Abstract
In this chapter, we consider the problem of determining an optimal set of winning suppliers in a procurement auction where the buyer wishes to procure high volumes of a homogeneous item in a staggered way in accordance with a predefined schedule and the suppliers respond with bids that specify volume discounts and also delivery lead times. We show that the winner determination problem, which turns out to be a multi-objective optimization problem, cannot be satisfactorily solved by traditional methods of multi-objective optimization. We formulate the problem first as an integer program with constraints capturing lead time requirements and show that the integer program is an extended version of the multiple knapsack problems. We discover certain properties of this integer program and exploit the properties to simplify it to a 0–1 mixed integer program (MIP), which can be solved more efficiently. We next explore a more efficient approach to solving the problem using a linear relaxation of the 0–1 MIP in conjunction with a greedy heuristic. Using extensive numerical experimentation, we show the efficacy of the 0–1 MIP and the proposed heuristic.
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References
Belenson S, Kapur K (1973) An algorithm for solving multi-criteria linear programming problems with examples. Oper Res Q 24(1):65–77
Bellosta M, Brigui I, Kornman S, Vanderpooten D (2004) A multi-criteria model for electronic auctions. In: Proceedings of the 2004 ACM symposium on applied computing, pp 759–765. ACM Press, New York
Bichler M (2000) An experimental analysis of multi-attribute auctions. Decis Support Syst 29(3):249–268
Bichler M, Kalagnanam J (2001) Winner determination in multi-attribute auctions. Technical report RC22478 (W0206-018), IBM
Buyukozkan G, Bilsel RU (2009) Multi-criteria models for e-health service evaluation. In: Dwivedi AN (ed) Handbook of research on information technology management and clinical data administration in healthcare, chapter 10. IGI Global, Hershey, pp 143–160
Chandrashekar TS, Narahari Y, Rosa CH, Kulkarni D, Dayama P, Tew JD (2007) Auction based mechanisms for electronic procurement. IEEE Trans Autom Sci Eng 4(3):297–321
Cohon (1978) Multi-objective programming and planning. In: Bellman R (ed) Mathematics in science and engineering, vol 140. Academic Press, New York, pp 115–127
Dang V, Jennings N (2003) Optimal clearing algorithms for multi-unit single-item and multiunit combinatorial auctions with demand-supply function bidding. Technical report, Department of Electronics and Computer Science, University of Southampton, UK
Davenport A, Kalagnanam J (2001) Price negotiations for direct procurement. Research report RC 22078, IBM Research, Yorktown Heights, NJ, USA
Dayama P, Narahari Y (2007) Design of multi-unit electronic exchanges through decomposition. IEEE Trans Autom Sci Eng 4(1):67–74
Eso M, Ghosh S, Kalagnanam J, Ladanyi L (2001) Bid evaluation in procurement auctions with piece-wise linear supply curves. Technical report IBM research report RC 22219, IBM
Gautam RK, Hemachandra H, Narahari Y, Prakash H, Kulkarni D, Tew JD (2009) An optimal mechanism for multi-unit procurement with volume discount bids. Int J Oper Res 6(1):70–91
Goossens DR, Maas JAT, Spieksma FCR, van de Klundert JJ (2007) Exact algorithms for procurement problems under a total quantity discount structure. Eur J Oper Res 178(2):603–626
Haimes Y (1973) Integrated system identification and optimization. In: Leondes C (ed) Control and dynamic system: advances in theory and application, vol 9. Academic Press, New York, pp 435–518
Hohner G, Rich J, Ng E, Reid G, Davenport A, Kalagnanam J, Lee H, An A (2003) Combinatorial and quantity-discount procurement auctions benefit, mars incorporated and its suppliers. Interfaces 33(1):23–35
Kalagnanam J, Parkes D (2003) Auctions, bidding, and exchange design. In: Simchi-Levi D, Wu SD, Shen ZM (eds) Supply chain analysis in the eBusiness area. Kluwer Academic Publishers, Norwell
Kameshwaran S, Narahari Y (2009) Efficient algorithms for non–convex linear knapsack problems. Eur J Oper Res 192(1):56–68
Kameshwaran S, Narahari Y, Rosa CH, Kulkarni DM, Tew JD (2006) Multi-attribute electronic procurement using goal programming. Eur J Oper Res 179(2):518–536
Kim T, Bilsel RU, Kumara S (2008) Supplier selection in dynamic competitive environments. Int J Serv Oper Inf 3(3–4):283–293
Klamroth K, Tind J, Zust S (2004) Integer programming duality in multiple objective programming. J Glob Optim 29(1):1–18
Kothari A, Parke DC, Suri S (2003) Approximately–strategy proof and tractable multi-unit auctions. In EC’03: proceedings of the 4th ACM conference on electronic commerce. ACM Press, New York, NY, USA, pp 166–175
Kumar A, Iyengar G (2006) Optimal procurement auctions for divisible goods with capacitated suppliers. Technical report TR-2006-01, Columbia University
Laumanns M, Thiele L, Zitzler E (2004) An efficient adaptive parameter variation scheme for matheuristics based on the epsilon-constraint method. Eur J Oper Res 169(3):932–942
Marler R, Arora J (2004) Survey of multi-objective optimization methods in engineering. Struct Multi-discip Optim 26(6):369–395
Ravindran A (2008) Operations research and management science handbook. CRC Press, Boca Raton
Ravindran A, Bilsel RU, Wadhwa V, Yang T (2010) Risk adjusted multi-criteria supplier selection models with applications. Int J Prod Res 48(2):405–424
Sandholm T (2007) Expressive commerce and its application to sourcing: how we conducted $35 billions of generalized combinatorial auctions. AI Mag 28(3):0
Verma DK (2006) Optimization models for multi-attribute auctions and exchanges. Technical report, Master of engineering dissertation, department of computer science and automation, Indian Institute of Science, Bangalore
Yokoyama R, Bae S, Morita T, Sasaki H (1988) Multi-objective optimal generation dispatch based on probability security criteria. IEEE Trans Power Syst 3(1):317–324
Zionts S (1977) Integer linear programming with multiple objectives. Ann Discret Math 1:551–562
Zionts S, Wallenius J (1976) An interactive programming method for solving multiple criteria problems. Manag Sci 22(6):652–663
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Verma, D.K., Hemachandra, N., Narahari, Y., Tew, J.D. (2014). Winner Determination in Multi-unit Procurement Auctions with Volume Discount Bids and Lead Time Constraints. In: Benyoucef, L., Hennet, JC., Tiwari, M. (eds) Applications of Multi-Criteria and Game Theory Approaches. Springer Series in Advanced Manufacturing. Springer, London. https://doi.org/10.1007/978-1-4471-5295-8_13
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