Optimal Order Allocation with Discount Pricing

  • Authors:

  • Boris Goldengorin;John Keane;Viktor Kuzmenko;Michael Tso

  • Affiliations:

  • Faculty of Economic Sciences, University of Groningen, P.O. Box 800, 9700 AV Groningen, The Netherlands, Department of Applied Mathematics, Khmelnitsky National University, Ukraine;School of Computer Science, University of Manchester, Oxford Road, P.O. Box 88, Manchester M60 1QD, UK;Glushkov Institute of Cybernetics, National Academy of Sciences of Ukraine, pr. Akademika Glushkova, 40, Kiev 03187, Ukraine;School of Mathematics, University of Manchester, Oxford Road, P.O.Box 88, Manchester M60 1QD, UK

  • Venue:
  • AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
  • Year:
  • 2007

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Abstract

We consider optimal order allocation (or procurement) problems with discount pricing and fixed charges. Such a problem is faced for example by an internet trading agent who seeks to fulfil an order for specified amounts of several products from a pre-arranged list of suppliers, taking into account availability and price. We present a mixed integer programming (MILP) formulation assuming that suppliers impose a discount schedule with multiple price breaks including fixed charges. We show that a modified capacitated facility location problem (CFLP) model is appropriate for the general case under consideration and outline a Lagrangean relaxation approach improved by open and close penalties. Our experimental results show that problems arising in practice can be handled within seconds by either LINGO or XPress-MP software.