January  2012, 8(1): 141-162. doi: 10.3934/jimo.2012.8.141

A common cycle approach for solving the economic lot and inspection scheduling problem

1. 

Department of Transportation Technology and Management, National Chiao Tung University, Hsinchu, 30010, Taiwan

2. 

Department of Industrial Engineering and Management, Hsiuping University of Science and Technology, Taichung, 41280, Taiwan

3. 

Department of Information Management, Tunghai University, Taichung, 40704, Taiwan

Received  October 2010 Revised  July 2011 Published  November 2011

In this study, we consider an imperfect production system in which the manager not only faces the Economic Lot Scheduling Problem, but also needs to conduct multiple inspections during a production lot of any product. Inspection plays an important role in an imperfect production system since it saves the cost from producing and restoring defective items though it also incurs extra inspection cost at the same time. In this study, we employ the common cycle approach in which all the products share the same replenishment cycle, and adopt a consensus inspection policy. The focus of this study is to determine the optimal cycle time and an optimal production and inspection schedule that minimize the total cost per unit time. We formulate a mathematical model in which we take into accounts both the production capacity and inspection capacity constraints. Also, we conduct full theoretical analysis and propose an effective search algorithm for solving an optimal solution. Our numerical experiments demonstrate the effectiveness of the proposed search algorithm.
Citation: Ming-Jong Yao, Shih-Chieh Chen, Yu-Jen Chang. A common cycle approach for solving the economic lot and inspection scheduling problem. Journal of Industrial & Management Optimization, 2012, 8 (1) : 141-162. doi: 10.3934/jimo.2012.8.141
References:
[1]

Y. C. Chen, Optimal inspection and economical production quantity strategy for an imperfect production process,, International Journal of Systems Science, 37 (2006), 295.  doi: 10.1080/00207720600566602.  Google Scholar

[2]

I. Djamaludin, R. J. Wilson, and D. N. P. Murthy, Lot sizing and testing for items with uncertain quality,, Stochastic Models in Engineering, 22 (1995), 35.  doi: 10.1016/0895-7177(95)00178-5.  Google Scholar

[3]

G. Dobson, The cyclic lot scheduling problem with sequence-dependent setups,, Operations Research, 40 (1992), 736.  doi: 10.1287/opre.40.4.736.  Google Scholar

[4]

S. E. Elmaghraby, The economic lot scheduling problem (ELSP): Review and extension,, Management Science, 24 (1978), 587.  doi: 10.1287/mnsc.24.6.587.  Google Scholar

[5]

B. Faaland, T. Schmitt and T. Arreola-Risa, Economic lot scheduling with lose sales and setup times,, IIE Transactions, 36 (2004), 629.  doi: 10.1080/07408170490278238.  Google Scholar

[6]

B. C. Giri, T. Dohi, T. Schmitt and T. Arreola-Risa, Inspection scheduling for imperfect production processes under free repair warranty contract,, European Journal of Operational Research, 183 (2007), 238.  doi: 10.1016/j.ejor.2006.09.062.  Google Scholar

[7]

F. Hanssmann, "Operations Research in Production and Inventory Control,", John Wiley & Sons, (1962).   Google Scholar

[8]

W. Hsu, On the general feasibility test of scheduling lot sizes for several products on one machine,, Management Science, 29 (1983), 93.  doi: 10.1287/mnsc.29.1.93.  Google Scholar

[9]

F. Hu and Q. Zong, Optimal production run time for a deteriorating production system under an extended inspection policy,, European Journal of Operational Research, 196 (2009), 979.  doi: 10.1016/j.ejor.2008.05.008.  Google Scholar

[10]

C. H. Kim and Y. Hong, An optimal production run length in deteriorating production processes,, International Journal of Production Economics, 58 (1999), 183.  doi: 10.1016/S0925-5273(98)00119-4.  Google Scholar

[11]

C. H. Kim, Y. Hong and S. Y. Chang, Optimal production run length and inspection schedules in a deteriorating production process,, IIE Transactions, 33 (2001), 421.  doi: 10.1080/07408170108936840.  Google Scholar

[12]

H. L. Lee and M. J. Rosenblatt, Simultaneous determination of production cycle and inspection schedules in a production system,, Management Science, 33 (1987), 1125.  doi: 10.1287/mnsc.33.9.1125.  Google Scholar

[13]

H. L. Lee and M. J. Rosenblatt, A production and maintenance planning model with restoration cost dependent on detection delay,, IIE Transactions, 21 (1989), 368.  doi: 10.1080/07408178908966243.  Google Scholar

[14]

J. S. Lee and K. S. Park, Joint determination of production cycle and inspection intervals in a deteriorating production system,, Journal of the Operational Research Society, 42 (1991), 775.   Google Scholar

[15]

C. S. Lin, C. H. Chen and D. E. Kroll, Integrated production-inventory models for imperfect production processes under inspection schedules,, Computers and Industrial Engineering, 44 (2003), 633.  doi: 10.1016/S0360-8352(02)00239-5.  Google Scholar

[16]

M. A. Lopez and B. G. Kingsmans, The economic lot scheduling problem: Theory and practice,, International Journal of Production Economics, 23 (1991), 147.  doi: 10.1016/0925-5273(91)90058-2.  Google Scholar

[17]

I. K. Moon, B. C. Cha and H. C. Bae, Hybrid genetic algorithm for group technology economic lot scheduling problem,, International Journal of Production Research, 44 (2006), 4551.  doi: 10.1080/00207540500534405.  Google Scholar

[18]

J. Neter, W. Wasserman and M. Kutner, "Applied Linear Statistical Models,", Irvine, (1996).   Google Scholar

[19]

H. Ouyang and X. Zhu, A economic lot scheduling problem for manufacturing and remanufacturing,, in, (2008).  doi: 10.1109/ICCIS.2008.4670892.  Google Scholar

[20]

E. L. Porteus, Optimal lot sizing, process quality improvement and setup cost reduction,, Operations Research, 34 (1986), 137.  doi: 10.1287/opre.34.1.137.  Google Scholar

[21]

E. L. Porteus, The impact of inspection delay on process and inspection lot sizing,, Management Science, 36 (1990), 999.  doi: 10.1287/mnsc.36.8.999.  Google Scholar

[22]

M. A. Rahim, Joint determination of production quantity inspection schedule, and control chart design,, International Journal of Production Research, 36 (1994), 277.  doi: 10.1080/002075498194047.  Google Scholar

[23]

J. Rogers, A computational approach to the economic lot scheduling problem,, Management Science, 36 (1958), 264.  doi: 10.1287/mnsc.4.3.264.  Google Scholar

[24]

M. J. Rosenblatt and H. L. Lee, Economic production cycle with imperfect production process,, IIE Transactions, 18 (1986), 48.  doi: 10.1080/07408178608975329.  Google Scholar

[25]

M. J. Rosenblatt and H. L. Lee, A comparative study of continuous and periodic inspection policies in deteriorating production systems,, IIE Transactions, 18 (1986), 2.  doi: 10.1080/07408178608975323.  Google Scholar

[26]

L. Salvietti and N. R. Smith, A profit-maximizing economic lot scheduling problem with price optimization,, European Journal of Operational Research, 184 (2008), 900.  doi: 10.1016/j.ejor.2006.11.031.  Google Scholar

[27]

C. A. Soman, D. P. Van Donk and G. Gaalman, A basic period approach to the economic lot scheduling problem with shelf life considerations,, International Journal of Production Research, 42 (2004), 1677.  doi: 10.1080/00207540310001645165.  Google Scholar

[28]

O. Tang and R. H. Teunter, Economic lot scheduling problem with returns,, Operations Management, 15 (2006), 488.  doi: 10.1111/j.1937-5956.2006.tb00158.x.  Google Scholar

[29]

R. Teunter, K. Kaparis and O. Tang, Multi-product economic lot scheduling problem with separate production lines for manufacturing and remanufacturing,, European Journal of Operational Research, 191 (2008), 1241.  doi: 10.1016/j.ejor.2007.08.003.  Google Scholar

[30]

B. Wagner and D. J. Davis, A search heuristic for the sequence-dependent economic lot scheduling problem,, European Journal of Operational Research, 141 (2002), 133.  doi: 10.1016/S0377-2217(01)00265-X.  Google Scholar

[31]

C. H. Wang and S. H. Sheu, Simultaneous determination of the optimal production-inventory and product inspection policies for a deteriorating production system,,, Computers and Operations Research, 28 (2001), 1093.  doi: 10.1016/S0305-0548(00)00030-7.  Google Scholar

[32]

C. H. Wang, Integrated production and product inspection policy for a deteriorating production system,, International Journal of Production Economics, 95 (2005), 123.  doi: 10.1016/j.ijpe.2003.11.012.  Google Scholar

[33]

M. J. Yao, "The Economic Lot Scheduling Problem with Extension to Multiple Resource Constraints,", Unpublished Ph.D thesis, (1999).   Google Scholar

[34]

M. J. Yao, S. E. Elmaghraby and I. C. Chen, On the feasibility testing of the economic lot scheduling problem using the extended basic period approach,, Journal of the Chinese Institute of Industrial Engineering, 20 (2003), 435.  doi: 10.1080/10170660309509249.  Google Scholar

[35]

M. J. Yao and Y. J. Chang, A genetic algorithm for solving the economic lot schedule problem with reworks,, Journal of the Chinese Institute of Industrial Engineering, 26 (2009), 411.  doi: 10.1080/10170660909509155.  Google Scholar

[36]

M. J. Yao and S. C. Chen, On the determination of the optimal replenishment and inspection schedule in an imperfect production-inventory system,, Journal of Operations and Logistics, 2 (2009), 1.   Google Scholar

[37]

R. H. Yeh and T. H. Chen, Optimal lot size and inspection policy for products sold with warranty,, European Journal of Operational Research, 174 (2006), 766.  doi: 10.1016/j.ejor.2005.02.049.  Google Scholar

show all references

References:
[1]

Y. C. Chen, Optimal inspection and economical production quantity strategy for an imperfect production process,, International Journal of Systems Science, 37 (2006), 295.  doi: 10.1080/00207720600566602.  Google Scholar

[2]

I. Djamaludin, R. J. Wilson, and D. N. P. Murthy, Lot sizing and testing for items with uncertain quality,, Stochastic Models in Engineering, 22 (1995), 35.  doi: 10.1016/0895-7177(95)00178-5.  Google Scholar

[3]

G. Dobson, The cyclic lot scheduling problem with sequence-dependent setups,, Operations Research, 40 (1992), 736.  doi: 10.1287/opre.40.4.736.  Google Scholar

[4]

S. E. Elmaghraby, The economic lot scheduling problem (ELSP): Review and extension,, Management Science, 24 (1978), 587.  doi: 10.1287/mnsc.24.6.587.  Google Scholar

[5]

B. Faaland, T. Schmitt and T. Arreola-Risa, Economic lot scheduling with lose sales and setup times,, IIE Transactions, 36 (2004), 629.  doi: 10.1080/07408170490278238.  Google Scholar

[6]

B. C. Giri, T. Dohi, T. Schmitt and T. Arreola-Risa, Inspection scheduling for imperfect production processes under free repair warranty contract,, European Journal of Operational Research, 183 (2007), 238.  doi: 10.1016/j.ejor.2006.09.062.  Google Scholar

[7]

F. Hanssmann, "Operations Research in Production and Inventory Control,", John Wiley & Sons, (1962).   Google Scholar

[8]

W. Hsu, On the general feasibility test of scheduling lot sizes for several products on one machine,, Management Science, 29 (1983), 93.  doi: 10.1287/mnsc.29.1.93.  Google Scholar

[9]

F. Hu and Q. Zong, Optimal production run time for a deteriorating production system under an extended inspection policy,, European Journal of Operational Research, 196 (2009), 979.  doi: 10.1016/j.ejor.2008.05.008.  Google Scholar

[10]

C. H. Kim and Y. Hong, An optimal production run length in deteriorating production processes,, International Journal of Production Economics, 58 (1999), 183.  doi: 10.1016/S0925-5273(98)00119-4.  Google Scholar

[11]

C. H. Kim, Y. Hong and S. Y. Chang, Optimal production run length and inspection schedules in a deteriorating production process,, IIE Transactions, 33 (2001), 421.  doi: 10.1080/07408170108936840.  Google Scholar

[12]

H. L. Lee and M. J. Rosenblatt, Simultaneous determination of production cycle and inspection schedules in a production system,, Management Science, 33 (1987), 1125.  doi: 10.1287/mnsc.33.9.1125.  Google Scholar

[13]

H. L. Lee and M. J. Rosenblatt, A production and maintenance planning model with restoration cost dependent on detection delay,, IIE Transactions, 21 (1989), 368.  doi: 10.1080/07408178908966243.  Google Scholar

[14]

J. S. Lee and K. S. Park, Joint determination of production cycle and inspection intervals in a deteriorating production system,, Journal of the Operational Research Society, 42 (1991), 775.   Google Scholar

[15]

C. S. Lin, C. H. Chen and D. E. Kroll, Integrated production-inventory models for imperfect production processes under inspection schedules,, Computers and Industrial Engineering, 44 (2003), 633.  doi: 10.1016/S0360-8352(02)00239-5.  Google Scholar

[16]

M. A. Lopez and B. G. Kingsmans, The economic lot scheduling problem: Theory and practice,, International Journal of Production Economics, 23 (1991), 147.  doi: 10.1016/0925-5273(91)90058-2.  Google Scholar

[17]

I. K. Moon, B. C. Cha and H. C. Bae, Hybrid genetic algorithm for group technology economic lot scheduling problem,, International Journal of Production Research, 44 (2006), 4551.  doi: 10.1080/00207540500534405.  Google Scholar

[18]

J. Neter, W. Wasserman and M. Kutner, "Applied Linear Statistical Models,", Irvine, (1996).   Google Scholar

[19]

H. Ouyang and X. Zhu, A economic lot scheduling problem for manufacturing and remanufacturing,, in, (2008).  doi: 10.1109/ICCIS.2008.4670892.  Google Scholar

[20]

E. L. Porteus, Optimal lot sizing, process quality improvement and setup cost reduction,, Operations Research, 34 (1986), 137.  doi: 10.1287/opre.34.1.137.  Google Scholar

[21]

E. L. Porteus, The impact of inspection delay on process and inspection lot sizing,, Management Science, 36 (1990), 999.  doi: 10.1287/mnsc.36.8.999.  Google Scholar

[22]

M. A. Rahim, Joint determination of production quantity inspection schedule, and control chart design,, International Journal of Production Research, 36 (1994), 277.  doi: 10.1080/002075498194047.  Google Scholar

[23]

J. Rogers, A computational approach to the economic lot scheduling problem,, Management Science, 36 (1958), 264.  doi: 10.1287/mnsc.4.3.264.  Google Scholar

[24]

M. J. Rosenblatt and H. L. Lee, Economic production cycle with imperfect production process,, IIE Transactions, 18 (1986), 48.  doi: 10.1080/07408178608975329.  Google Scholar

[25]

M. J. Rosenblatt and H. L. Lee, A comparative study of continuous and periodic inspection policies in deteriorating production systems,, IIE Transactions, 18 (1986), 2.  doi: 10.1080/07408178608975323.  Google Scholar

[26]

L. Salvietti and N. R. Smith, A profit-maximizing economic lot scheduling problem with price optimization,, European Journal of Operational Research, 184 (2008), 900.  doi: 10.1016/j.ejor.2006.11.031.  Google Scholar

[27]

C. A. Soman, D. P. Van Donk and G. Gaalman, A basic period approach to the economic lot scheduling problem with shelf life considerations,, International Journal of Production Research, 42 (2004), 1677.  doi: 10.1080/00207540310001645165.  Google Scholar

[28]

O. Tang and R. H. Teunter, Economic lot scheduling problem with returns,, Operations Management, 15 (2006), 488.  doi: 10.1111/j.1937-5956.2006.tb00158.x.  Google Scholar

[29]

R. Teunter, K. Kaparis and O. Tang, Multi-product economic lot scheduling problem with separate production lines for manufacturing and remanufacturing,, European Journal of Operational Research, 191 (2008), 1241.  doi: 10.1016/j.ejor.2007.08.003.  Google Scholar

[30]

B. Wagner and D. J. Davis, A search heuristic for the sequence-dependent economic lot scheduling problem,, European Journal of Operational Research, 141 (2002), 133.  doi: 10.1016/S0377-2217(01)00265-X.  Google Scholar

[31]

C. H. Wang and S. H. Sheu, Simultaneous determination of the optimal production-inventory and product inspection policies for a deteriorating production system,,, Computers and Operations Research, 28 (2001), 1093.  doi: 10.1016/S0305-0548(00)00030-7.  Google Scholar

[32]

C. H. Wang, Integrated production and product inspection policy for a deteriorating production system,, International Journal of Production Economics, 95 (2005), 123.  doi: 10.1016/j.ijpe.2003.11.012.  Google Scholar

[33]

M. J. Yao, "The Economic Lot Scheduling Problem with Extension to Multiple Resource Constraints,", Unpublished Ph.D thesis, (1999).   Google Scholar

[34]

M. J. Yao, S. E. Elmaghraby and I. C. Chen, On the feasibility testing of the economic lot scheduling problem using the extended basic period approach,, Journal of the Chinese Institute of Industrial Engineering, 20 (2003), 435.  doi: 10.1080/10170660309509249.  Google Scholar

[35]

M. J. Yao and Y. J. Chang, A genetic algorithm for solving the economic lot schedule problem with reworks,, Journal of the Chinese Institute of Industrial Engineering, 26 (2009), 411.  doi: 10.1080/10170660909509155.  Google Scholar

[36]

M. J. Yao and S. C. Chen, On the determination of the optimal replenishment and inspection schedule in an imperfect production-inventory system,, Journal of Operations and Logistics, 2 (2009), 1.   Google Scholar

[37]

R. H. Yeh and T. H. Chen, Optimal lot size and inspection policy for products sold with warranty,, European Journal of Operational Research, 174 (2006), 766.  doi: 10.1016/j.ejor.2005.02.049.  Google Scholar

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