Single-leg shipping revenue management for expedited services with ambiguous elasticity in transit-time-sensitive demand

The growing demand for expedited shipping services from transit-time-sensitive (TTS) shippers poses a dilemma for ocean carriers, who must navigate the trade-off between transit time and the associated fuel costs. Charging a premium for expedited services offers a potential solution, but it requires careful consideration to avoid detrimental effects on demand. This study focuses on single-leg shipping revenue management (S-SRM) to optimize the pricing strategies of ocean carriers, which simplifies complex real-world phenomena, provides a concise representation of the underlying mechanism, and forms a foundation for multi-leg shipping revenue management. Specifically, the study addresses the challenge faced by ocean carriers when they possess partial prior knowledge about the distribution of shippers’ willingness to pay for expedited services on a single shipping leg. By developing a model that captures the TTS demand and accounts for uncertainties in shippers’ willingness to pay, the analysis explores various decision-making approaches under uncertainty, such as maximax, maximin, and the Hurwicz criterion. Leveraging the insights gained from the TTS demand model, the study derives closed-form solutions to optimize pricing strategies, shedding light on the intricacies of the S-SRM problem. In addition, we investigate the tramp shipping fixture and the joint optimization of sailing speed and freight rate. The practical application of the proposed model is further demonstrated through a case study of salmon transportation using a reefer vessel, highlighting its relevance in different scenarios.