The bidding selection and assignment problem with minimum quantity commitment

A. Lim, Zhou Xu, F. Wang

Research output: Journal article publicationJournal articleAcademic researchpeer-review

5 Citations (Scopus)


This paper studies the bidding selection and assignment problem with a novel constraint, namely minimum quantity commitment (MQC), motivated by the Royal Philips Electronics Company. Responding to the stipulations by the US Federal Maritime Commission, any shipping agent transporting to the US must satisfy a minimum quantity of containers. To insure this MQC for shipping agents, the Royal Philips Electronics Company, with a large number of shipping needs, has to assign enough containers to each selected shipping agent to transport cargos to the US. This restriction creates difficulties for Philips as the company seeks to satisfy its shipping needs with minimum total costs. To solve this problem, we first formulate it by a mixed-integer programming model. In order for both linear programming relaxation and Lagrangian relaxation to provide good lower bounds, we then strengthen the model by a few valid inequalities. Furthermore, a Lagrangian-based heuristic and a branch and cut solver are applied to solve the problem. Extensive experiments show the effectiveness of all the models and methods.
Original languageEnglish
Pages (from-to)693-702
Number of pages10
JournalJournal of the Operational Research Society
Issue number5
Publication statusPublished - 13 May 2008
Externally publishedYes


  • Lagrangian relaxation
  • Linear programming
  • Minimum quantity commitment
  • Selection and assignment

ASJC Scopus subject areas

  • Management Information Systems
  • Strategy and Management
  • Management Science and Operations Research
  • Marketing


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