Fractional Price Matching Policies Arising from the Ocean Freight Service Industry

Chung Yee Lee, Christopher S. Tang, Rui Yin, Jaehyung An

Research output: Contribution to journalArticlepeer-review

44 Scopus citations


We consider a situation in which shippers (customers) can purchase ocean freight services either directly from a carrier (service provider)in advance or from the spot market just before the departure of an ocean liner. The price is known in the former case, while the spot price is uncertain ex-ante in the latter case. Consequently, some shippers are reluctant to book directly from the carrier in advance unless the carrier is willing to "partially match" the realized spot price when it is lower than the regular price. This study is an initial attempt to examine if the carrier should bear some of the "price risk" by offering a "fractional" price matching contract that can be described as follows. The shipper pays the regular freight price in advance; however, the shipper will get a refund if the realized spot price is below the regular price, where the refund is a "fraction" of the difference between the regular price and the realized spot price. By modeling the dynamics between the carrier and the shippers as a sequential game, we show that the carrier can use the fractional price matching contract to generate a higher demand from the shippers compared to no price matching contract by increasing the "fraction" in equilibrium. However, as the carrier increases the "fraction," the carrier should increase the regular price to compensate for bearing additional risk. By selecting the fractional price matching contract optimally, we show that the carrier can afford to offer this price matching mechanism without incurring revenue loss: the optimal fractional price matching contract is "revenue neutral."

Original languageEnglish (US)
Pages (from-to)1118-1134
Number of pages17
JournalProduction and Operations Management
Issue number7
StatePublished - Jul 1 2015


  • fractional price matching
  • ocean freight
  • pricing contracts

ASJC Scopus subject areas

  • Management Science and Operations Research
  • Industrial and Manufacturing Engineering
  • Management of Technology and Innovation


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