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 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 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 stock - and price-dependent demand for deteriotating items based on limited space

2022 ◽  
Vol 12 (1) ◽  
pp. 0-0
Keyword(s):  
Optimal Solution ◽  
Selling Price ◽  
Order Quantity ◽  
Inventory Models ◽  
Stock Level ◽  
Numerical Examples ◽  
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 Retailer’s optimal ordering policies for EOQ model with imperfective items under a temporary discount

2016 ◽  
Vol 26 (2) ◽  
pp. 219-240
Author(s):  
Wen Lin ◽  
Horng Chang
Keyword(s):  
Economic Order Quantity ◽  
Order Quantity ◽  
Objective Functions ◽  
Inventory Models ◽  
Screening Process ◽  
Numerical Examples ◽  
Closed Form Solutions ◽  
Eoq Model ◽  
Optimal Ordering ◽  
Special Order

In this article, we study inventory models to determine the optimal special order and maximum saving cost of imperfective items when the supplier offers a temporary discount. The received items are not all perfect and the defectives can be screened out by the end of 100% screening process. Three models are considered according to the special order occurs at regular replenishment time, non-regular replenishment time, and screening time of economic order quantity cycle. Each model has two sub-cases to be discussed. In temporary discount problems, in general, there are integer operators in objective functions. We suggest theorems to find the closed-form solutions to these kinds of problems. Furthermore, numerical examples and sensitivity analysis are given to illustrate the results of the proposed properties and theorems.

scholarly journals Imperfect production supply chain model considering price-sensitive demand and quantity discounts under free distribution approach

2020 ◽  
Author(s):  
Hemapriya S ◽  
uthayakumar R
Keyword(s):  
Lead Time ◽  
Optimal Solution ◽  
Chain Model ◽  
Quantity Discounts ◽  
Order Quantity ◽  
Defective Items ◽  
Free Distribution ◽  
Supply Chain Model ◽  
Precautionary Measures ◽  
The Impact

During production process, we may experience with some imperfect things disregarding every single precautionary measures. The imperfect things are each of two dismissed promptly at the season of production or reworked and sold as great ones or customers are given plenty discount to keep up the generosity of the organization. This article considers about this practical circumstances and includes price-sensitive demand. As production propels, we have defective items as a part of result. The customer’s demand is pretended to be price-sensitive dependent to increment the quantity of offers, and the vendor offers a quantity discount to persuade the buyer to purchase more amounts. Here, the lead time demand follows a free distribution. Therefore, the integrated model is used to find the optimizing values for the total number of shipments, order quantity, safety factor and retail price. An efficient iterative algorithm is designed to obtain the optimal solution of the model numerically and sensitivity analysis table formulate to show the impact of different parameter.

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.

On Optimal Inventory Model for Obsolescence Perishable Products under Unpermitted-Stockout

2011 ◽  
Vol 201-203 ◽  
pp. 1292-1295
Author(s):  
Xiao Liang Xie
Keyword(s):  
Optimal Solution ◽  
Inventory Model ◽  
Economic Order Quantity ◽  
Inventory Level ◽  
Order Quantity ◽  
Short Life ◽  
Numerical Examples ◽  
Fast Change ◽  
Demand Rate ◽  
Long Life

With the advancement of science and technology and the fast change of buyer requirements, the short-life products have been shortened at large, some formerly long-life products gradually turn to value deterioration products. The ratio of value deterioration products to modern products is getting higher and higher. This paper develops a deterministic economic order quantity EOQ inventory model, where the demand rate depends on the on-hand inventory when inventory level exceeds certain quantity , otherwise the demand rate is constant. The effects of obsolescence are taken into account, for it is related to the demand rate. The results are discussed through two numerical examples. A sensitivity analysis of the optimal solution with respect to parameters of the system is carried out.

Reliability Analysis of Truss Structures by Using Matrix Method

1980 ◽  
Vol 102 (4) ◽  
pp. 749-756 ◽  
Author(s):  
Y. Murotsu ◽  
H. Okada ◽  
K. Niwa ◽  
S. Miwa
Keyword(s):  
Lower Bound ◽  
Failure Probability ◽  
Matrix Method ◽  
Failure Criteria ◽  
Upper Bounds ◽  
Truss Structures ◽  
Lower And Upper Bounds ◽  
Numerical Examples ◽  
Modes Of Failure ◽  
Complete Failure

This paper proposes a method of systematically generating the failure criteria of truss structures by using Matrix Method. The resulting criterion for a statically determinate truss is simple and its failure probability is easily evaluated. In case of a statically indeterminate truss, however, there are many possible modes or paths to complete failure of the structure and it is impossible in practice to generate all of them. Hence, the failure probability is estimated by evaluating its lower and upper bounds. The lower bound is evaluated by selecting the dominant modes of failure and calculating their probabilities. The upper bound is evaluated by assuming that the redundant truss behaves itself like a statically determinate truss, i.e., the structure fails if any one member is subject to failure. Numerical examples are provided to demonstrate the applicability of the propsed methods.

scholarly journals Novel Solution Method for Inventory Models with Stochastic Demand and Defective Units

2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Xu-Ren Luo ◽  
Chun-Hsiao Chu ◽  
Henry C. J. Chao
Keyword(s):  
Solution Method ◽  
Optimal Solution ◽  
Convergent Sequence ◽  
Threshold Value ◽  
The Other ◽  
Inventory Models ◽  
Previous Approach ◽  
Numerical Examples ◽  
Distinct Features ◽  
Ordering Quantity

This paper is a response to two papers. We improve the lengthy proof for the first paper by an elegant verification. For the second paper, we point out the three-sequence approach will result in different convergent rates such that when the other two sequences are converged, the ordering quantity sequence may still not converge to the optimal solution. We construct a novel iterative method to simplify the previous approach proposed by the three-sequence approach for the optimal solution. By the same numerical examples of three published papers, we demonstrate that we can control our findings to converge more accurately than previous results. Moreover, we show that there are three distinct features of our proposed approach. (i) It converges to the desired solution within the preassigned threshold value. (ii) We estimate the convergent ratio. (iii) We find the dominant factors for our proposed convergent sequence.

EOQ Model with Stock-Level Dependent Demand and Different Holding Cost Functions

2017 ◽  
Vol 8 (4) ◽  
pp. 59-75 ◽  
Author(s):  
H.S. Shukla ◽  
R.P. Tripathi ◽  
Neha Sang
Keyword(s):  
Order Approximation ◽  
Optimal Solution ◽  
Optimal Order ◽  
Order Quantity ◽  
Inventory Cost ◽  
Stock Level ◽  
Numerical Examples ◽  
Eoq Model ◽  
Holding Cost ◽  
Dependent Demand

This paper presents EOQ (Economic Order Quantity) model with stock- level dependent demand and different types of holding cost function. We show that the total relevant inventory cost per unit time is convex with respect to cycle time. Mathematical models are established to determine optimal order quantity and total relevant inventory cost. Numerical examples are provided for two different models i.e. (i): Instantaneous replenishment with inventory dependent holding cost and (ii) Instantaneous replenishment with quadratic time dependent carrying cost. Numerical examples are provided to illustrate the proposed model. Sensitivity analysis of the optimal solution with respect to the parameters of the system is carried out. The second order approximation is used for finding closed form optimal solution. Mathematica 5.2 software is used to find numerical results.

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