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

Differential evolution to solve the lot size problem.

An Advanced Resource Planning model is presented to support optimal lot size decisions for performance improvement of a production system in terms of either delivery time or setup related costs. Based on a queueing network, a model is developed for a mix of multiple products following their own specific sequence of operations on one or more resources, while taking into account various sources of uncertainty, both in demand as well as in production characteristics. In addition, the model includes the impact of parallel servers and different time schedules in a multi-period planning setting. The corrupting influence of variabilities from rework and breakdown is explicitly modeled. As a major result, the differential evolution algorithm is able to find the optimal lead time as a function of the lot size. In this way, we add a conclusion on the debate on the convexity between lot size and lead time in a complex production environment. We show that differential evolution outperforms a steepest descent method in the search for the global optimal lot size. For problems of realistic size, we propose appropriate control parameters for the differential evolution in order to make its search process more efficient.Production planning; Lot sizing; Queueing networks; Differential evolution;

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

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

Production lot sizing with rework and fixed quantity deliveries

This paper is concerned with determination of the optimal lot size for an economic production quantity (EPQ) model with the reworking of random defective items and fixed quantity multiple deliveries. Classic EPQ model assumes continuous issuing policy for satisfying product demand and perfect quality production for all items produced. However, in real life vendor-buyer integrated production-inventory system, multi-delivery policy is used practically in lieu of the continuous issuing policy and generation of defective items during production run is inevitable. In this study, all nonconforming items produced are considered to be repairable and are reworked in each cycle when regular production ends. The finished items can only be delivered to customers if the whole lot is quality assured at the end of the rework. Fixed quantity multiple installments of the finished batch are delivered to customers at a fixed interval of time. The long-run average integrated cost function per unit time is derived. A closed-form optimal batch size solution to the problem is obtained. A numerical example demonstrates its practical usage

Effect of variable shipping frequency on production-distribution policy in a vendor-buyer integrated system

This paper investigates the effect of variable shipping frequency on production-distribution policy in a vendor-buyer integrated system. In a recent article Chiu et al. [1] derived the optimal replenishment lot size for an economic production quantity problem with multi-delivery and quality assurance, based on an assumption that the number of shipment is a given constant. However, in a vendor-buyer integrated system in supply chain environment, joint determination of replenishment lot size and number of shipments may help such a system to gain significant competitive advantage in terms of becoming a low-cost producer as well as having tight linkage to customer. For this reason, the present study extends the work of Chiu et al. [1] by considering shipping frequency as one of the decision variables and incorporating customer’s stock holding cost into system cost analysis. Hessian matrix equations are employed to certify the convexity of cost function that contains two decision variables, and the effect of variable shipping frequency on production-distribution policy is investigated. A numerical example is provided to demonstrate practical usage of the research result

Optimal production-shipment decisions for the finite production rate model with scrap

This paper is concerned with the decision-making on the optimal production batch size and optimal number of shipments for a finite production rate model with random scrap rate. The classic finite production rate (FPR) model assumes a continuous inventory issuing policy for satisfying product demand and perfect quality for all items produced. However, in a real life vendor-buyer integrated production-inventory system, a multiple shipment policy is practically used in lieu of the continuous issuing policy, and it is inevitable to generate defective items during a production run. All nonconforming items produced are assumed to be scrap, and the finished (perfect quality) products can only be delivered to customers if the whole lot is quality assured at the end of the production run. The fixed-quantity multiple instalments of the finished batch are delivered to customers at a fixed interval of time. Mathematical modelling is employed and the renewal reward theorem is used to cope with the variable production cycle length. The long-run average cost for the proposed model is derived, and its convexity is proved by the use of the Hessian matrix equations. A closed-form optimal production-shipment policy for such an imperfect FPR model is obtained and a special case is discussed. Finally, a numerical example is provided to demonstrate the model’s practical usage

Design and evaluation of in-line product repair strategies for defect reduction in the production of electric drives

Manufacturing companies are continuously facing the challenge of operating their manufacturing processes and systems in order to deliver the required production rates of high quality products of increasing complexity, with limited use and waste of resources. This aspect is particularly critical in emerging sectors, such as the e-mobility industry, where state of the art quality and process control technologies show strong limitations. This paper proposes new solutions for implementing in-line product repair strategies in the production of electric drives for the automotive industry. Moreover, it develops an innovative quantitative tool to estimate the impact of the proposed strategies on the overall process-chain performance. The benefits of the approach are validated within a real industrial context