A stochastic optimization approach for the supply vessel planning problem under uncertain demand

Abstract

This paper presents a two-stage stochastic programming with recourse methodology to solve the Supply Vessel Planning Problem with Stochastic Demands (SVPPSD), a problem arising in offshore logistics and which generalizes the Periodic Vehicle Routing Problem with Stochastic Demands and Time Windows. In the SVPPSD, a fleet of vessels is used to deliver a regular supply of commodities to a set of offshore installations to ensure continuous production, with each installation requiring one or more visits per week and having stochastic demands. Both the onshore depot where the product to be distributed is kept and the offshore installations have time windows, and voyages are allowed to span more than one day. A solution to the SVPPSD consists in the identification of an optimal fleet of vessels and the corresponding weekly schedule. As a solution methodology, we embed a discrete-event simulation engine within a genetic search procedure to approximate the cost of recourse and arrive at the minimized expected cost solution. We make comparisons with two alternative approaches: an expected value problem with upscaled demand, and a chance-constrained algorithm. While alternative methodologies yield robust schedules, robustness is achieved mainly through an increase in fleet size. In contrast, a two-stage stochastic programming with recourse algorithm, by accounting for the cost of recourse in the search phase, and exploring a wider solution space, allows arriving at robust schedules with a smaller fleet size, thereby yielding significant cost savings. For the tested problem instances, the proposed algorithm leads to savings of approximately 10 to 15 million USD per year.