A Branch-and-Price-and-Cut Method for Ship Scheduling with Limited Risk

Authors:
Hee-Su Hwang;Siriwat Visoldilokpun;Jay M. Rosenberger
Affiliations:
US Airways, Tempe, Arizona 85281;Department of Industrial and Manufacturing Systems Engineering, University of Texas at Arlington, Arlington, Texas 76019;Department of Industrial and Manufacturing Systems Engineering, University of Texas at Arlington, Arlington, Texas 76019
Venue:
Transportation Science
Year:
2008

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Abstract

Maritime logistics operations are full of uncertainty such as severe weather, mechanical problems, strikes, and fluctuating freight rates. Traditional ship-scheduling models ignore uncertainty, even in highly volatile markets. Although ship operators can increase revenue by delivering many spot cargoes, they have to embrace the risk of the fluctuation of spot rates. We present a set-packing model that limits risk using a quadratic variance constraint. We use a traditional Kelley's cutting plane algorithm and a delayed column-and-cut generation (branch-and-price-and-cut) algorithm on medium-sized ship-scheduling problems with restricted variance. We develop a second set of cuts that are more restrictive under certain conditions. Computational results show that the variance of profit can be significantly reduced with a reasonable increase in cost.