Batching Work and Rework Processes with Limited Deterioration of Reworkables (original) (raw)
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Batching Work and rework Processes on Dedicated Facilities to Minimize the Makespan
OMEGA, Vol. 38, No. 6, 2010, 522 - 527
We study a planning problem of an imperfect production of a single product. The product is assumed to be continuously divisible. There are two facilities: a main facility dedicated to the original production and a facility dedicated to re-manufacturing defective units coming from the main facility. Units fabricated on the main facility are inspected for quality in batches.
Batching for work and rework processes on dedicated facilities to minimize the makespan
Omega, 2010
We study a planning problem of an imperfect production of a single product. The product is assumed to be continuously divisible. There are two facilities: a main facility dedicated to the original production and a facility dedicated to re-manufacturing defective units coming from the main facility. Units fabricated on the main facility are inspected for quality in batches.
International Journal of Production Economics, Vol. 105, 2007, 345 - 356., 2007
The problem of scheduling the production of new and recovering defective items of the same product manufactured on the same facility is studied. The items are produced in batches. The processing of a batch includes two stages. In the first stage, all items of a batch are manufactured and good quality items go to the inventory to satisfy given demands. In the second stage, defective items of the same batch are reworked. After rework each item has the required good quality. During waiting for rework defective items are assumed to deteriorate. This results in an increase in time and cost for performing rework processes. It is assumed that the percentage of defective items is the same in each batch, and that they are uniformly distributed in each batch. A setup time as well as a setup cost is required to start batch processing and to switch from production to rework. The objective is to find batch sizes such that all demands are satisfied and total setup, rework and inventory holding cost is minimized. Polynomial time algorithms are presented to solve two realistic special cases of this problem. A generalization to a multiple product case is discussed.
Optimal manufacturing batch size with rework process at a single-stage production system
Determining an optimal batch quantity in a production system that produces defective items has been the primary focus recently among the researchers. While most of the work has been reported to explore the traditional optimal inventory level in ideal cases, little appears to have been done with rework option. In this paper, models have been developed to determine the optimum batch quantity in a single-stage system in which rework is done under two different operational policies to minimize the total system cost. The first policy deals with rework being completed within the same cycle. The second policy deals with the rework being done after N cycles causing less than the desired quantity of good products in each cycle. The models have been validated with illustrating numerical examples and the sensitivity of optimal batch size and total system cost with respect to the defective proportion have also been performed.
Optimal batch sizing in a multi-stage production system with rework consideration
European Journal of Operational Research, 2008
In a production system, rework process plays an important role in eliminating waste and effectively controlling the cost of manufacturing. Determining the optimal batch size in a system that allows for rework is, therefore, a worthwhile objective to minimize the inventory cost of work-in-processes and the finished goods. In this paper, models for the optimum batch quantity in a multi-stage system with rework process have been developed for two different operational policies. Policy 1 deals with the rework within the same cycle with no shortage and policy 2 deals with the rework done after N cycles, incurring shortages in each cycle. The major components that play a role in minimizing this cost of the system are manufacturing setups, work-in-processes, storage of finished goods, rework processing, waiting-time, and penalty costs to discourage the generation of defectives. The mathematical structure of this rework processing model falls under a nonlinear convex programming problems for which a closed-form solution has been proposed and results are demonstrated through numerical examples, followed by sensitivity analyses of different important parameters. It is concluded that the total cost in policy 2 tends to be smaller than that in policy 1 at lower proportion of defectives if the in-process carrying cost is low. Policy 2 may be preferred when the work-in-process carrying cost is low and the penalty cost is negligible.
Computers & Industrial Engineering, 2008
This paper presents a simple derivation of the two inventory policies proposed by [Jamal, A. A. M., Sarker, B. R., & Mondal, S. (2004). Optimal manufacturing batch size with rework process at single-stage production system. Computers and Industrial Engineering, 47(1), 77-89.]. In order to find the optimal solutions for both policies they used differential calculus. Our simple derivation is based on an algebraic derivation. The final results that we obtained are equivalent to the results that [Jamal, A. A. M., Sarker, B. R., & Mondal, S. (2004). Optimal manufacturing batch size with rework process at single-stage production system. Computers and Industrial Engineering, 47(1), 77-89.] found. But, our results are more simple and easy to compute manually. We also established the range of real values of proportion of defectives products for which there is an optimal solution, the closed-form for the total inventory cost for both policies, the mathematical expressions for determining the cost penalty and the additional total cost for working with a non-optimal solution.
Multiproduct batching and scheduling with buffered rework: The case of a car paint shop
Naval Research Logistics (NRL), 2014
We study a problem of scheduling products on the same facility, which is motivated by a car paint shop. Items of the same product are identical. Operations on the items are performed sequentially in batches, where each batch is a set of operations on the same product. Some of the produced items are of the required good quality and some items can be defective. Defectiveness of an item is determined by a given simulated function of its product, its preceding product, and the position of its operation in the batch. Defective items are kept in a buffer of a limited capacity, and they are then remanufactured at the same facility. A minimum waiting time exists for any defective item before its remanufacturing can commence. Each product has a sequence independent setup time which precedes its first operation or its operation following an operation of another product. A due date is given for each product such that all items of the same product have the same due date and the objective is to find a schedule which minimizes maximum lateness of product completion times with respect to their due dates. The problem is proved NP-hard in the strong sense, and a heuristic Group Technology (GT) solution approach is suggested and analyzed. The results justify application of the GT approach to scheduling real car paint shops with buffered rework.
Logistic planning and control of reworking perishable production defectives
We consider a production line that is dedicated to a single product. Produced lots may be non-defective, reworkable defective, or non-reworkable defective. The production line switches between production and rework. After producing a fixed number (N) of lots, all reworkable defective lots are reworked. Reworkable defectives are perishable, i.e., worsen while held in stock. We assume that the rework time and the rework cost increase linear with the time that a lot is held in stock. Therefore, N should not be too large. On the other hand, N should not be too small either, since there are set-up times and costs associated with switching between production and rework. For a given N, we derive an explicit expression for the average profit (sales revenue minus costs). Using that expression, the optimal value for N can be determined numerically.
A Single-Stage Manufacturing Model with Imperfect Items, Inspections, Rework, and Planned Backorders
Mathematics, 2019
Each industry prefers to sell perfect products in order to maintain its brand image. However, due to a long-run single-stage production system, the industry generally obtains obstacles. To solve this issue, a single-stage manufacturing model is formulated to make a perfect production system without defective items. For this, the industry decides to stop selling any products until whole products are ready to fulfill the order quantity. Furthermore, manufacturing managers prefer product qualification from the inspection station especially when processes are imperfect. The purpose of the proposed manufacturing model considers that the customer demands are not fulfilled during the production phase due to imperfection in the process, however customers are satisfied either at the end of the inspection process or after reworking the imperfect products. Rework operation, inspection process, and planned backordering are incorporated in the proposed model. An analytical approach is utilized t...
Scientia Iranica, 2018
In this paper, we consider a deficient production system with permissible shortages. The production system consists of a unique machine that manufactures a number of products that a part of them are imperfect in form of rework or scrap. These defective products are identified by 100% inspection during production, then, they are whether reworked or disposed of after normal production process. Like real-world production systems, there are diverse kinds of errors creating dissimilar breakdown severity and rework. Moreover, reworks have non-zero setup times that makes the problem closer to real-world instances where machines require some preparations before starting a new production cycle. Thus, we introduce an economic production quantity (EPQ) problem for an imperfect manufacturing system with non-zero setup times for rework items. The rework items are classified into several categories based on their type of failure and rework rate. The aim of this study is to obtain optimum production time and shortage in each period that minimizes total inventory system costs. Convexity of the objective function and exact solution procedure for the current nonlinear optimization problem are also proposed. Finally, a numerical example is proposed to assess efficiency and validation of proposed algorithm.