Manufacturing lot sizing with backordering, scrap, and random breakdown occurring in inventory-stacking period

Authors:
Singa Wang Chiu;Jyh-Chau Yang;Shu-Ying Chen Kuo
Affiliations:
Department of Business Administration, Chaoyang University of Technology, Wufong, Taichung, Taiwan;Department of Business Administration, Chaoyang University of Technology, Wufong, Taichung, Taiwan;Department of Automation Engineering, Ta Hwa Institute of Technology, Qionglin Shiang, Hsinchu County, Taiwan
Venue:
WSEAS Transactions on Mathematics
Year:
2008

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Abstract

This paper is concerned with determination of optimal lot size for an economic manufacturing quantity model with backordering, scrap and breakdown occurring in inventory-stacking period. Generation of defective items and random breakdown of production equipment are inevitable in most real-life manufacturing systems. To cope with the stochastic machine failures, production planners practically calculate the mean time between failures (MTBF) and establish the robust plan accordingly, in terms of optimal lot size that minimizes total production-inventory costs for such an unreliable system. Random scrap rate is considered in this study, and breakdown is assumed to occur in inventory stacking period. Mathematical modeling and analysis is used and the renewal reward theorem is employed to cope with the variable cycle length. An optimal manufacturing lot size that minimizes the long-run average costs for such an imperfect system is derived. Numerical example is provided to demonstrate its practical usages.