Joint Replenishment of Partially Substitutable Imperfect Items with Cost of Substitution

Document Type : Research/ Original/ Regular Article

Authors

Department of Industrial Engineering, South Tehran Branch, Islamic Azad University, Tehran, Iran

Abstract

In inventory management, some items can be substituted for others. This means that in case of a shortage, some of the demand can be met by the substitute item, leading to reduced shortage costs. This paper examines two partially substitutable products with imperfect items in the order       quantity. Imperfect items are removed after inspection. The two items have the same cycle time, and in the case of a shortage, part of the demand is substituted. The model is presented and solved symbolically for some special cases, and a numerical example is provided for the general case. The findings show that increasing substitution costs, decreasing holding costs of the substitutable item, and decreasing the percentage of substitution could reduce the time with a shortage.     Moreover, increasing substitution and holding costs increases the total inventory costs, while the increase in the percentage of substitution could either increase or decrease the total inventory costs in different intervals.
 

Keywords

Main Subjects

Smiley face

References

[1] M. Erfanian, and B. Bayani, “Simulation Based Optimization Multi Echelon Inventory system with uncertain and prioritize Demand”, Iranian Journal of Supply Chain Management, vol. 20, no. 61, pp. 29-33, 2019, DOR: 20.1001.1.20089198.1397.20.61.3.6. [In Persian]
[2] Z. Drezner, H. Gurnani, and B.A. Pasternack, “An EOQ model with substitutions between products”, J. Oper. Res. Soc., vol. 46, no. 7,  pp. 887-891, 1995, https://doi.org/10.1057/jors.1995.120.
[3]  H. Gurnani, and Z. Drezner, “Deterministic hierarchical substitution inventory models”, J. Oper. Res. Soc., vol. 51, no. 1, pp. 129-133, 2000, https://doi.org/10.1057/palgrave.jors.2600843.
[4] H. Y. Kang, A.H. Lee, and C.M. Lai, “An integrated replenishment model with quantity discounts, reentry and downward substitution for control wafers”, J. Intell. Manuf., vol. 23, no. 5, pp. 1745-176, 2012, https://doi.org/10.1007/s10845-010-0479-z.
[5]  A. A. Taleizadeh, M. Noori-daryan, and L.E. Cárdenas-Barrón, “Joint optimization of price, replenishment frequency, replenishment cycle and production rate in vendor managed inventory system with deteriorating items”, Int. J. Prod. Econ., vol. 159, pp. 285-295, 2015, https://doi.org/10.1016/j.ijpe.2014.09.009
[6]  S. M. Seyedhoseini, R. Rashid, I. Kamalpour, and E.Zangeneh, “Application of queuing theory in inventory systems with substitution flexibility”, J. Ind. Eng. Int., vol. 11, pp. 37-44. 2015, https://doi.org/10.1007/s40092-015-0099-5.
[7] A. Burnetas, and O. Kanavetas, “Inventory policies for two products under Poisson demand: Interaction between demand substitution, limited storage capacity and replenishment time uncertainty”, Nav. Res. Logist., vol. 65, no. 8, pp. 676-698, 2018,  https://doi.org/10.1002/nav.21788.
[8] B. Maddah,  M. Kharbeche,  S. Pokharel, and A. Ghoniem, “Joint replenishment model for multiple products with substitution”, Appl. Math. Model., vol. 40, no. 17-18, pp. 7678-7688, 2016, https://doi.org/10.1016/j.apm.2016.03.027.
[9] B.A. Pasternack, and Z. Drezner, “Optimal inventory policies for substitutable commodities with stochastic demand”, Nav. Res. Logist., vol. 38, no. 2, pp. 221-240, 1991, https://doi.org/10.1002/1520-6750(199104)38:2%3C221::AID-NAV3220380208%3E3.0.CO;2-7
[10] R. N. Giri, S. K. Mondal, and M. Maiti, “Joint replenishment model of both-ways and one-way substitution among products in fixed time horizon”, Int. J. Math. Oper. Res., vol. 14, no. 1, pp. 30-52, 2019, https://doi.org/10.1504/IJMOR.2019.096977.
[11] H. Mokhtari, “Economic order quantity for joint complementary and substitutable items”, Int. J. Math. Comput. Simul., vol. 154, pp. 34-47, 2018, https://doi.org/10.1016/j.matcom.2018.06.004.
[12] R. K. Mishra, and V. K. Mishra, “Effect of Deterioration and Partial Substitution on Optimal Inventory Decisions for Complementary and Substitutable Items with Cost of Substitution under Joint Replenishment”, Int. J. Inf. Manag. Sci., vol. 31, no. 4, pp. 393-422, 2020, https://doi.org/10.6186/IJIMS.202012_31(4).0005.
[13] R. H. Teunter, and S. Kuipers, “Inventory control with demand substitution: new insights from a two-product Economic Order Quantity analysis”, Omega, vol. 113, pp. 102712, 2022, https://doi.org/10.1016/j.omega.2022.102712
 [14] M. Salameh, and M. Jaber, “Economic production quantity model for items with imperfect quality”, Int. J. Prod. Econ., vol. 64, no. 1, pp. 59-64, 2000, https://doi.org/10.1016/S0925-5273(99)00044-4.
[15] S. K. Goyal, and L. E. Cárdenas-Barrón, “Note on: economic production quantity model for items with imperfect quality–a practical approach”, Int. J. Prod. Econ., vol. 77, no. 1, pp. 85-87, 2002, https://doi.org/10.1016/S0925-5273(01)00203-1.
[16] J. Rezaei, “Economic order quantity model with backorder for imperfect quality items”, Proceedings. 2005 IEEE International Engineering Management Conference, 2005., St. John's, NL, Canada, 2005, pp. 466-470, DOI: 10.1109/IEMC.2005.1559191.
[17] J. C.Yu, H. M. Wee, and J. M. Chen, “Optimal ordering policy for a deteriorating item with imperfect quality and partial backordering”, J. Chin. Inst. Chem. Eng., vol. 22, no. 6, pp. 509-520. 2005, https://doi.org/10.29977/JCIIE.200511.0007.
[18] S. Papachristos, and I. Konstantaras, “Economic ordering quantity models for items with imperfect quality”, Int. J. Prod. Econ., vol. 100, no. 1, pp. 148-15, 2006, https://doi.org/10.1016/j.ijpe.2004.11.004.
[19] B. Maddah, and M. Y. Jaber, “Economic order quantity for items with imperfect quality: revisited”, Int. J. Prod. Econ., vol. 112, no. 2, pp. 808-815, 2008, https://doi.org/10.1016/j.ijpe.2007.07.003.
[20] B. Maddah, M. K. Salameh, and L. Moussawi-Haidar, “Order overlapping: A practical approach for preventing shortages during screening”, Comput. Ind. Eng., vol. 58, no. 4, pp. 691-695, 2010, https://doi.org/10.1016/j.cie.2010.01.014.
[21] S. S. Sana, “A production-inventory model of imperfect quality products in a three-layer supply chain”, Decis. Support Syst., vol. 50, no. 2, pp. 539-547, 2011, https://doi.org/10.1016/j.dss.2010.11.012.
[22] S. Paul, M.I.M. Wahab, and P. Ongkunaruk, “Joint replenishment with imperfect items and price discoun”, Comput. Ind. Eng., vol. 74, pp. 179-18, 2014, https://doi.org/10.1016/j.cie.2014.05.015.
[23] L. Moussawi-Haidar, M. Salameh, and W. Nasr, “Effect of deterioration on the instantaneous replenishment model with imperfect quality items”, Appl. Math. Model., vol. 38, no. 24, pp. 5956-596. 2014, https://doi.org/10.1016/j.apm.2014.05.003.
[24] J. Bhowmick, “Optimal inventory policies for imperfect inventory with price dependent stochastic demand and partially backlogged shortages”, Yugoslav Journal of Operations Research, vol. 22, no. 2, pp. 199-223, 2012, https://doi.org/10.2298/YJOR101011007B
 [25] A. Mukhopadhyay, and A. Goswami, “An inventory model with shortages for imperfect items using substitution of two products”, Int. J. Oper. Res., vol. 30, no. 2, pp. 193-219, 2017, https://doi.org/10.1504/IJOR.2017.086525.

Files

History

  • Receive Date: 19 November 2023
  • Revise Date: 30 December 2023
  • Accept Date: 06 February 2024

Share

How to cite

Statistics