The train fueling cost minimization problem with fuzzy fuel prices

The train fueling cost minimization problem is to find a scheduling and fueling strategy such that the fueling cost is minimized and no train runs out of fuel. Since fuel prices vary by location and time from month to month, we estimate them by fuzzy variables in this paper. Furthermore, we propose a fuzzy fueling cost minimization model by minimizing the expected fueling cost under the traversing time constraint, maximal allowable speed constraint, tank capacity constraint, and so on. In order to solve the model, we decompose it into a nonlinear scheduling strategy model and a linear fueling strategy model. Based on the Karush-Kuhn-Tucker conditions, we design an iterative algorithm to solve the scheduling strategy model, and furthermore design a numerical algorithm to solve the fuzzy fueling cost minimization model. Finally, some numerical examples are presented for showing the efficiency of the proposed approach on saving fueling cost.