Imperfect Quality Items Research Articles

Replenishment policies for imperfect inventory system under natural idle time and shortages

Most of the offline businesses do not run continuously for the entire day, therefore, the concept of idle time is inevitable. Natural idle time is referred to as the closing time when no demand is being fulfilled by the seller, the unproductive time when labor is not getting utilized but could be. In view of this, this paper investigates replenishment policies for the retailer who runs his business for only a part of a day and closes his shop for the remaining time. The demand gets fulfilled only during the opening time period while no customer is entertained during the closing part of the day. The retailer also faces issues of imperfect quality items in the lot received from his supplier. Thus, he carries out a rigorous inspection process of the entire lot so as to fulfill the demand with perfect quality items only. Under the above-stated circumstances, it is difficult to avoid shortages in the model. Thus, the model assumes fully backlogged shortages and is solved under a profit maximizing framework. The model is exemplified to understand its behavior. Further, to gain some managerial insights and to check the robustness of the model parameters, detailed sensitivity analysis is performed.

An EPQ inventory model considering an imperfect production system with probabilistic demand and collaborative approach

PurposeThe purpose of this paper is to propose an economic production quantity (EPQ) inventory model considering imperfect items and probabilistic demand for a two-echelon supply chain. The production process is imperfect and the imperfect quality items are removed from the lot size. The demand rate of the inventory system is random and follows an exponential probability density function and the demand of the retailers is depending on the initiatives of the sales team.Design/methodology/approachTwo approaches are examined. In the non-collaborative approach, any member of the supply chain can be the leader and takes decisions to optimize the profits, and in the collaborative system, all members make joint decisions about the production, supply, sales and inventory to optimize the profits of the supply chain members. The calculus approach is applied to find the maximum profit related to the members of the supply chain.FindingsA numerical example is presented to illustrate the performance of the EPQ model. The results show that collaborative approach generates greater profits to the supply chain and the market’s demand represents the variable behavior and uncertainty that is generated in the replenishment of a supply chain.Originality/valueThe new and major contributions of this research are: the inventory model considers demand for products is random variable which follows an exponential probability distribution function and it also depends on the initiatives of sales teams, the imperfect production system generates defective items, different cycle time are considered in manufacturer and retailers and collaborative and non-collaborative approaches are also studied.

EFFECTS OF LEARNING ON THE ECONOMIC ORDERING POLICIESFOR DEFECTIVE ITEMS UNDER FUZZY ENVIRONMENT WITH PERMISSIBLE DELAY IN PAYMENTS

The phenomenon of learning canand has been implemented in several distinct disciplines such as environmental protection techniques, manufacturing processes as well as business transactions. As a matter of fact, learning effect is a phenomenon which occurs almost every where and enables the employees to perform new tasks with better performance after fluent repititons over a course of time. The learning effect acts as a considerable function for cost reduction. It consists of perfect and imperfect quality item’s severance from the lot and instantly selling them at different prices. This paper is an adjunct of the commendable work by Jaggi et al.(2013) which considers learning in holding costs and percentage of defective items, follows the learning curve effects underthe fuzzy environment and in addition focuses on proving the concreteness of the fact, that the percentage of defective items together with the holding costs follow the learning effect. In obedience with the economic order quantity (EOQ) model, the ordered lot has 100% perfect items, but this is only suppositional. On contemplation and practical analysis, we have arrived to learn that some lots possess defective items because of process retrogression and other such factors.This research paper refines the economic order quantity model in the context that there are defective items present in each ordered lot confirmed after initial inspection and shortages are allowed under trade credit financingin accordance with the learning effect. The defective items are separated from the considered lot through vigilant inspection and are sold again at a fixed decisive cost price. Conclusively, we de-fuzzify the total profit functions using the triangular method, and for verification of the same, numerical examples and sensitive analysis have been presented in this paper for a clear understanding. KEYWORDS: Inventory, Learning effect,Imperfect items, Shortages, Trade credit financing, Fuzzy system MSC: 90B05

Economic production quantity model with backorders and items with imperfect/perfect quality options

In this paper, an economic production quantity (EPQ) model with backorders considering two options for replenishing of items is proposed; with partially imperfect and perfect quality items. First option assumes a produced shipment contains a fraction of imperfect quality items and supplier does not conduct a full inspection. Therefore, these items are detected by a fully perfect screening process by buyer and are sold as a single batch at a discounted price. While the second one assumes that all items that are produced are fully inspected by supplier and all delivered items are perfect; of course with higher unit production price. Ordering size and backordering level are used as decision variables to derive the closed-form optimal solution. The proposed model is ilustrated and discussed by a numerical example. Finally, a sensitivity analysis is done for identifying the impact of crucial parameters on the optimal solution.

Economic Order Quantity for Imperfect Quality Items Under Inspection Errors, Batch Replacement and Multiple Sales of Returned Items

In classical inventory control problems, it is usually assumed that all of items are of perfect quality, and the inspection process works perfectly well. However, in practice, the order lots often contain imperfect quality items, and the inspection process, for recognition of these items, is not necessarily error-free. In this article, we extend the economic order quantity model under imperfect quality items where the inspection process involves type I and II errors. The type I error can lead to recognition of perfect quality items as defective, while the type II error can lead to delivery of imperfect quality items to customers even for several consecutive times. We present two cases depending on the length of special inspection process and determine optimal order sizes, analytically, for maximizing total profit per unit time for both cases. A numerical example is provided to compare two cases and a sensitivity analysis is discussed to assess the effect of main parameters on the total profit per unit time.

Optimizing profit for pricing and advertisement sensitive demand under unreliable production system

ABSTRACT This article deals with an imperfect economic production quantity (EPQ) model with an unreliable production system where the customers' demand depends on both selling price and advertisement. During the long run production process the machinery system goes into ‘out-of-control’ state after a random time τ and after that the system produces both perfect and imperfect quality items together. The imperfect or defective quality items are reworked to get it back as the perfect ones at a cost just after the regular production run time. The production process of imperfect quality items depends on the reliability of the machinery system where the failure rate may be variable. Here, we consider that the random time variable τ follows the two parameters ‘Weibull distribution’. The objective of this article is to maximize the expected average profit function of the unreliable system with respect to ordering lot size, selling price and frequency of advertisement. We use the incomplete gamma function to formulate the expected average profit function. The model is validated by numerical examples and sensitivity analysis is provided to illustrate the model.

A New Hybrid Method for Optimizing Vendor-Managed Inventory Model

This research proposes an effective procedure that is considered in exact solution methods category for solving a nonlinear model of single-manufacturer multi-retailer with multi-product supply chain which uses vendor-managed inventory (VMI) policy. The objective is to maximize total profit for the vendor while satisfying retailers’ benefit under the various operational constraints. Since most of the time there are defective goods in each delivery, this model investigates the inspection and screening process in which imperfect quality items are rejected and the retailers may encounter the shortage at the end of each cycle. Due to complexity and nonlinearity of the model, in the first step genetic algorithm (GA) is used to generate a suitable solution. Then barrier algorithm with applying the steepest descent method (GA/barrier) is developed to further optimize the solution acquired by GA and to achieve the more efficient solutions concluding the wholesale and retail prices of items, replenishment cycles and backlogging rates as decision variables. At the end, the efficiency of GA/barrier and GA algorithms are compared together in a numerical example. The results show that GA/barrier algorithm is able to provide significantly more efficient solutions comparing to GA.

A cloudy fuzzy economic order quantity model for imperfect-quality items with allowable proportionate discounts

In the traditional economic order quantity/economic production quantity model, most of the items considered are of perfect type. But this situation rarely takes place in practice. Thus, in this paper, an economic order quantity model with imperfect-quality items is developed. 100% screening process is performed, and the items of imperfect quality are sold as a single batch. A proportionate rate of discount for the items of imperfect quality has also been studied. Moreover, a case study has been incorporated to comprehend the model. To nullify the issues of non-random uncertainties of demand rate in business scenario, cloudy fuzzy method has been utilized here. Numerical study reveals that cloud model along with its new defuzzification methods can give maximum profit of the model all the time instead of deterministic ones. Finally, sensitivity analysis and graphical illustrations are made to justify the novelty of the model.

Effects of product reliability dependent demand in an EPQ model considering partially imperfect production

In this article, an economic production quantity (EPQ) model with partially imperfect production system has been considered where both perfect and imperfect quality items are produced and demand of the product has been assumed as a function of selling price, reliability of the product and advertisement. Perfect quality items are ready for sale but imperfect quality items are reworked at a cost to become perfect one. Reworking cost, reliability of the product and reliability parameter of the manufacturing system can be improved by introducing the time dependent development cost and also by improving the quality of the raw material used in the production system. Under such circumstances, a profit function has been developed and maximised by optimising the reliability parameter of the manufacturing system, reliability of the product and duration of production. Finally, the model has been illustrated with some numerical examples.

Effects of learning on retailer ordering policy for imperfect quality items with trade credit financing

Effects of learning on retailer ordering policy for imperfect quality items with trade credit financing

A sustainable economic production model: effects of quality and emissions tax from transportation

Faced with pressure from the public, governments, and environmental agencies, it is becoming essential for manufacturing firms to identify and implement sustainable operations aiming at reducing the negative social and environmental impacts while enhancing the firm’s public image and increasing its economic performance. This paper investigates a production model that incorporates the quality of different types of components/raw material parts used in the production process along with their transportation emissions tax. It is assumed that the various types of components contain both perfect and imperfect quality items. The percentage of perfect quality components of a particular type is a random variable having a known probability distribution. Based on results regarding the probability distribution and the expected value of the minimum of a set of random variables, a mathematical model is developed and the total production/inventory cost is obtained. A closed form formula approximating the optimal solution is derived in terms of the expected value of the minimum of a set of random variables related to the percentages of perfect quality components. The case in which the percentages of perfect quality components are uniformly distributed is investigated and a numerical example is given to illustrate this case. The accuracy of the approximated solution is assessed via a simulation algorithm that can also be used to approximate the optimal lot size in the case when the percentages of perfect quality components are not all uniformly distributed.

Vendor-buyer integrated production-inventory system for imperfect quality item under trade credit finance and variable setup cost

This paper model a vendor-buyer integrated production-inventory system by considering issues of imperfect quality of the item, trade credit finance, setup cost reduction and shortages including partial backlogging and lost sale. The vendor produces a lot in one production setup and sends to the buyer in multiple shipments to fulfill customers’ demand. Due to imperfect production and/or unsafe transportation, the received lot of the buyer contains the imperfect quality of the item, which is detected through the screening process, and is sold at a discounted price in a single batch at the end of the process. To accelerate bulk purchasing, the vendor offers a trade credit period to the buyer to settle the amount. In this regard, we develop a methodology to account the opportunity cost and opportunity gain. Depending upon the screening period μ, trade credit period M, shortage beginning time t and the buyer’s scheduling period T, we consider four cases: (1) M < μ < t < T, (2) μ < M < t < T, (3) μ < t < M < T and (4) μ < t < T < M. The proposed integrated model is testified with numerical experiment and sensitivity analysis by changing the value of key parameters.

A Multi-Objective Optimization of Energy, Economic, and Carbon Emission in a Production Model under Sustainable Supply Chain Management

Nowadays, many industries are focusing on automation in manufacturing for high production and good quality to meet the needs of customers in a short period of time. This trend has produced a forward shift in technology in the form of advancement, which ultimately increases energy demand. For that reason, researchers have started working on sustainable development associated with cleaner-energy policies to avoid increasing energy consumption for enhanced manufacturing technology in developed countries. The other important issue affecting our world is global warming, which is the result of greenhouse gas emissions. That is the reason, renewable energies like solar energy have dramatically increased during recent years to compensate for the energy demand and reduced carbon footprint for cleaner production. This paper considers a supply chain management of automobile part manufacturing industry with suppliers to optimize the production quantity with multiple objectives i.e., minimizing the total cost of production including minimum quantity lubrication is a first objective, reduction of the carbon footprint is the second, and minimizing the cost of energy considering renewable energy is the last objective. This study considers a situation, where imperfect quality items are managed and controlled by the suppliers as outsourcing operations. A weighted goal programming methodology is utilized to solve the proposed mathematical model including sustainable suppliers. Sensitivity analysis of the model is performed for different scenarios with respect to the energy utilization. The optimal result of minimum production cost and carbon emissions is the evidence of successful pragmatic application in automobile industry. The results validate the model to provide the basis for sustainability in supply chain environment considering manufacturer and suppliers.

Interval valued EOQ model with two types of defective items

In the classical inventory model, the issue of quality of the product is not considered. It is assumed that all the items procured are of perfect quality. However, in real life production environment it is observed that some of the items produced are defective. Here, we have considered an Economic Order Quantity (EOQ) model with imperfect quality items where the incoming lot has fractions of scrap and re-workable items. These fractions are considered to be known with a certain given percentage. The demand from customers end is met with the perfect and re-worked items and the scrap items are sold differently at a salvage cost in a secondary market. Also to represent the real life situations, the inventory parameters have been taken as interval numbers. The corresponding mathematical problem has been formulated as an un-constrained optimization problem and has been solved using Particle Swarm Optimization (PSO) technique. Finally, the model has been illustrated with a numerical example.

Impact of Reparation for Imperfect Quality Items having Shortages in the System under Multi-Trade-Credit-Period

Impact of Reparation for Imperfect Quality Items having Shortages in the System under Multi-Trade-Credit-Period

Modelling a type-2 fuzzy inventory system considering items with imperfect quality and shortage backlogging

In this paper, an inventory model considering items with imperfect quality is developed in fuzzy environment, wherein shortages are allowed and are backlogged. In order to detect the items with imperfect quality, all items are screened before they are sent for consumption, and all imperfect quality items are sold at discounted price, called salvage value. In view of the fact that demand may not be predicted precisely, because it depends upon many uncertain and perturbing market activities, it is assumed to be a type-2 fuzzy variable. Quantity of imperfect quality items in the received lot may not be predicted precisely; hence percentage of imperfect quality items is also considered as a type-2 fuzzy variable. In this regard, this study developed a de-fuzzification method of type-2 fuzzy variable pertaining to interval approximation. The mathematical model is analysed to find closed form formulae of order quantity and backlogging quantity. Finally, the proposed methodology and model are testified on numerical examples, and sensitivity of decision variables is examined and discussed to underline the managerial insights as well as to establish the robustness of the mathematical model.

Multi-item sustainable green production system under trade-credit and partial backordering

This study develops a green production quantity model with random imperfect quality items, trade-credit policy, service level constraints, and failure in reworking. In practice, not only the green production system but also the rework process is often imperfect. The presence of a single machine in the production system outcomes in limits for green production and partial backordering. It is assumed that the green production system may generate defective items, which are reworked. As a reworked process is also not perfect, it produces a random number of scrapped items. On the other hand, the supplier also offers a trade-credit policy to the buyer, which minimizes the on-hand stock and boosts sales. In fact, this model will help organizations to minimize their costs through cooperation in industry. The objective of this research is to find the optimal green production and backordered quantity of each item such that the projected total cost is minimized. The optimal solution for each scenario is derived and the application of the designed model is validated with two numerical examples. The results for both examples show that the minimum total cost for the green production system is achieved when the permissible delay-period given by the supplier to the buyer is greater than or equal to the aggregated sum of production uptime, reworking time, production downtime, and allowed shortage time. Sensitivity analysis of the proposed study is also done to illustrate the realistic usage.

Supply chain models with imperfect quality items when end demand is sensitive to price and marketing expenditure

This paper studies supply chain model for imperfect quality items under which unit price and unit marketing expenditure imposed by the buyer, regulates the demand of the item. It is presumed that with the accustomed supply chain model, all produced items are of good quality, coincidentally, it engrosses some percentage of defective items. Thus, inspection process becomes essential for the buyer to segregate the defective items, which are then sold at discounted price at the end of the screening process. In this paper, a supply chain model is ensued to substantiate the interaction and democracy of the participants in the supply chain, the buyer and seller, is pitched by non-cooperative and cooperative game theoretical approaches. In the non-cooperative method, the Stackelberg game approach is used in which one player behaves as a leader and another one as a follower. The co-operative game approach is based on a Pareto efficient solution concept, in which both the players work together to enhance their profit. Lastly, to demonstrate the significance of the theory of the paper, numerical examples including sensitivity analysis are presented.

Two-echelon Supply Chain Considering Multiple Retailers with Price and Promotional Effort Sensitive Non-linear Demand

This study deals with the effects of a supply chain (SC) with single product, multiple retailers and a manufacturer, where the manufacturer(he) produces lotsize of the product that contains a random portion of imperfect quality item. The imperfect quality products are sold in a secondary shop. The new contribution of this paper is a new non-linear demand function. Demand of the end customers varies with pricing and promotional effort of the rivalry amongst the retailers which can be used for the electronic goods, new lunched products, etc. We investigate the behavior of the supply chain under Manufacturer-Stackelberg(MS), and Retailer-Stackelberg(RS) model structures. The nature of the mentioned models provides great insights to a firm’s manager for achieving optimal strategy in a competitive marketing system. Within the framework of any bilevel decision problem, a leader's decision is influenced by the reaction of his followers. In MS model structure, following the method of replacing the lower level problem with its Kuhn-Tucker optimality condition, we transform the nonlinear bilevel programming problem into a nonlinear programming problem with the complementary slackness constraint condition. The objective of this paper is to determine the optimal selling price and promotional effort of each retailer, while the optimal wholesale price of the perfect quality products are determined by the manufacturer so that the above strategies are maximized. Finally, numerical examples with sensitivity analysis of the key parameters are illustrated to investigate the proposed model.

An Production Inventory Model with Imperfect Production and Risk

A single item production system has been considered in this proposed work. It is also assumed that the system produced some imperfect items. For this purpose a screening process has been considered here to separate the perfect quality items and imperfect quality items. The perfect quality items have a demand in the market which is depended on the advertisement of the product as well as the selling price of the product. The imperfect quality items are sold in a lot after the production period. As the depreciation rate of the product increases and number of imperfect product increases then there will be a risk in the system of loss in profit. So a risk function has been considered here depending on the depreciation rate of the demand and imperfect production rate of the item. Keeping these phenomenon the proposed model has been maximize for profit and minimize for the risk with numerical illustration.