An optimization problem of manufacturing systems with stochastic machine breakdown and rework process

This paper is concerned with optimization of production run time that takes stochastic breakdown and the reworking of defective items into consideration. In a real-life manufacturing process, production of imperfect quality items as well as random breakdowns of production equipment is inevitable. All defective items produced are assumed to be repairable through a rework process right after the regular production stops in each cycle. This research starts with derivations of the cost functions for production systems with breakdown (no-resumption policy is considered) and without breakdown taking place, respectively. Then cost functions of both cases are integrated. Theorems on conditional convexity of the overall cost function and bounds for optimal production run time are proposed and proved. This study concludes that although the optimal run time cannot be expressed in a closed form, it falls within the range of bounds. Hence, it can be pinpointed by the use of the bisection method based on the intermediate value theorem. A numerical example is provided to demonstrate its practical usages. Copyright © 2007 John Wiley & Sons, Ltd.

[1]  DaeSoo Kim,et al.  Optimal two-stage lot sizing and inventory batching policies , 1999 .

[2]  Tonya Boone,et al.  The Impact of Imperfect Processes on Production Run Times , 2000, Decis. Sci..

[3]  Chiun-Ming Liu,et al.  Clustering techniques for stock location and order-picking in a distribution center , 1999, Comput. Oper. Res..

[4]  Sumer C. Aggarwal.  A review of current inventory theory and its applications , 1974 .

[5]  C. H. Kim,et al.  An optimal production run length in deteriorating production processes , 1999 .

[6]  Meir J. Rosenblatt,et al.  Economic Production Cycles with Imperfect Production Processes , 1986 .

[7]  Tadashi Dohi,et al.  Exact formulation of stochastic EMQ model for an unreliable production system , 2004, J. Oper. Res. Soc..

[8]  A. Seidmann,et al.  Production lot sizing with machine breakdowns , 1992 .

[9]  David F. Pyke,et al.  Inventory management and production planning and scheduling , 1998 .

[10]  Kun-Jen Chung.  Bounds for production lot sizing with machine breakdowns , 1997 .

[11]  Kuo-Lung Hou,et al.  An optimal production run time with imperfect production processes and allowable shortages , 2003, Comput. Oper. Res..

[12]  Y. Chiu.  Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging , 2003 .

[13]  Meir J. Rosenblatt,et al.  Simultaneous determination of production cycle and inspection schedules in a production system , 1987 .

[14]  Bhaba R. Sarker,et al.  Optimal manufacturing batch size with rework process at a single-stage production system , 2004, Comput. Ind. Eng..

[15]  Andrew M. Gleason,et al.  Calculus (2nd ed.) , 1998 .

[16]  T.C.E. Cheng,et al.  An Economic Order Quantity Model with Demand-Dependent Unit Production Cost and Imperfect Production Processes , 1991 .

[17]  Yuan-Shyi Peter Chiu,et al.  Note on “Effects of Random Defective Rate and Imperfect Rework Process on Economic Production Quantity Model” , 2006 .

[18]  Mohamed Ben-Daya,et al.  The economic production lot-sizing problem with imperfect production processes and imperfect maintenance , 2002 .

[19]  Viliam Makis,et al.  An EMQ model with inspections and random machine failures , 1998, J. Oper. Res. Soc..

[20]  Bin Liu,et al.  Analysis of a production-inventory system with machine breakdowns and shutdowns , 1999 .

[21]  P. A. Hayek,et al.  Production lot sizing with the reworking of imperfect quality items produced , 2001 .

[22]  S. W. Chiu.  Optimal replenishment policy for imperfect quality EMQ model with rework and backlogging , 2006 .

[23]  Singa Wang Chiu,et al.  Mathematical modeling for production system with backlogging and failure in repair , 2006 .