Intermodal pricing using network flow techniques

Shangyao Yan, David Bernstein, Yosef Sheffi

Research output: Contribution to journalArticlepeer-review

37 Scopus citations


Traditional cost calculations do not accurately estimate the opportunity costs of using conveyances in intermodal operations, thus, results in many short-term pricing problems. The objective of this research is to develop a framework for estimating the opportunity costs of using conveyances in trailer-on-flatcar (TOFC) operations to assist carriers in improving their pricing strategies under highly competitive market conditions. The framework is based on a network model that simulates current operations in order to find the reduced costs and the opportunity costs of serving the loads. The network model is formulated as a linear network flow problem with side constraints. To find the reduced costs, a technique using Lagrangian Relaxation, a minimum cost algorithm, and a shortest path algorithm were developed in the research. We illustrate this model with a case study of a major north American railroad. The results show that opportunity costs do affect the accuracy of calculated system contributions for services. Moreover, the opportunity costs and system incremental costs (SICs) are unstable over time. To handle the instability we make use of a new risk-pricing approach.

Original languageEnglish
Pages (from-to)171-180
Number of pages10
JournalTransportation Research Part B: Methodological
Issue number3
StatePublished - Jun 1995


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