This paper studies a robust maritime inventory routing problem with time windows and stochastic travel times. One of the novelties of the problem is that the length and placement of the time windows are also decision variables. Such problems arise in the design and negotiation of long-term delivery contracts with customers who require on-time deliveries of high-value goods throughout the year. We formulate the problem as a two-stage stochastic mixed-integer program and propose a two-phase solution approach that considers a sample set of disruptions as well as their recovery solutions. In the first phase, we introduce two planning strategies to generate robust routes in which time buffers are spread among deliveries and consecutive deliveries at a port are separated by at least some minimum number of periods. In the second phase, we propose a multi-scenario construction heuristic to obtain good feasible solutions. Computational results reveal that our integrated solution procedure with judicious placement of time buffers and committed time windows leads to robust solutions that are less vulnerable to unplanned disruptions and have lower expected costs.
Georgia Institute of Technology, 2015