Multi-objective vehicle refueling planning using mixed integer programming

For point-to-point direct delivery over the transportation network, timely delivery of commodity and reduction of total fuel cost are both important objectives to consider. Since fuel prices can vary significantly over a broad region, often there is a tradeoff between fuel cost and travel time. A short path may not be economical in terms of fuel cost while routing through areas with lower fuel prices may take more time. In this paper, we address multi-objective refueling optimization problems in the context of two priority models regarding fuel cost and travel time. Unlike the shortest path problem, optimal refueling paths may not be simple paths, which complicates the setup of mixed integer programs. We first start with arbitrage-free vehicle refueling planning that restricts refueling paths to simple paths in the network only. We then show how we can augment the mixed integer formulation for vehicle refueling planning without the arbitrage-free assumption.