Efficient robust linear optimization for large repositioning problems

Abstract

The economic uncertainty and demand volatility put the maritime carriers under operational pressure and the obligation of better planning and better benchmarking of solutions. One of the ways to tackle uncertainty is to operate with robust plans. This paper investigates a robust optimization framework and uses well-known time-expanded networks and appropriate linear programs to study and solve three variants of a robust optimization empty container repositioning problem. We propose a new, dynamic generation constraints approach and effectively solve all these variants for a real world look-like set of instances. We use a list of global maritime ports to build artificial instances while exploring computational limits of the classic and dynamic approach. We are able to solve instances with hundreds of millions of additional, linear constraints. Our experimentation shows that this approach is efficient as well as indispensable for such big instances. © 2011 Springer-Verlag.