Economic production quantity concerning learning and the reworking of imperfect items
DOI:
https://doi.org/10.2298/YJOR091109012TKeywords:
rework, imperfect quality, learning effect, economic production quantityAbstract
The classical economic production quantity (EPQ) model assumes that items produced are of perfect quality and the production rate is constant. However, production quality depends on the condition of the process. Due to process deterioration or other factors, the production process may shift and produce imperfect quality items. These imperfect quality items sometimes can be reworked and repaired; hence, overall production-inventory costs can be reduced significantly. In addition, it can be found in practice that the time or cost required to repetitively produce a unit of a product decreases when the number of units produced by a worker or a group of workers increases. Under this circumstance, the unit production cost cannot be regarded as constant and, therefore, cannot be ignored when taking account of the total cost. This paper incorporates the effects of learning and the reworking of defective items on the EPQ model since they were not considered in existing models. An optimal operation policy that minimizes the expected total cost per unit time is derived. A numerical example is provided to illustrate the proposed model. In addition, sensitivity analysis is performed and discussed.References
Adler, G.L., and Nanda, R., “The effects of learning on optimal lot size determination-single product case”, AIIE Transactions, 6 (1974a) 14-20.
Adler, G.L., and Nanda, R., “The effects of learning on optimal lot size determination-multiple product case”, AIIE Transactions, 6 (1974b) 21-27.
Argote, L., and Epple, D., “Learning curves in manufacturing”, Science, 247 (1990) 920-924.
Barketau, M.S., Cheng, T.C.E., and Kovalyov, M.Y., “Batch scheduling of deteriorating reworkables”, European Journal of Operational Research, 189 (2008) 1317–1326.
Buscher, U., and Lindner, G., “Optimizing a production system with rework and equal sized batch shipments”, Computers and Operations Research, 34 (2007) 515–535.
Camm, J.D., “A note on learning curve parameters”, Decision Sciences, 16 (1985) 325–327.
Camm, J.D., Evans, J.R., and Womer, N.K., “The unit learning curve approximation of total cost”, Computers and Industrial Engineering, 12 (2004) 205–213.
Cardenas-Barron, L.E., “Optimal manufacturing batch size with rework in a single-stage production system - a simple derivation”, Computers and Industrial Engineering, 55 (2008) 758–765.
Cheng, T.C.E., “An economic order quantity model with demand-dependent unit production cost and imperfect production processes”, IIE Transactions, 23 (1991) 23–28.
Chiu, H.N., and Chen, H.M., “An optimal algorithm for solving the dynamic lot-sizing model with learning and forgetting in setups and production”, International Journal of Production Economics, 95 (2005) 179–193.
Chiu, S.W., Wang, S.L., and Chiu, Y.P., “Determining the optimal run time for EPQ model with scrap, rework, and stochastic breakdowns”, European Journal of Operational Research, 180 (2007) 664–676.
Chiu, Y.P., “Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging”, Engineering Optimization, 35 (2003) 427–437.
Elmaghraby, S.E., “Economic manufacturing quantities under conditions of learning and forgetting”, Production Planning and Control, 1 (1990) 196–208.
Freimer, M., Thomas, D., and Tyworth, J., “The value of setup cost reduction and process improvement for the economic production quantity model with defects”, European Journal of Operational Research, 173 (2006) 241-251.
Hayek, P.A., and Salameh, M.K., “Production lot sizing with the reworking of imperfect quality items produced”, Production Planning and Control, 12 (2001) 584–590.
Hou, K.L., “An EPQ model with setup cost and process quality as functions of capital expenditure”, Applied Mathematical Modelling, 31 (2007) 10–17.
Inderfurth, K., Lindner, G., and Rachaniotis, N.P., “Lot sizing in a production system with rework and product deterioration”, International Journal of Production Research, 43 (2005) 1355–1374.
Inderfurth, K., Kovalyov, M.Y., Ng, C.T., and Werner, F., “Cost minimizing scheduling of work and rework processes on a single facility under deterioration of reworkables”, International Journal of Production Economics, 105 (2007) 345–356.
Jaber, M.Y., and Guiffrida, A.L., “Learning curves for processes generating defects requiring reworks”, European Journal of Operational Research, 159 (2004) 663-672.
Jaber, M.Y., and Kher, H.V., “The dual-phase learning-forgetting model”, International Journal of Production Economics, 76 (2002) 229–242.
Jaber, M.Y., and Bonney, M., “Economic manufacture quantity (EMQ) model with lot-size dependent learning and forgetting rates”, International Journal of Production Economics, 108 (2007) 359-367.
Jaber, M.Y., and Bonney, M., “Lot sizing with learning and forgetting in set-ups and in product quality”, International Journal of Production Economics, 83 (2003) 95-111.
Jaber, M.Y., “Lot sizing for an imperfect production process with quality corrective interruptions and improvements, and reduction in setups”, Computers and Industrial Engineering, 51 (2006) 781-790.
Jamal, A.A.M., Sarker, B.R., and Mondal, S., “Optimal manufacturing batch size with rework process at single-stage production system”, Computers and Industrial Engineering, 47 (2004) 77–89.
Keachie, E.C., and Fontana, R.J., “Effects of learning on optimal lot size”, Management Science, 32 (1966) 102-108.
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