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Effects of Unequal Lot Size and Variable Transportation in Unreliable Supply Chain Management

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  • Soumya Kanti Hota

    (Department of Mathematics, Kazi Nazrul University, Nazrul Road, Kalla Bypass More, P.O.—Kalla (C. H.) Asansol, West Bengal 713340, India
    Department of Mathematics, Debra Thana Sahid Kshudiram Smriti Mahavidyalaya, Debra, Paschim Medinipur, West Bengal 721101, India)

  • Biswajit Sarkar

    (Department of Industrial Engineering, Yonsei University, 50 Yonsei-ro, Sinchon-dong, Seodaemun-gu, Seoul 03722, Korea)

  • Santanu Kumar Ghosh

    (Department of Mathematics, Kazi Nazrul University, Nazrul Road, Kalla Bypass More, P.O.—Kalla (C. H.) Asansol, West Bengal 713340, India)

Abstract

The effect of unreliable players on the supply chain management with a single-setup-multi-unequal-increasing-delivery-policy (SSMUID) along with a service-dependent demand and investment is discussed in this model. The manufacturer is unreliable which causes an increase of lead time and shortage. For solving the shortage problem and reducing lead time crashing cost (LTCC), an investment is utilized with the variable backorder price discounts. The number of transportation increases due to the new transportation policy and it causes pollution. Besides the fixed transportation and carbon emission cost (FTCEC), a container dependent carbon emission cost is applied. Some investments for setup cost reduction (SCR), ordering cost reduction (OCR), and quality improvement (QI) are considered. The lead time demand follows a normal distribution. The total cost of the supply chain is optimized and the model is tested numerically. The main intent of this study is to solve the shortage problem which occurs due to unreliability of the manufacturer. The study helps to reduce the unreliability issue of the manufacturer. The objective function is solved by using the classical optimization technique. Numerical results show that the discount for partial backorder enhances the profitability of the manufacturer. The sensitiveness of the parameters are discussed through the sensitivity of analysis and some special cases. Managerial insights provide the applicability of this study among different sectors.

Suggested Citation

  • Soumya Kanti Hota & Biswajit Sarkar & Santanu Kumar Ghosh, 2020. "Effects of Unequal Lot Size and Variable Transportation in Unreliable Supply Chain Management," Mathematics, MDPI, vol. 8(3), pages 1-24, March.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:3:p:357-:d:329061
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    1. Mukhopadhyay, Samar K. & Ma, Huafan, 2009. "Joint procurement and production decisions in remanufacturing under quality and demand uncertainty," International Journal of Production Economics, Elsevier, vol. 120(1), pages 5-17, July.
    2. Gruson, Matthieu & Cordeau, Jean-François & Jans, Raf, 2018. "The impact of service level constraints in deterministic lot sizing with backlogging," Omega, Elsevier, vol. 79(C), pages 91-103.
    3. Glock, C. H., 2012. "Lead time reduction strategies in a single-vendor-single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand," Publications of Darmstadt Technical University, Institute for Business Studies (BWL) 57816, Darmstadt Technical University, Department of Business Administration, Economics and Law, Institute for Business Studies (BWL).
    4. Chen, Frank Y. & Krass, Dmitry, 2001. "Inventory models with minimal service level constraints," European Journal of Operational Research, Elsevier, vol. 134(1), pages 120-140, October.
    5. Jain, Aditya & Bala, Ram, 2018. "Differentiated or integrated: Capacity and service level choice for differentiated products," European Journal of Operational Research, Elsevier, vol. 266(3), pages 1025-1037.
    6. Pan, Jason Chao-Hsien & Lo, Ming-Cheng & Hsiao, Yu-Cheng, 2004. "Optimal reorder point inventory models with variable lead time and backorder discount considerations," European Journal of Operational Research, Elsevier, vol. 158(2), pages 488-505, October.
    7. Inderfurth, K. & Kiesmüller, G.P., 2015. "Exact and heuristic linear-inflation policies for an inventory model with random yield and arbitrary lead times," European Journal of Operational Research, Elsevier, vol. 245(1), pages 109-120.
    8. Biswajit Sarkar & Sharmila Saren & Debjani Sinha & Sun Hur, 2015. "Effect of Unequal Lot Sizes, Variable Setup Cost, and Carbon Emission Cost in a Supply Chain Model," Mathematical Problems in Engineering, Hindawi, vol. 2015, pages 1-13, November.
    9. Lin, Yu-Jen, 2008. "Minimax distribution free procedure with backorder price discount," International Journal of Production Economics, Elsevier, vol. 111(1), pages 118-128, January.
    10. Glock, Christoph H., 2012. "Lead time reduction strategies in a single-vendor–single-buyer integrated inventory model with lot size-dependent lead times and stochastic demand," International Journal of Production Economics, Elsevier, vol. 136(1), pages 37-44.
    11. Goyal, Suresh K. & Nebebe, Fassil, 2000. "Determination of economic production-shipment policy for a single-vendor-single-buyer system," European Journal of Operational Research, Elsevier, vol. 121(1), pages 175-178, February.
    12. Sarkar, Biswajit & Ganguly, Baishakhi & Sarkar, Mitali & Pareek, Sarla, 2016. "Effect of variable transportation and carbon emission in a three-echelon supply chain model," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 91(C), pages 112-128.
    13. Song Xu & Xiaotong Zhang & Lipan Feng & Wenting Yang, 2020. "Disruption risks in supply chain management: a literature review based on bibliometric analysis," International Journal of Production Research, Taylor & Francis Journals, vol. 58(11), pages 3508-3526, June.
    14. Evan L. Porteus, 1986. "Optimal Lot Sizing, Process Quality Improvement and Setup Cost Reduction," Operations Research, INFORMS, vol. 34(1), pages 137-144, February.
    15. Albrecht, Martin, 2017. "Optimization of safety stocks in models with an order service level objective or constraint," European Journal of Operational Research, Elsevier, vol. 263(3), pages 900-909.
    16. Sawik, Tadeusz, 2019. "Disruption mitigation and recovery in supply chains using portfolio approach," Omega, Elsevier, vol. 84(C), pages 232-248.
    17. Kaczmarczyk, Waldemar, 2020. "Valid inequalities for proportional lot-sizing and scheduling problem with fictitious microperiods," International Journal of Production Economics, Elsevier, vol. 219(C), pages 236-247.
    18. Hill, Roger M., 1997. "The single-vendor single-buyer integrated production-inventory model with a generalised policy," European Journal of Operational Research, Elsevier, vol. 97(3), pages 493-499, March.
    19. Ullah, Mehran & Sarkar, Biswajit, 2020. "Recovery-channel selection in a hybrid manufacturing-remanufacturing production model with RFID and product quality," International Journal of Production Economics, Elsevier, vol. 219(C), pages 360-374.
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    1. Hota, Soumya Kanti & Sarkar, Biswajit & Ghosh, Santanu Kumar & Cheikhrouhou, Naoufel & Treviño-Garza, Gerardo, 2024. "What should be the best retail strategy to deal with an unequal shipment from an unreliable manufacturer?," Journal of Retailing and Consumer Services, Elsevier, vol. 76(C).

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