Optimal manufacturing batch size with rework process at a single-stage production system
A.M.M. Jamala, Bhaba R. Sarkerb,*, Sanjay Mondalb
Department of Management, Southeastern Louisiana University, Hammond, LA 70402, USA Department of Industrial & Manufacturing Systems Engineering, Louisiana StateUniversity, Baton Rouge, LA 70803-6409, USA Received 17 February 2003; revised 24 February 2004; accepted 2 March 2004 Available online 5 June 2004
Abstract 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 inideal 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 doneafter 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. q 2004 Elsevier Ltd. All rights reserved.
Keywords: Rework; Single and multiple cycles; Manufacturing batches;Sensitivity analysis
1. Introduction Determining an optimal batch size in a traditional production–inventory system has received attention among the researchers in recent decades. Researchers developed many optimal batch size models under various conditions to minimize the total system cost. The proper evaluation of an inventory system policy requires determining an optimal batch-sizing model alongwith inventory
* Corresponding author. Tel.: þ1-225-578-5370; fax: þ1-225-578-5109. E-mail address: firstname.lastname@example.org (B.R. Sarker). 0360-8352/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.cie.2004.03.001
A.M.M. Jamal et al. / Computers & Industrial Engineering 47 (2004) 77–89
b C Cp Cs Cw D H1 H2 N P Q S ts
proportion of defectives ineach cycle processing cost in ﬁrst operational policy ($/unit) unit penalty cost per unit outage per unit time, $/unit/year setup cost in policy 2, $/year unit in-process inventory carrying cost, $/unit/year demand rate, units per planning period, units/year inventory carrying cost in policy 1, $/unit/year inventory carrying cost in policy 2, $/unit/year number of production cycles after which thedefective items are reworked production rate, units per planning period, units/year batch quantity per cycle, units/batch or units/cycle setup cost in policy 1, $/batch setup time, year/setup
holding cost, setup cost, processing cost and shortage cost. An optimal batch quantity or an economic lot size depends on the demand pattern and the production rate of the system. In a single-stageproduction system, a certain amount of defective items results due to various reasons including poor production quality and material defects, and subsequently a portion of them may be scrapped as well. Depending on the proportion of defectives, the amount of optimal batch size also varies depending on several cost factors such as setup cost, processing cost, and inventory carrying cost. A productionsystem may have a repair or rework facility at which the defective items are reworked and/or corrected to ﬁnish products. The ﬁrst attempt of an industrial engineer should be to eliminate rework and inventory. When technical and/or economic considerations do not allow for this, an optimal strategy to rework defective products may be adopted. In a production system where there is no repair or rework...