Non-defective Items Research Articles

A Novel Model for Economic Recycle Quantity with Two-Level Piecewise Constant Demand and Shortages

This paper focuses on the production systems that may produce a proportion of recyclable defective products. The developed model is called an Economic Recycle Quantity (ERQ) model with the assumption of a full recovery of defective items. The defective parts are collected during the production-off time and can be used during the next production cycle of the same category. The demand rate of the non-defective items is a two-level piecewise factor—one during the production-run time and another during the production-off time. The developed model aims to optimize the total inventory cost, the order quantity, and the amount of recyclable defective items that represent the ERQ. The mathematical formulations of the model are deduced theoretically. The model was solved analytically, and the optimal results are illustrated. Sensitivity analysis is carried out to investigate the effect of varying system parameters and validate the proposed model. Results of the sensitivity analysis show that the consideration of defective part recycling reduces the total inventory cost where the raw material is reduced. The cost reduction is about 1%; of course, the environmental impact is more appreciated. Furthermore, the managerial implications are described, and the future perspectives are discussed.

A Study on Two-Warehouse Inventory Systems with Integrated Multi-Purpose Production Unit and Partitioned Rental Warehouse

A study of two warehouse inventory systems with a production unit is developed in this article with some constraints which are of practical applicability to optimize the total production cycle and its cost. A production unit evolves in three different states to retain its quality and prolong its lifetime: the state of producing items, the state of reworking the identified defective items, and the state of being idle. It processes the items up to a certain time point. The screening process starts immediately after a product comes out of the production unit. The classified non-defective items are first stored in own warehouse (OW), after filling to its maximum capacity, and the remaining items fill in the first block RW1 of the rental warehouse RW. All identified defective items are stored in the second block RW2 of RW. The holding cost of an item is higher in RW than OW. All defective items are sent to the production unit for re-do processes as a single lot immediately after the stop of the production and re-do items are stored in RW1 to satisfy the demand. The items in the RW1 are of higher priority in satisfying the demands after the stop of the production unit in producing new items as to deduce the total cost. Demand is assumed as both time and advertisement dependent and is encouraged once production starts. The deterioration rate differs in both warehouses. No backlog is entertained. The study is directed to achieve optimum total cycle cost towards the attainment of the optimum production time slot and the entire cycle of the system. We have arrived at explicit expressions for the total cost function of the entire production cycle. An analytic optimization process of the discriminant method is employed in the form of an algorithm to arrive at the optimum total cost. It provides a numerical illustration of a specific environment. The implications of the current research work are as follows. The optimum utility of production units in three different states in arriving at the optimum total cost is extensively studied with respect to deterioration, demand, and production rates. It also examined the influence of fluctuating deterioration, demand, and production parameters in arriving at optimum deterioration cost, holding cost, and total cycle cost, as they have important managerial insights. The effect of rental charges on the optimum total cost is examined as the system is used for multi-purpose storage.

A Supply Chain Model with Learning Effect and Credit Financing Policy for Imperfect Quality Items under Fuzzy Environment

In this paper, the seller offers a credit period to his buyer for more sales and the buyer accepts the seller’s policy to gain more profit, and it is assumed that the seller has defective and non-defective items. When the seller provides lots for sale to his buyer then, the buyer separates the whole lots with the help of inspection process into defective and perfect quality items. Further, in this scenario, the percentage of defective items present in the lot follows the S-shape learning curve and it is also considered that the demand rate is imprecise in nature. Here, the demand rate assumes a triangular fuzzy number due to the imprecise nature and it is the model assumption. Based on this assumption, we developed an inventory model with the effect of learning and trade credit strategy under a fuzzy environment for the buyer. The buyer’s total profit has been optimized concerning the order quantity in the fuzzy environment where order quantity has been assumed as a decision variable. The results of this model were verified with the help of numerical examples and sensitivity analysis. We compared the buyer’s total profit in a crisp and fuzzy environment and the buyer gained more profit in a fuzzy environment compared to the crisp environment. Moreover, we compared the results with and without the effect of learning and trade credit on the buyer’s ordering policy and obtained a positive effect on the ordering policy in the numerical section. We determined positive results from the sensitivity analysis, which proved that the trade credit policy will be beneficial for both partners of the supply chain.

Impact of Credit Financing on the Ordering Policy for Imperfect Quality Items With Learning and Shortages

The paper develops an order quantity model with trade credit plus shortages under learning effects for deteriorating imperfect quality products. Generally, when the lot has imperfect items, the inspection of a lot is necessary to improve the quality of the lot. In this article, the seller provides a defective lot to his buyer under credit financing scheme, and after that buyer separates the whole lot under the screening process into two categories, one is defective and the other is non-defective items. The buyer sells out defective items at a low price as compared to non-defective items. It is assumed that customers' demand of good quality items is greater than the inspection rate for the whole lot to neglect the shortages situation. After keeping all points together, the buyer optimized his total profit concerning order quantity and shortage. A suitable numerical example and a sensitivity analysis have been provided for the validity of this model. The aim and utility of this paper have been presented in the conclusion section.

Ordering Policy Estimation for High Utility Item-Sets Considering Negative Item Values in Large Databases

Utility mining with negative item values has recently received interest in the data mining field due to its practical considerations. Previously, the values of utility item-sets have been taken into consideration as positive. However, in real-world applications an item-set may be related to negative item values. This paper presents a method for redesigning the ordering policy by including high utility item-sets with negative items. Initially, utility mining algorithm is used to find high utility item-sets. Then, ordering policy is estimated for high utility items considering defective and non-defective items. A numerical example is illustrated to validate the results

A Sustainable Economic Recycle Quantity Model for Imperfect Production System with Shortages

Recycling of products has a great impact on contemporary sustainable business strategies. In this study, a sustainable recycling process in a production-inventory model for an imperfect production system with a fixed ratio of recyclable defective products is introduced. The piecewise constant demand rates of the non-defective items are considered under production run-time, production off-time with positive stock, and production off-time with shortages under varying conditions. Based on the production process, two cases are studied using this model. The first case does not consider recycling processes, while the second case picks up all defective items before sending these items to recycling during the production off-time; the recycled items are added to the main inventory. The aim of this study is to minimize the total cost and identify the optimal order quantity. The manufacturing process with the recycling process provides a better result compared to without recycling in the first case. Some theoretical derivations are developed to enunciate the objective function using the classical optimization technique. To validate the proposed study, sensitivity analysis is performed, and numerical examples are given. Finally, some managerial insights and the scope of future research are provided.

Two-echelon imperfect production supply chain with probabilistic deterioration rework and reliability under fuzziness

This paper develops an integrated fuzzy two-layer supply chain for manufacturers and retailers with defective and non-defective types of products. The manufacturer produces up to a specific time, including both faulty and non-defective items, and post-screening only the non-defective item sends to the retailer. The strategy of the retailer is to do the screening of items received from the manufacturer. Subsequently, the perfect quality items use to fulfill the demand of the customer, and the defective items are reworked. The retailer considers that customer demand is time and reliability dependent. The proposed supply chain considers probabilistic deterioration for the manufacturer and retailers. The optimum solution of the given model is evaluated for both the cases of crisp and fuzzy environments on the strategies such as production rate, unit production cost, idle time, screening, rework, etc. Managerial insights and the effect of parameters on the optimal inventory under fuzziness are presented.

Two-echelon imperfect production fuzzy supply chain model for reliability dependent demand with probabilistic deterioration and rework

This paper develops a fuzzy two-layer supply chain for manufacturer and retailer with defective and non-defective types of products. The manufacturer produces up to a specific time, including faulty and non-defective items, and after the screening, the non-defective item sends to the retailer. The retailer’s strategy is to do the screening of items received from the manufacturer; subsequently, the perfect quality items are used to fulfill the customer’s demand, and the defective items are reworked. The retailer considers that customer demand is time and reliability dependent. The supply chain considers probabilistic deterioration for the manufacturer and retailers along with the strategies such as production rate, unit production cost, cost of idle time of manufacturer, screening, rework, etc. The optimum average profit of the integrated model is evaluated for both the cases crisp and fuzzy environments. Managerial insights and the effect of changes in the parameters’ values on the optimal inventory policy under fuzziness are presented.

Imperfect and variable production cost in three-layer supply chain system incorporating deterioration and screening effect

This paper develops a three-layer supply chain for defective and non-defective types of produced items by supplier and manufacturer. The condition of the chain that without any financial liability on the manufacturer, defective items will be sent back to the supplier after screening. In the subsequent stage, the retailer accepts the non-defective items produced by the manufacturer after the screening and sends back the defective items to the manufacturer. Hence the retailer receives the perfect quality items for selling to the customers, but the retailer considers the effect of the deterioration of items. This model also considers the impact of several business strategies such as; optimal order size of raw materials, production rate, unit production cost, idle time costs of the supplier, and manufacturer in a collaborative marketing system, etc. to determine the optimum average profit of the integrated model. This study discusses the selling price of the retailer, demand rate of the customer, purchase cost of supplier and holding cost, which can be a significant breakthrough in expanding the profit of the business in real terms. Numerical example and sensitivity analysis are presented to illustrate the phenomenon of theoretical study and demonstrate the managerial implication of the model.

The effect of human errors on an integrated stochastic supply chain model with setup cost reduction and backorder price discount

This study develops an integrated vendor–buyer inventory model for a supply chain where quality issues and human error affect its coordination. Each lot shipped to the buyer contains defective items, with a rate which randomly changes from a lot to the other. The buyer inspects every shipped lot to segregate defective items. However, the inspection process at the buyer’s end goes wrong in the classification of defective and non-defective items. On the other hand, the buyer may run out of inventory, but in order to avoid lost sales, he/she offers a price discount on the backlogged items to his/her customers. Due to the vendor-buyer relationship, the buyer invests in reducing the setup cost of the vendor. Supply chain’s lead-time is considered variable, and two models are developed based on the probability distribution of the lead-time demand. In the first model, it is assumed that lead-time demand follows a normal distribution, while in the latter one, it does not follow any certain distribution. Two models are developed to determine the joint optimal decision variables that minimize the total cost of the supply chain. Two iterative algorithms are developed to obtain the optimal solution for both models. A set of numerical analysis and sensitivity analysis are conducted to gain insights.

A game theoretic approach for pricing under a return policy and a money back guarantee in a closed loop supply chain

Closed Loop Supply Chain (CLSC) has attracted the attention of many researchers in recent years. This paper introduces for the first time a CLSC consisting of one manufacturer and two retailers in which sold items can be returned from customers in the two categories of non-defective and defective items. The first retailer exercises a Money Back Guarantee (MBG) policy for defective items with a full refund. He also offers an MBG with a partial refund for non-defective items. The manufacturer collects the defective items returned to remanufacture and sell them to a second retailer. The first retailer sells non-defective items returned as open box items at a discount in a second market while the second retailer sells remanufactured items in a third market. Two scenarios are also considered: one in which the manufacturer pays to the first retailer the wholesale price for defective items, and the other in which the manufacturer pays the first retailer's price in order to motivate him to offer exercise the MBG policy for defective items. A numerical Example is finally introduced and the relevant parametric analysis is carried out while managerial insights are extracted from the solution. Results show that the first scenario is more beneficial to all the parties in the supply chain because it not only increases both the manufacturer's and the retailers' profits but also reduces the retailers' prices.

Imperfect inspection with directional information: A general failure probability model

Suppose that the entire sequence of items produced is divided into a stream of nondefective items, followed by a stream of defective items. We propose a sequential inspection procedure for the production process that has a general failure probability–increasing, constant, or decreasing failure patterns. We also consider the inspector’s classification errors as well as the costs of inspection and misclassifications. In numerical analysis, we show that other inspection models are special cases of our general model and analyze the effects of failure patterns on the inspection cost for various combinations of the type I and II errors.

An economic design of rectifying single sampling plans via maxima nomination sampling in the presence of inspection errors

Economic design for acceptance sampling plans (ASP) has attracted the attention of many researchers. In this article, rectifying single ASP is checked by using the maxima nomination sampling method and the plan’s parameters are obtained while sum of consumer and producer loss is minimized. In the presence of inspection errors, the lots are rectified in two ways: the detected defective items are discarded or replaced with non-defective items. To illustrate the advantages of the economic design of MNS, it is compared with SRS plan by using a real world example.

Single-vendor multi-buyer integrated inventory system for multi-item

In this paper, a single-vendor multi-buyer supply chain system is considered in which several products. The demand of this supply chain for each product is a stochastic variable and it is assumed to follow a normal distribution. The lead time of receiving products from vendor to buyer is a variable which controllable by the adding extra cost. During the consumption period, the shortages are allowed and they are completely backlogged in the next replenishment. The production process is assumed to be imperfect, i.e., all the finished products need not consumable, so the buyer implements a screening process to separate the defective and non-defective items and the vendor pay warranty cost for each defective item to the buyer. We investigated the economic order quantity (EOQ), lead time and number of shipments such that total cost of the supply chain have been minimised. At last numerical illustration and sensitivity analysis are given.

Improving the Construction Industry Quality Using the Seven Basic Quality Control Tools

The organizations used quality tools to develop their processes and gain satisfaction from the customers. The main objective of this study is to develop levels of quality in the construction industry through the use of the seven basic quality control tools. Such tools are extremely crucial tools which are used worldwide in the industries for continual improvement. The seven basic quality tools are Check Sheet, Histogram, Pareto Chart, Fishbone Diagram, Control Chart, Flowchart and Scatter Diagram. They were implemented in various steps of the process in order to define the problems, measure its impacts, find out its root causes and solve these problems to ensure the production of non-defective items. The study shows how the seven basic tools of quality are very useful and effective in identifying and removal of defects from the manufacturing process. These tools are helpful in every stage of the defect removal process. This study was conducted on Cleopatra Group Company. This company succeeded to serve the public and private projects in the Egyptian construction sectors.

On Finding a Subset of Non-Defective Items from a Large Population

In this paper, we derive mutual information based upper bounds on the number of nonadaptive group tests required to identify a given number of “non-defective” items from a large population containing a small number of “defective” items. In the asymptotic regime with the population size $N \rightarrow \infty$ , to identify $L$ nondefective items out of a population containing $K$ defective items, our results show that $\frac{C_s K}{1-o(1)} (\Phi (\alpha _0, \beta _0) + o(1))$ measurements are sufficient when the tests are reliable. Here, $C_s$ is a constant independent of $N, K$ , and $L$ , and $\Phi (\alpha _0, \beta _0)$ is a bounded function of $\alpha _0 \triangleq \lim _{N\rightarrow \infty } \frac{L}{N-K}$ and $\beta _0 \triangleq \lim _{N\rightarrow \infty } \frac{K}{N-K}$ . In contrast, the necessary number of tests using the conventional approach of first identifying the $K$ defective items and picking the required number of nondefective items from the complement set grows with $N$ as $O\left(K \log N \right)$ . We also derive upper bounds on the number of tests under both dilution and additive noise models. Our results are obtained under a very general sparse signal model, by virtue of which, they are also applicable to other important sparse signal based applications such as compressive sensing.

Reliability Assessment and Study of Quality Control Tools on Intermixer and Dump Mill of a Tyre Manufacturing Industry

Quality plays a very important role in today's highly competitive industrial environment. Quality leads to an improvement in the productivity. Quality control tools are used to solve more than 90% of the problems faced by the organizations in improving its effectiveness and meeting the customer expectation on a continuous basis. The success of the quality control procedure depends greatly on the method of data collection and its accuracy. Quality control tools are used worldwide in manufacturing industries for continual improvement and are implemented in different steps of manufacturing process to define the problem, measure its impact, finding out its root cause and its removal to ensure the production of non-defective items. The present work includes collection of failure data of intermix and dump mill of a tyre manufacturing unit located in Karnataka. The failure data collected for one year has been analysed to find out the major causes of breakdown. Quality control tools such as Pareto chart, Bar chart, Histogram, Fish bone diagram have been used to find out the root causes and identifying the action plans to eradicate them. Reliability assessment (theoretical) of intermix and dump mill has been conducted using the failure data. The reliability and maintainability curves speak about the present state of working of maintenance department in regard to addressing of breakdown problems and also help in setting future working standards.

Reliability Assessment and Study of Quality Control Tools on Intermixer and Dump Mill of a Tyre Manufacturing Industry

Quality plays a very important role in today's highly competitive industrial environment. Quality leads to an improvement in the productivity. Quality control tools are used to solve more than 90% of the problems faced by the organizations in improving its effectiveness and meeting the customer expectation on a continuous basis. The success of the quality control procedure depends greatly on the method of data collection and its accuracy. Quality control tools are used worldwide in manufacturing industries for continual improvement and are implemented in different steps of manufacturing process to define the problem, measure its impact, finding out its root cause and its removal to ensure the production of non-defective items. The present work includes collection of failure data of intermix and dump mill of a tyre manufacturing unit located in Karnataka. The failure data collected for one year has been analysed to find out the major causes of breakdown. Quality control tools such as Pareto chart, Bar chart, Histogram, Fish bone diagram have been used to find out the root causes and identifying the action plans to eradicate them. Reliability assessment (theoretical) of intermix and dump mill has been conducted using the failure data. The reliability and maintainability curves speak about the present state of working of maintenance department in regard to addressing of breakdown problems and also help in setting future working standards.

Computationally Tractable Algorithms for Finding a Subset of Non-Defective Items From a Large Population

In the classical non-adaptive group testing setup, pools of items are tested together, and the main goal of a recovery algorithm is to identify the complete defective set given the outcomes of different group tests. In contrast, the main goal of a non-defective subset recovery algorithm is to identify a subset of non-defective items given the test outcomes. In this paper, we present a suite of computationally efficient and analytically tractable non-defective subset recovery algorithms. By analyzing the probability of error of the algorithms, we obtain bounds on the number of tests required for non-defective subset recovery with arbitrarily small probability of error. Our analysis accounts for the impact of both the additive noise (false positives) and dilution noise (false negatives). By comparing with information theoretic lower bounds, we show that the upper bounds on the number of tests are orderwise tight up to a $\log ^{2}K$ factor, where $K$ is the number of defective items. We also provide simulation results that compare the relative performance of the different algorithms and reveal insights into their practical utility. The proposed algorithms significantly outperform the straightforward approaches of testing items one-by-one, and of first identifying the defective set and then choosing the non-defective items from the complement set, in terms of the number of measurements required to ensure a given success rate.

Price-sensitive imperfect production inventory model with exponential partial backlogging

ABSTRACTIn this paper, we present an imperfect economic production inventory model considering partially backlogged situations at the beginning of the cycle. Here, all defective/imperfect quality items are reworked after the regular production process and the reworked items are considered as similar as good quality products. During production process demand is met by non-defective items only. Rework is inevitable in those industries where end product is expensive and raw materials are inadequate. The ratio of defective item production rate and production rate is taken to be a random variable. In this model, demand is taken as price sensitive and it is a monotonic decreasing function of selling price. Our objective is to optimise the expected average profit for the model of the decision variables: selling price, order quantity and backorder level. The sensitivity of the key parameters is examined to test the feasibility of the model. Finally, a numerical example is provided to investigate the proposed model.