Mixed Integer Programing for Multi-Tier Rebate with Discontinuous Cost Function
One challenge faced by procurement decision-maker during the acquisition process is how to compare similar products from different suppliers and allocate orders among different products or services. This work focuses on allocating orders among multiple suppliers considering rebate. The objective function is to minimize the total acquisition cost including purchasing cost and rebate benefit. Rebate benefit is complex and difficult to estimate at the ordering step. Rebate rules vary for different suppliers and usually change over time. In this work, we developed a system to collect the rebate policies, standardized the rebate policies and developed two-stage optimization models for ordering allocation. Rebate policy with multi-tiers is considered in modeling. The discontinuous cost function of rebate benefit is formulated for different scenarios. A piecewise linear function is used to approximate the discontinuous cost function of rebate benefit. And a Mixed Integer Programing (MIP) model is built for order allocation problem with multi-tier rebate. A case study is presented and it shows that our optimization model can reduce the total acquisition cost by considering rebate rules.
Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1317272Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 255
 M. Prince, J. C. Smith, and J. Geunes, “Procurement allocation planning with multiple suppliers under competition,” in International Journal of Production Research, vol. 51, 2013, pp. 23–24.
 Z. Degraeve, E. Labro, and F. Roodhooft, “An evaluation of vendor selection models from a total cost of ownership perspective,” in European Journal of Operational Research, vol. 125, 2000, pp. 34–58.
 D. R. Goossens, A. J. T. Maas, F. C. R. Spieksma, and J. J. Klundert, “Exact algorithms for procurement problems under a total quantity discount structure,” in European Journal of Operational Research, vol. 178(2), 2007, pp. 603-626.
 M. Marksa, and R. Crosonb, “Alternative rebate rules in the provision of a threshold public good: An experimental investigation,” in Journal of Public Economics, vol. 67(2), 1998, pp. 195-220.
 P. Katz, A. A. Sadrian, and P. Tendick, “Telephone companies analyze price quotations with Bellcore’s PDSS Software,” in Interfaces, vol. 24(1), 1994, pp. 50–63.
 A. A. Sadrian, and Y. S. Yoon, “A procurement decision support system in business volume discount environments,” in Operations Research, vol. 42(1), 1994, pp. 14–23.
 M. Prince, J. C. Smith, J. Geunes, “A three-stage procurement optimization problem under uncertainty,” in Naval Research Logistics, vol. 60, issue 5, 2013, pp. 395-412.
 Y. Long, L. H. Lee, and E. P. Chew, “The Sample Average Approximation Method for Empty Container Repositioning with Uncertainties”. In European Journal of Operational Research, vol. 222(1), 2012, pp. 65–75.
 J. C. Smith, C. Lim, and F. Sudargho, “Survivable network design under optimal and heuristic interdiction scenarios,” In J Glob Opt, vol. 38, 2007, pp. 181-199.
 M. Eso, S. Ghosh, J. R. Kalagnanam, and L. Ladanyi, “Bid evaluation in procurement auctions with piece-wise linear supply curves,” in IBM Research Report RC22219, 2001.
 A. Kothari, D. Parkes, and S. Suri, Approximately-strategy proof and tractable multi-unit auctions. In Proceedings 4th ACM Conference on Electronic Commerce (EC-2003), San Diego, June 2003. ACM, pp. 166–175.