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A variable neighborhood search heuristic for supply chain coordination using dynamic price discounts

  • Research Paper
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EURO Journal on Transportation and Logistics

Abstract

This research studies the problem of supply chain coordination using temporary price discounts. The supplier decides how much discount should be introduced in each period to each of the customers, aiming to maximize its profit, while giving the customers the incentive to order in the desired periods. To solve this problem, a variable neighborhood search is introduced. The results of computational experiments indicate that the variable neighborhood search outperforms the mixed integer-based heuristic introduced earlier in the literature for this problem. Our metaheuristic procedure found the optimal solution for small instances in more than 80% of the cases. Moreover, an advantage of this metaheuristic is the significantly shorter computing time that allows applying it to larger instances.

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References

  • Arshinder K, Kanda A, Deshmukh SG (2008) Supply chain coordination: perspectives, empirical studies and research directions. Int J Prod Econ 115(2):316–335

    Article  Google Scholar 

  • Ben-Daya M, Darwish M, Ertogral K (2008) The joint economic lot sizing problem: review and extensions. Eur J Oper Res 185(2):726–742

    Article  Google Scholar 

  • Buhayenko V, van Eikenhorst E (2016) Synchronization of customers’ orders using discounts. Int J Syst Sci Oper Logist 3(3):148–162

    Google Scholar 

  • Buhayenko V, den Hertog D (2017) Adjustable robust optimisation approach to optimise discounts for multi-period supply chain coordination under demand uncertainty. Int J Prod Res 55(22):6801–6823

    Article  Google Scholar 

  • Busher U, Lindner G (2004) Ensuring feasibility in ‘a generalized quantity discount pricing model to increase supplier’s profits’. J Oper Res Soc 55(6):667–670

    Article  Google Scholar 

  • Cachon PG (2003) Supply chain coordination with contracts. In: Handbooks in operations research and management science, vol 11, pp 227–339

    Google Scholar 

  • Cha BC, Moon IK (2005) The joint replenishment problem with quantity discounts under constant demand. OR Spectr 27(4):569–581

    Article  Google Scholar 

  • Chang CT, Chiou CC, Yang YW, Chang SC, Wang W (2010) A three-echelon supply chain coordination with quantity discounts for multiple items. Int J Syst Sci 41(5):561–573

    Article  Google Scholar 

  • Chung W, Talluri S, Narasimhan R (2011) Price markdown scheme in a multi-echelon supply chain in a high-tech industry. Eur J Oper Res 215(3):581–589

    Article  Google Scholar 

  • Elmaghraby W, Keskinocak P (2003) Dynamic pricing in the presence of inventory considerations: research overview, current practices, and future directions. Manag Sci 49(10):1287–1309

    Article  Google Scholar 

  • Eppen GD, Martin RK (1987) Solving multi-item capacitated lot-sizing problems using variable redefinition. Oper Res 35(6):832–848

    Article  Google Scholar 

  • Glock CH (2012) The joint economic lot size problem: a review. In J Prod Econ 135(2):671–686

    Article  Google Scholar 

  • Goyal SK, Satir AT (1989) Joint replenishment inventory control: deterministic and stochastic models. Eur J Oper Res 38(1):2–13

    Article  Google Scholar 

  • Heydari J (2014a) Coordinating suppliers reorder point: a coordination mechanism for supply chains with long supplier lead time. Comput Oper Res 48:89–101

    Article  Google Scholar 

  • Heydari J (2014b) Supply chain coordination using time-based temporary price discounts. Comput Ind Eng 75:96–101

    Article  Google Scholar 

  • Heydari J (2015) Coordinating replenishment decisions in a two-stage supply chain by considering truckload limitation based on delay in payments. Int J Syst Sci 46(10):1897–1908

    Article  Google Scholar 

  • Heydari J, Norouzinasab Y (2015) A two-level discount model for coordinating a decentralized supply chain considering stochastic price-sensitive demand. J Ind Eng Int 11(4):531–542

    Article  Google Scholar 

  • Heydari J, Mahmoodi M, Taleizadeh AA (2016) Lead time aggregation: a three-echelon supply chain model. Transp Res Part E Logist Transp Rev 89:215–233

    Article  Google Scholar 

  • Heydari J, Choi TM, Radkhah S (2017a) Pareto improving supply chain coordination under a money-back guarantee service program. Serv Sci 9(2):91–105

    Article  Google Scholar 

  • Heydari J, Govindan K, Jafari A (2017b) Reverse and closed loop supply chain coordination by considering government role. Transp Res Part D Transp Environ 52:379–398

    Article  Google Scholar 

  • Heydari J, Rastegar M, Glock CH (2017c) A two-level delay in payments contract for supply chain coordination: the case of credit-dependent demand. Int J Prod Econ 191:26–36

    Article  Google Scholar 

  • Ke GY, Bookbinder JH (2012) The optimal quantity discount that a supplier should offer. J Oper Res Soc 63(3):354–367

    Article  Google Scholar 

  • Khouja M, Goyal S (2008) A review of the joint replenishment problem literature: 1989–2005. Eur J Oper Res 186(1):1–16

    Article  Google Scholar 

  • Kim KH, Hwang H (1988) An incremental discount pricing schedule with multiple customers and single price break. Eur J Oper Res 35(1):71–79

    Article  Google Scholar 

  • Kohli R, Park H (1989) A cooperative game theory model of quantity discounts. Manag Sci 35(6):693–707

    Article  Google Scholar 

  • Lal R, Staelin R (1984) An approach for developing an optimal quantity discount pricing policy. Manag Sci 30(12):1524–1539

    Article  Google Scholar 

  • Li J, Liu L (2006) Supply chain coordination with quantity discount policy. Int J Prod Econ 101(1):89–99

    Article  Google Scholar 

  • Lightfoot HW, Baines TS, Smart P (2012) Emerging technology and the service delivery supply chain. In: Chan KH, Lettice F, Durowoju AO (eds) Decision-making for supply chain integration: supply chain integration. Springer, London, pp 211–226

    Chapter  Google Scholar 

  • Marban S, van der Zwaan R, Grigoriev A, Hiller B, Vredeveld T (2012) Dynamic pricing problems with elastic demand. Oper Res Lett 40(3):175–179

    Article  Google Scholar 

  • Martin GE (1994) Note on an EOQ model with a temporary sale price. Int J Prod Econ 37(2–3):241–243

    Article  Google Scholar 

  • Monahan JP (1984) A quantity discount pricing model to increase vendor profits. Manag Sci 30(6):720–726

    Article  Google Scholar 

  • Munson CL, Rosenblatt MJ (2001) Coordinating a three-level supply chain with quantity discount. IIE Trans 33(5):371–384

    Google Scholar 

  • Phillips RL (2005) Pricing and revenue optimization. Stanford Business Books, Stanford

    Google Scholar 

  • Rosenblatt MJ, Lee HL (1985) Improving profitability with quantity discounts under fixed demand. IIE Trans 17(4):388–394

    Article  Google Scholar 

  • Sari DP, Rusdiansyah A, Huang L (2012) Models of joint economic lot-sizing problem with time-based temporary price discounts. Int J Prod Econ 139(1):145–154

    Article  Google Scholar 

  • Simatupang TM, Sandroto IV, Lubis SH (2004) Supply chain coordination in a fashion firm. Supply Chain Manag Int J 9(3):256–268

    Article  Google Scholar 

  • Solano-Charris E, Prins C, Santos AC (2015) Local search based metaheuristics for the robust vehicle routing problem with discrete scenarios. Appl Soft Comput 32:518–531

    Article  Google Scholar 

  • Tersine RJ (1994) Principles of inventory and materials management. Prentice-Hall, Englewood Cliffs

    Google Scholar 

  • Wagner HM, Whitin TM (1958) Dynamic version of the economic lot size model. Manag Sci 5(1):89–96

    Article  Google Scholar 

  • Wang Q (2005) Discount pricing policies and the coordination of decentralized distribution systems. Decis Sci 36(4):627–646

    Article  Google Scholar 

  • Wee HM, Yu J (1997) A deteriorating inventory model with a temporary price discount. Int J Prod Econ 53(1):81–90

    Article  Google Scholar 

Download references

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Authors and Affiliations

  1. Department of Economics and Business Economics, CORAL, Aarhus University, Aarhus, Denmark

    Viktoryia Buhayenko & Anders Thorstenson

  2. Department of Systems Engineering and Engineering Management, The Chinese University of Hong Kong, Sha Tin, Hong Kong

    Sin C. Ho

Authors
  1. Viktoryia Buhayenko
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  2. Sin C. Ho
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  3. Anders Thorstenson
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Correspondence to Viktoryia Buhayenko.

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Buhayenko, V., Ho, S.C. & Thorstenson, A. A variable neighborhood search heuristic for supply chain coordination using dynamic price discounts. EURO J Transp Logist 7, 363–385 (2018). https://doi.org/10.1007/s13676-018-0122-2

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  • DOI: https://doi.org/10.1007/s13676-018-0122-2

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