Optimal batch quantity models for a lean production system with rework and scrap

In an imperfect manufacturing process, the defective items are produced with finished goods. Rework process is necessary to convert those defectives into finished goods. As the system is not perfect, some scrap is produced during this process of rework. In this research, inventory models for a single-stage production process are developed where defective items are produced and reworked, where scrap is produced, detected and discarded during the rework. Two policies of rework processes are considered (a) First policy: rework is done within the cycle, and (b) Second policy: rework is done after N cycles of normal production. Also, three types of scrap production and detection methods are considered for each policy, such as (i) scrap is detected before rework, (ii) scrap is detected during rework and (iii) scrap is detected after rework. Based on these inventory situations, the total cost functions for a single-stage imperfect manufacturing system are developed to find the optimum operational policy. Some numerical examples are provided to validate the model and a sensitivity analysis is carried out with respect to different parameters used to develop the model

Determining replenishment lot size and shipment policy for an extended EPQ model with delivery and quality assurance issues

AbstractThis paper derives the optimal replenishment lot size and shipment policy for an Economic Production Quantity (EPQ) model with multiple deliveries and rework of random defective items. The classic EPQ model assumes a continuous inventory issuing policy for satisfying demand and perfect quality for all items produced. However, in a real life vendor–buyer integrated system, multi-shipment policy is practically used in lieu of continuous issuing policy and generation of defective items is inevitable. It is assumed that the imperfect quality items fall into two groups: the scrap and the rework-able items. Failure in repair exists, hence additional scrap items generated. The finished items can only be delivered to customers if the whole lot is quality assured at the end of rework. Mathematical modeling is used in this study and the long-run average production–inventory-delivery cost function is derived. Convexity of the cost function is proved by using the Hessian matrix equations. The closed-form optimal replenishment lot size and optimal number of shipments that minimize the long-run average costs for such an EPQ model are derived. Special case is examined, and a numerical example is provided to show its practical usage

Trade Credit Policies for Supplier, Manufacturer, and Retailer: An Imperfect Production-Inventory System with Rework

In this study, we developed a trade credit policy for a three-layer supply chain consisting of a supplier, a manufacturer and a retailer. We propose an optimal production rate and selling price for the manufacturer and the retailer under an imperfect production system. The suggested coordination policy optimizes the profit of each supply chain member. Two models were formulated for two real-life strategies respectively. The first one is a collaborative (integrated) system and the second one is a Stackelberg leadership system. Both strategies were analyzed for various credit periods, respectively offered by the supplier to the manufacturer, by the manufacturer to the retailer, and by the retailer to the customers, by considering price-sensitive demand and a certain replenishment rate. Finally, we concluded which strategy will be better for inventory management under the given restrictions in the form of propositions. The concavity property for the net profit function was established with respect to the selling price and the production rate, which was also described graphically and analyzed by numerical examples

A production inventory model with exponential demand rate and reverse logistics

The objective of this paper is to develop an integrated production inventory model for reworkable items with exponential demand rate. This is a three-layer supply chain model with perspectives of supplier, producer and retailer. Supplier delivers raw material to the producer and finished goods to the retailer. We consider perfect and imperfect quality products, product reliability and reworking of imperfect items. After screening, defective items reworked at a cost just after the regular manufacturing schedule. At the beginning, the manufacturing system starts produce perfect items, after some time the manufacturing system can undergo into “out-of-control” situation from “in-control” situation, which is controlled by reverse logistic technique. This paper deliberates the effects of business strategies like optimum order size of raw material, exponential demand rate, production rate is demand dependent, idle times and reverse logistics for an integrated marketing system. Mathematica is used to develop the optimal solution of production rate and raw material order for maximum expected average profit. A numerical example and sensitivity analysis is illustrated to validate the model

Trade Credit Policies for Supplier, Manufacturer, and Retailer: An Imperfect Production-Inventory System with Rework

In this study, we developed a trade credit policy for a three-layer supply chain consisting of a supplier, a manufacturer and a retailer. We propose an optimal production rate and selling price for the manufacturer and the retailer under an imperfect production system. The suggested coordination policy optimizes the profit of each supply chain member. Two models were formulated for two real-life strategies respectively. The first one is a collaborative (integrated) system and the second one is a Stackelberg leadership system. Both strategies were analyzed for various credit periods, respectively offered by the supplier to the manufacturer, by the manufacturer to the retailer, and by the retailer to the customers, by considering price-sensitive demand and a certain replenishment rate. Finally, we concluded which strategy will be better for inventory management under the given restrictions in the form of propositions. The concavity property for the net profit function was established with respect to the selling price and the production rate, which was also described graphically and analyzed by numerical examples

Production planning and control of closed-loop supply chains

More and more supply chains emerge that include a return flow of materials. Many original equipment manufacturers are nowadays engaged in the remanufacturing business. In many process industries, production defectives and by-products are reworked. These closed-loop supply chains deserve special attention. Production planning and control in such hybrid systems is a real challenge, especially due to increased uncertainties. Even companies that are engaged in remanufacturing operations only, face more complicated planning situations than traditional manufacturing companies.We point out the main complicating characteristics in closed-loop systems with both remanufacturing and rework, and indicated the need for new or modified/extended production planning and control approaches. An overview of the existing scientific contributions is given. It appears that we only stand at the beginning of this line of research, and that many more contributions are needed and expected in the future.closed-loop supply chains;Production planning and control

An economic manufacturing quantity model for a two-stage assembly system with imperfect processes and variable production rate

[[abstract]]This article considers a two-stage assembly system with imperfect processes. The former is an automatic stage in which the required components are manufactured. The latter is a manual stage which deals with taking the components to assemble the end product. In addition, the component processes are independent of each other, and the assembly rate is variable. Shortage is allowed, and the unsatisfied demand is completely backlogged. Then, we formulate the proposed problem as a cost minimization model where the assembly rate and the production run time of each component process are decision variables. An algorithm for the computations of the optimal solutions under the constraint of assembly rate is also provided. Finally, a numerical example and sensitivity analysis are carried out to illustrate the model.[[notice]]補正完畢[[incitationindex]]SCI[[booktype]]紙

Impacts of Common Components in Multistage Production System under Uncertain Conditions

Abstract The work desires: i) to determine the optimum level of batch size in bottleneck facility and ii) to analyze the effect of common components on work-in-process (WIP) level and cycle time in a multistage production system under uncertainties. The uncertainty is created by machine breakdown and quality variation. Few simulation models are developed based on a live case from a company. The models are verified and validated with the historical data from the company and by face validity. Taguchi approach for orthogonal array is used in designing experiments and these are executed in WITNESS. It is observed that the variation in level of common component in the system has significant impact on the production WIP level and cycle time. The main contribution of this research is determination of the optimal level of batch size in a bottleneck resource under the uncertainties. This approach can be generalized to any multistage production system, regardless of the precedence relationships among the various production stages in the system

Optimal Configuration of Inspection and Rework Stations in a Multistage Flexible Flowline

Inspection and rework are two important issues of quality control. In this research, an N-stage flowline is considered to make decisions on these two issues. When defective items are detected at the inspection station the items are either scrapped or reworked. A reworkable item may be repaired at the regular defect-creating workstation or at a dedicated off-line rework station. Two problems (end-of-line and multistage inspections) are considered here to deal with this situation. The end-of-line inspection (ELI) problem considers an inspection station located at the end of the line while the multistage inspection (MSI) problem deals with multiple in-line inspection stations that partition the flowline into multiple flexible lines. Models for unit cost of production are developed for both problems. The ELI problem is formulated for determining the best decision among alternative policies for dealing with defective items. For an MSI problem a unit cost function is developed for determining the number and locations of in-line inspection stations along with the alternative decisions on each type of defects. Both of the problems are formulated as fractional mixed-integer nonlinear programming (f-MINLP) to minimize the unit cost of production. After several transformations the f-MINLP becomes a mixed-integer linear programming (MILP) problem. A construction heuristic, coined as Inspection Station Assignment (ISA) heuristic is developed to determine a sub-optimal location of inspection and rework stations in order to achieve minimum unit cost of production. A hybrid of Ant-Colony Optimization-based metaheuristic (ACOR) and ISA is devised to efficiently solve large instances of MSI problems. Numerical examples are presented to show the solution procedure of ELI problems with branch and bound (B&B) method. Empirical studies on a production line with large number of workstations are presented to show the quality and efficiency of the solution processes involved in both ELI and MSI problems. Computational results present that the hybrid heuristic ISA+ACOR shows better performance in terms of solution quality and efficiency. These approaches are applicable to many discrete product manufacturing systems including garments industry