scholarly journals Ordering Cost Reduction in Inventory Model with Defective Items and Backorder Price Discount

2014 ◽  
Vol 2014 ◽  
pp. 1-14 ◽  
Author(s):  
Karuppuchamy Annadurai ◽  
Ramasamy Uthayakumar
Keyword(s):  
Cost Reduction ◽  
Optimal Solution ◽  
Computer Code ◽  
Inventory Model ◽  
Inventory Models ◽  
Price Discount ◽  
Defective Items ◽  
Numerical Examples ◽  
Ordering Cost Reduction ◽  
Real Market

In the real market, as unsatisfied demands occur, the longer the length of lead time is, the smaller the proportion of backorder would be. In order to make up for the inconvenience and even the losses of royal and patient customers, the supplier may offer a backorder price discount to secure orders during the shortage period. Also, ordering policies determined by conventional inventory models may be inappropriate for the situation in which an arrival lot contains some defective items. To compensate for the inconvenience of backordering and to secure orders, the supplier may offer a price discount on the stockout item. The purpose of this study is to explore a coordinated inventory model including defective arrivals by allowing the backorder price discount and ordering cost as decision variables. There are two inventory models proposed in this paper, one with normally distributed demand and another with distribution free demand. A computer code using the software Matlab 7.0 is developed to find the optimal solution and present numerical examples to illustrate the models. The results in the numerical examples indicate that the savings of the total cost are realized through ordering cost reduction and backorder price discount.

scholarly journals Inventory Models with Defective Units and Sub-Lot Inspection

Mathematics ◽  
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.

scholarly journals An Integrated Vendor-Buyer Cooperative Inventory Model for Items with Imperfect Quality and Shortage Backordering

2012 ◽  
Vol 2012 ◽  
pp. 1-19 ◽  
Author(s):  
Jia-Tzer Hsu ◽  
Lie-Fern Hsu
Keyword(s):  
Probability Density Function ◽  
Cost Reduction ◽  
Optimal Solution ◽  
Solution Procedure ◽  
Variable Number ◽  
Defective Items ◽  
Numerical Examples ◽  
Imperfect Quality ◽  
Integrated Cost ◽  
Independent Decision

We develop a model to determine an integrated vendor-buyer inventory policy for items with imperfect quality and planned backorders. The production process is imperfect and produces a certain number of defective items with a known probability density function. The vendor delivers the items to the buyer in small lots of equally sized shipments. Upon receipt of the items, the buyer will conduct a 100% inspection. Since each lot contains a variable number of defective items, shortages may occur at the buyer. We assume that shortages are permitted and are completely backordered. The objective is to minimize the total joint annual costs incurred by the vendor and the buyer. The expected total annual integrated cost is derived and a solution procedure is provided to find the optimal solution. Numerical examples show that the integrated model gives an impressive cost reduction in comparison to an independent decision by the buyer.

scholarly journals Technical Note on(Q,r,L)Inventory Model with Defective Items

2010 ◽  
Vol 2010 ◽  
pp. 1-8 ◽  
Author(s):  
Cheng-Tan Tung ◽  
Yu-Wen Wou ◽  
Shih-Wei Lin ◽  
Peter Deng
Keyword(s):  
Analytical Approach ◽  
Optimal Solution ◽  
Technical Note ◽  
Inventory Model ◽  
Reasonable Assumption ◽  
Robust Method ◽  
Inventory Models ◽  
Defective Items ◽  
Stochastic Inventory ◽  
Stochastic Inventory Models

Under a reasonable assumption, we derive an analytical approach that verifies uniqueness of the optimal solution for stochastic inventory models with defective items. Our approach implies a robust method to find the optimal solution.

scholarly journals Integrated inventory model involving quality improvement investment and advance-cash-credit payments

2021 ◽  
Author(s):  
Chih-Te Yang ◽  
Chien-Hsiu Huang ◽  
Liang-Yuh Ouyang
Keyword(s):  
Optimal Solution ◽  
Inventory Model ◽  
Decision Makers ◽  
Optimal Solutions ◽  
Order Quantity ◽  
Defective Items ◽  
Numerical Examples ◽  
Proposed Model ◽  
Production Inventory ◽  
Total Profit

This paper investigates the effects of investment and inspection policies on an integrated production–inventory model involving defective items and upstream advance-cash-credit payment provided by the supplier. In this model, retailers offer customers a downstream credit period. Furthermore, the defective rate of the item can be improved through capital co-investment by the supplier and retailer. The objective of this study was to determine the optimal shipping quantity, order quantity, and investment alternatives for maximizing the supply chain's joint total profit per unit time. An algorithm was developed to obtain the optimal solution for the proposed problem. Several numerical examples are used to demonstrate the proposed model and analyze the effects of parameters changes on the optimal solutions. Finally, management implications for relevant decision makers are obtained from the numerical examples.

scholarly journals An Inventory Model under Trapezoidal Type Demand, Weibull-Distributed Deterioration, and Partial Backlogging

2014 ◽  
Vol 2014 ◽  
pp. 1-10 ◽  
Author(s):  
Lianxia Zhao
Keyword(s):  
Sensitivity Analysis ◽  
Waiting Time ◽  
Optimal Solution ◽  
Inventory Model ◽  
Partial Backlogging ◽  
Inventory Models ◽  
Numerical Examples ◽  
Replenishment Policy ◽  
Demand Rate ◽  
Theoretical Results

This paper studies an inventory model for Weibull-distributed deterioration items with trapezoidal type demand rate, in which shortages are allowed and partially backlogging depends on the waiting time for the next replenishment. The inventory models starting with no shortage is are to be discussed, and an optimal inventory replenishment policy of the model is proposed. Finally, numerical examples are provided to illustrate the theoretical results, and a sensitivity analysis of the major parameters with respect to the optimal solution is also carried out.

Supply Chain Coordination Under Service Level Constraint and Controllable Lead Time

2016 ◽  
Vol 7 (2) ◽  
pp. 84-106 ◽  
Author(s):  
Prashant Jindal ◽  
Anjana Solanki
Keyword(s):  
Supply Chain ◽  
Cost Reduction ◽  
Lead Time ◽  
Cost Allocation ◽  
Optimal Solution ◽  
Service Level ◽  
Decision Variable ◽  
Allocation Model ◽  
Controllable Lead Time ◽  
Ordering Cost Reduction

This paper investigates the coordination issue in a decentralized supply chain having a vendor and a buyer for a defective product. The authors develop two inventory models with controllable lead time under service level constraint. The first one is propose under decentralized mode based on the Stackelberg model, the other one is propose under centralized mode of the integrated supply chain. Ordering cost reduction is also including as a decision variable along with shipping quantity, lead time and number of shipments. Computational findings using the software Matlab 7.0 are provided to find the optimal solution. The results of numerical examples show that centralized mode is better than that of decentralized mode, and to induce both vendor and buyer for coordination, proposed cost allocation model is effective. The authors also numerically investigate the effects of backorder parameter on the optimal solutions. Benefit of ordering cost reduction in both models is also provided.

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