Replenishment policy for an economic production quantity model considering rework and multiple shipments

  • Authors

    • Usman Ghani
    • Mubashir Hayat
    2020-08-24
    https://doi.org/10.14419/ijet.v9i3.31034
  • Economic Production Quantity (EPQ) Model, Optimal Replenishment Lot Size, Shipment Policy, Imperfection in Production Process, Backorders.

  • Abstract

    Determining the optimal replenishment lot size and shipment policy for a production setup has been of greater interest during the last few years. This paper derives the optimal replenishment lot size and shipment policy for an Economic Production Quantity (EPQ) model with rework of defective items. However, in a real life situation, multi-shipment policy is used in lieu of continuous issuing policy and generation of defective items is inevitable. The proposed research assume that all imperfect quality items are reworked to perfect quality items and then all perfect quality items are delivered to the customers. Mathematical modeling is used in this study and the long-run average production–inventory-delivery cost function is derived. Convexity of the cost function is proved by using the Hessian matrix equations. The closed-form optimal replenishment lot size and optimal number of shipments that minimize the long-run average costs for such an EPQ model are derived.

     

     

  • References

    1. [1] M.J. Rosenblatt, H.L. Lee, Economic production cycles with imperfect production process, IIE Trans. 18 (1986) 48–55. https://doi.org/10.1080/07408178608975329.

      [2] M.K. Salamh, M.Y. Jaber, Economic production quantity model for items with imperfect quality, Int. J. Prod. Econ. 64 (2000) 59–64. https://doi.org/10.1016/S0925-5273(99)00044-4.

      [3] A. Eroglu, G. Ozdemir, An economic ordering quantity model with defective items and shortages, Int. J. Prod. Econ. 106 (2007) 544–549. https://doi.org/10.1016/j.ijpe.2006.06.015.

      [4] E.L. Porteus, Optimal lot sizing process quality improvement and setup cost reduction, Oper. Res. 34 (1986) 137–144. https://doi.org/10.1287/opre.34.1.137.

      [5] C. Tapiero, Production learning and quality control, IIE Trans. 19 (1987) 362–370. https://doi.org/10.1080/07408178708975408.

      [6] P.A. Hayek, M.K. Salameh, Production lot sizing with the reworking of imperfect quality items produced, Prod. Plann. Control 12 (6) (2001) 584–590. https://doi.org/10.1080/095372801750397707.

      [7] K.L. Hou, L.C. Lin, Optimal production run length and capital investment with an imperfect production processes, Int. J. Syst. Sci. 35 (2004) 133–137. https://doi.org/10.1080/00207720410001671723.

      [8] P.Y. Chiu, Determining the optimal lot size for the finite production model with random defective rate, the rework process, and backlogging, Eng. Optim. 35 (4) (2003) 427–437. https://doi.org/10.1080/03052150310001597783.

      [9] K.N.F. Leung, A generalized geometric-programming solution to an economic production quantity model with flexibility and reliability considerations, Eur. J. Oper. Res. 176 (1) (2007) 240–251. https://doi.org/10.1016/j.ejor.2005.06.049.

      [10] K.L. Hou, An EPQ model with setup cost and process quality as functions of capital expenditure, Appl. Math. Modell. 31 (2007) 10–17. https://doi.org/10.1016/j.apm.2006.03.034.

      [11] S.S. Sana, An economic production lot size model in an imperfect production system, Eur. J. Oper. Res. 201 (2010) 158–170. https://doi.org/10.1016/j.ejor.2009.02.027.

      [12] S.S. Sana, A production-inventory model of imperfect quality products in a three-layer supply chain, Decis. Support Syst. 50 (2) (2011) 539–547. https://doi.org/10.1016/j.dss.2010.11.012.

      [13] M. Khan, M.Y. Jaber, M.I.M. Wahab, Economic order quantity model for items with imperfect quality with learning in inspection, Int. J. Prod. Econ. 124 (1) (2010) 87–96. https://doi.org/10.1016/j.ijpe.2009.10.011.

      [14] M.I.M. Wahab, M.Y. Jaber, Economic order quantity model for items with imperfect quality, different holding costs, and learning effects: a note, Comput. Ind. Eng. 58 (1) (2010) 186–190. https://doi.org/10.1016/j.cie.2009.07.007.

      [15] M. Khan, M.Y. Jaber, A.L. Guiffrida, S. Zolfaghari, A review of the extensions of a modified EOQ model for imperfect quality items, Int. J. Prod. Econ. 132 (1) (2011) 1–12. https://doi.org/10.1016/j.ijpe.2011.03.009.

      [16] J.-T. Hsu, L.-F. Hsu, Two EPQ models with imperfect production processes, inspection errors, planned backorders, and sales returns, Comput. Ind. Eng. 64 (1) (2013) 389–402. https://doi.org/10.1016/j.cie.2012.10.005.

      [17] J.-T. Hsu, L.-F. Hsu, An EOQ model with imperfect quality items, inspection errors, shortage backordering, and sales returns, Int. J. Prod. Econ. 143 (1) (2013) 162–170. https://doi.org/10.1016/j.ijpe.2012.12.025.

      [18] J. Taheri-Tolgari, A. Mirzazadeh, F. Jolai, An inventory model for imperfect items under inflationary conditions with considering inspection errors, Comput. Math. Appl. 63 (6) (2012) 1007–1019. https://doi.org/10.1016/j.camwa.2011.09.050.

      [19] B. Sarkar, I. Moon, An EPQ model with inflation in an imperfect production system, Appl. Math. Comput. 217 (13) (2011) 6159–6167. https://doi.org/10.1016/j.amc.2010.12.098.

      [20] M.Y. Jaber, S. Zanoni, L.E. Zavanella, An entropic economic order quantity (EnEOQ) for items with imperfect quality, Appl. Math. Modell. 37 (6) (2013) 3982–3992. https://doi.org/10.1016/j.apm.2012.07.046.

      [21] M. Khan, M.Y. Jaber, A.-R. Ahmad, An integrated supply chain model with errors in quality inspection and learning in production, Omega 42 (1) (2014) 16–24. https://doi.org/10.1016/j.omega.2013.02.002.

      [22] M.Y. Jaber, S. Zanoni, L.E. Zavanella, An economic order quantity models for imperfect items with buy and repair options, Int. J. Prod. Econ. 78 (2014) 89, https://doi.org/10.1016/j.ijpe.2013.10.014.

      [23] Ertogral, K., M. Darwish and M. Ben-Daya (2007). "Production and shipment lot sizing in a vendor–buyer supply chain with transportation cost." European Journal of Operational Research 176(3): 1592-1606. https://doi.org/10.1016/j.ejor.2005.10.036.

      [24] Sajadieh, M. S. and M. R. A. Jokar (2009). "Optimizing shipment, ordering and pricing policies in a two-stage supply chain with price-sensitive demand." Transportation Research Part E: Logistics and Transportation Review 45(4): 564-571. https://doi.org/10.1016/j.tre.2008.12.002.

      [25] Chiu, Y. P., S. Liu, C. Chiu and H. Chang (2011). "Mathematical modeling for determining the replenishment policy for EMQ model with rework and multiple shipments." Mathematical and Computer Modelling 54(9): 2165-2174. https://doi.org/10.1016/j.mcm.2011.05.025.

      [26] Chiu, S. W., L. Lin, K. Chen and C. Chou (2013). "Determining production–shipment policy for a vendor–buyer integrated system with rework and an amending multi-delivery schedule." Economic Modelling 33: 668-675. https://doi.org/10.1016/j.econmod.2013.05.020.

      [27] Kropf, A. and P. Sauré (2014). "Fixed costs per shipment." Journal of International Economics 92(1): 166-184. https://doi.org/10.1016/j.jinteco.2013.10.003.

      [28] Ekici, A., B. Altan and O. Ö. Özener (2016). "Pricing decisions in a strategic single retailer/dual suppliers setting under order size constraints." International Journal of Production Research 54(7): 1887-1898. https://doi.org/10.1080/00207543.2015.1054451.

      [29] Giri, B., A. Chakraborty and T. Maiti (2017). "Consignment stock policy with unequal shipments and process unreliability for a two-level supply chain." International Journal of Production Research 55(9): 2489-2505. https://doi.org/10.1080/00207543.2016.1233362.

      [30] Sağlam, Ü. and A. Banerjee (2017). "Integrated multiproduct batch production and truck shipment scheduling under different shipping policies." Omega. https://doi.org/10.2139/ssrn.2820717.

  • Downloads

  • How to Cite

    Ghani, U., & Hayat, M. (2020). Replenishment policy for an economic production quantity model considering rework and multiple shipments. International Journal of Engineering & Technology, 9(3), 758-763. https://doi.org/10.14419/ijet.v9i3.31034

    Received date: 2020-07-23

    Accepted date: 2020-07-29

    Published date: 2020-08-24