Multiple unit auctions with economies and diseconomies of scale

Mingzhou Jin, S. David Wu, Murat Erkoc

Research output: Contribution to journalArticlepeer-review

13 Scopus citations


This paper discusses multiple unit auctions for industrial procurement where the cost structures of suppliers capture economies and diseconomies of scale caused by the nature of the production cost and the opportunity value of suppliers' capacities. The problem of winner determination and demand allocation is proven to be NP-complete. We propose a binary tree algorithm with bounds (BTB) which efficiently exploits the model's optimality properties. BTB outperforms general integer optimization software in computational time, especially with existence of substantial economies and diseconomies of scale. The algorithm complexity is linear in demand volume. This property allows for efficient handling of high volume auctions and thus leads to increased benefit for the overall system. Under the assumption of the myopic best response strategies, we investigate the behavior of suppliers and price dynamics for iterative (multiple round) bidding with appropriate allocation and stopping rules. The allocation rules, featured by several tie breakers for multiple optimal solutions to the allocation model in each round, are proposed to induce suppliers' dominant strategies and to improve the system's performance.

Original languageEnglish (US)
Pages (from-to)816-834
Number of pages19
JournalEuropean Journal of Operational Research
Issue number2
StatePublished - Oct 16 2006


  • Economies of scale
  • Multiple unit auction
  • Optimization

ASJC Scopus subject areas

  • Information Systems and Management
  • Management Science and Operations Research
  • Statistics, Probability and Uncertainty
  • Applied Mathematics
  • Modeling and Simulation
  • Transportation


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