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 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 Optimal policies for inventory model with shortages, time-varying holding and ordering costs in trapezoidal fuzzy environment

2021 ◽  
Vol 12 (2) ◽  
pp. 557-574
Author(s):  
Pavan Kumar
Keyword(s):  
Fuzzy Model ◽  
Continuous Functions ◽  
Inventory Model ◽  
Inventory Problem ◽  
Distance Method ◽  
Fuzzy Environment ◽  
Optimal Policies ◽  
Demand Rate ◽  
Holding Cost ◽  
Fuzzy Inventory

This paper proposes the optimal policies for a fuzzy inventory model considering the holding cost and ordering cost as continuous functions of time. Shortages are allowed and partially backlogged. The demand rate is assumed in such to be linearly dependent on time during on-hand inventory, while during the shortage period, it remains constant. The inventory problem is formulated in crisp environment. Considering the demand rate, holding cost and ordering cost as trapezoidal fuzzy numbers, the proposed problem is transformed into fuzzy model. For this fuzzy model, the signed distance method of defuzzification is applied to determine the average total cost (ATC) in fuzzy environment. The objective is to optimize the ATC and the order quantity. One solved example is provided in order to show the applicability of the proposed model. The convexity of the cost function is verified with the help of 3D-graph.

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.

scholarly journals A fuzzy inventory model with imperfect items and backorder with allowable proportionate discount

2018 ◽  
Vol 39 (1) ◽  
pp. 39-46
Author(s):  
Rojalini Patro ◽  
Sujit Acharya ◽  
Mitali Nayak ◽  
Milu Acharya
Keyword(s):  
Inventory Model ◽  
Imperfect Items ◽  
Fuzzy Inventory ◽  
Fuzzy Inventory Model

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 TWO-STORAGE FUZZY INVENTORY MODEL WITH TIME DEPENDENT DEMAND AND HOLDING COST UNDER ACCEPTABLE DELAY IN PAYMENT

2020 ◽  
Vol 25 (3) ◽  
pp. 441-460
Author(s):  
Boina Anil Kumar ◽  
Susanta Kumar Paikray ◽  
Umakanta Mishra
Keyword(s):  
Solution Procedure ◽  
Inventory Model ◽  
Time Dependent ◽  
Peak Time ◽  
Fuzzy Environment ◽  
Holding Cost ◽  
Variable Holding Cost ◽  
Fuzzy Inventory ◽  
End Stage ◽  
Dependent Demand

If we observe a real business market, the demand for items in each cycle is not in the same pattern, that is, for specific business cycle it may increase, stable or decrease (for instance, cool drinks from end stage of the summer to winter; the demand goes on decreasing, and from the end of winter to peak time of summer; the demand goes on increasing). Also, if the supplier permits for delay in payment, retailer wishes to buy more goods, and for which the retailer may need extra storage (in terms of a rented warehouse). Moreover, the retailer has always wished to sell the items before they expire and accordingly order is placed. Mostly the parameters in a real world inventory model are imprecise. Thus, in the proposed study an inventory model having decreasing time dependent demand pattern with variable holding cost for TwoStorage facility under acceptable delay in payment has been developed. Mathematical model of the problem and its solution procedure is discussed for both crisp and fuzzy environment in order to obtain the optimal replenishment time and cost. Also, numerical examples are discussed to validate the study. Finally, sensitivity analysis is also studied to describe the fluctuating scenario of associated parameters.

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 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.

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