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A production-inventory model in an imperfect production process

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  • Sana, Shib Sankar

Abstract

The paper develops a model to determine the optimal product reliability and production rate that achieves the biggest total integrated profit for an imperfect manufacturing process. The basic assumption of the classical Economic Manufacturing Quantity (EMQ) model is that all manufacturing items are of perfect quality. The assumption is not true in practice. Most of the production system produces perfect and imperfect quality items. In some cases the imperfect quality (non conforming) items are reworked at a cost to restore its quality to the original one. Rework cost may be reduced by improvements in product reliability (i.e., decreasing in product reliability parameter). Lower value of product reliability parameter results in increase development cost of production and also smaller quantity of nonconforming products. The unit production cost is a function of product reliability parameter and production rate. As a result, higher development cost increases unit production cost. The problem of optimal planning work and rework processes belongs to the broad field of production-inventory model which deals with all kinds of reuse processes in supply chains. These processes aim to recover defective product items in such a way that they meet the quality level of 'good item'. The benefits from imperfect quality items are: regaining the material and value added on defective items and improving the environment protection. In this point of view, a model is introduced here to guide a firm/industry in addressing variable product reliability factor, variable unit production cost and dynamic production rate for time-varying demand. The paper provides an optimal control formulation of the problem and develops necessary and sufficient conditions for optimality of the dynamic variables. In this purpose, the Euler-Lagrange method is used to obtain optimal solutions for product reliability parameter and dynamic production rate. Finally, numerical examples are given to illustrate the proposed model.

Suggested Citation

  • Sana, Shib Sankar, 2010. "A production-inventory model in an imperfect production process," European Journal of Operational Research, Elsevier, vol. 200(2), pages 451-464, January.
  • Handle: RePEc:eee:ejores:v:200:y:2010:i:2:p:451-464
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    References listed on IDEAS

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    1. Ray, J. & Chaudhuri, K. S., 1997. "An EOQ model with stock-dependent demand, shortage, inflation and time discounting," International Journal of Production Economics, Elsevier, vol. 53(2), pages 171-180, November.
    2. Sana, S. & Goyal, S. K. & Chaudhuri, K. S., 2004. "A production-inventory model for a deteriorating item with trended demand and shortages," European Journal of Operational Research, Elsevier, vol. 157(2), pages 357-371, September.
    3. Gupta, Yash P. & Somers, Toni M., 1992. "The measurement of manufacturing flexibility," European Journal of Operational Research, Elsevier, vol. 60(2), pages 166-182, July.
    4. Datta, T. K. & Pal, A. K., 1991. "Effects of inflation and time-value of money on an inventory model with linear time-dependent demand rate and shortages," European Journal of Operational Research, Elsevier, vol. 52(3), pages 326-333, June.
    5. Bengtsson, Jens & Olhager, Jan, 2002. "Valuation of product-mix flexibility using real options," International Journal of Production Economics, Elsevier, vol. 78(1), pages 13-28, July.
    6. Pal, S. & Goswami, A. & Chaudhuri, K. S., 1993. "A deterministic inventory model for deteriorating items with stock-dependent demand rate," International Journal of Production Economics, Elsevier, vol. 32(3), pages 291-299, November.
    7. Harvey M. Wagner & Thomson M. Whitin, 1958. "Dynamic Version of the Economic Lot Size Model," Management Science, INFORMS, vol. 5(1), pages 89-96, October.
    8. Bylka, S.Stanislaw & Rempala, Ryszarda, 2004. "Heuristics for impulse replenishment with continuous periodic demand," International Journal of Production Economics, Elsevier, vol. 88(2), pages 183-190, March.
    9. Sarker, Bhaba R. & Pan, Haixu, 1994. "Effects of inflation and the time value of money on order quantity and allowable shortage," International Journal of Production Economics, Elsevier, vol. 34(1), pages 65-72, February.
    10. Urban, Timothy L., 1995. "Inventory models with the demand rate dependent on stock and shortage levels," International Journal of Production Economics, Elsevier, vol. 40(1), pages 21-28, June.
    11. Skouri, K. & Papachristos, S., 2003. "Optimal stopping and restarting production times for an EOQ model with deteriorating items and time-dependent partial backlogging," International Journal of Production Economics, Elsevier, vol. 81(1), pages 525-531, January.
    12. Datta, T. K. & Paul, K. & Pal, A. K., 1998. "Demand promotion by upgradation under stock-dependent demand situation - a model," International Journal of Production Economics, Elsevier, vol. 55(1), pages 31-38, June.
    13. Urban, Timothy L., 2005. "Inventory models with inventory-level-dependent demand: A comprehensive review and unifying theory," European Journal of Operational Research, Elsevier, vol. 162(3), pages 792-804, May.
    14. Gupta, Yash P. & Goyal, Sameer, 1989. "Flexibility of manufacturing systems: Concepts and measurements," European Journal of Operational Research, Elsevier, vol. 43(2), pages 119-135, November.
    15. Sana, Shib Sankar & Goyal, Suresh Kumar & Chaudhuri, Kripasindhu, 2007. "An imperfect production process in a volume flexible inventory model," International Journal of Production Economics, Elsevier, vol. 105(2), pages 548-559, February.
    16. Hariga, Moncer A. & Benkherouf, Lakdere, 1994. "Optimal and heuristic inventory replenishment models for deteriorating items with exponential time-varying demand," European Journal of Operational Research, Elsevier, vol. 79(1), pages 123-137, November.
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