Value Of Money ◽  
Fuzzy Environment ◽  
Purchase Cost ◽  
Stock Dependent Demand ◽  
Fuzzy Goal ◽  
Dependent Demand

Multi-item inventory model for deteriorating items with stock dependent demand under two-warehouse system is developed in fuzzy environment (purchase cost, investment amount and storehouse capacity are imprecise ) under inflation and time value of money. For display and storage, the retailers hire one warehouse of finite capacity at market place, treated as their own warehouse (OW), and another warehouse of imprecise capacity which may be required at some place distant from the market, treated as a rented warehouse (RW). Joint replenishment and simultaneous transfer of items from one warehouse to another is proposed using basic period (BP) policy. As some parameters are fuzzy in nature, objective (average profit) functions as well as some constraints are imprecise in nature, too. The model is formulated so to optimize the possibility/necessity measure of the fuzzy goal of the objective functions, and the constraints satisfy some pre-defined necessity. A genetic algorithm (GA) is used to solve the model, which is illustrated on a numerical example.

scholarly journals Inventory Model with Demand Dependant on Unit Cost- Input Parameters as Triangular Fuzzy Numbers

2021 ◽  
Vol 12 (2) ◽  
Author(s):  
R. Kasthuri, Et. al.
Keyword(s):  
Fuzzy Numbers ◽  
Unit Cost ◽  
Inventory Model ◽  
Average Total Cost ◽  
Triangular Fuzzy Numbers ◽  
Lot Size ◽  
Distance Method ◽  
Total Cost ◽  
Signed Distance ◽  
Fuzzy Environment

This paper considers an inventory model in which the shortages are backlogged and the demand is dependent on unit cost. An optimum value for average total cost is calculated by considering various input costs, lot size and maximum inventory under fuzzy environment. The process of defuzzification is done by using the signed distance method. Numerical example and sensitivity analysis is given for calculating both crisp and fuzzy values of the total cost.

Solution of Basic Inventory Model in Fuzzy and Interval Environments

2017 ◽  
pp. 65-95
Author(s):  
Sankar Prasad Mondal
Keyword(s):  
Differential Equation ◽  
Fuzzy Number ◽  
Interval Number ◽  
Inventory Model ◽  
Time Dependent ◽  
Equation Approach ◽  
Numerical Examples ◽  
Fuzzy Environment

In this present paper a basic inventory model is solved in different imprecise environments. Four different cases are discussed: 1) Crisp inventory model, that is, the quantity at present and demand is crisp number; 2) Inventory model in fuzzy environment, that is, the quantity and demand both are fuzzy number; 3) Inventory model in interval environment, that is, the quantity and demand both are interval number and lastly; 4) Inventory model in time dependent fuzzy environment, that is, quantity and demand are both time dependent fuzzy number. Different numerical examples are used to illustrate the model as well as to compute the efficiency of imprecise differential equation approach to solve the model.

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