A Mathematical Model for the Locomotive Refueling Problem

This problem corresponds to refueling locomotives at different station yards during the course of its journey. Locomotive tanks have a fixed fuel capacity and prices of fuel vary across yards. In addition, there is a fixed cost for hiring a refueling truck at a yard and every refueling stop that the locomotive makes. Locomotives can power different train sets during a cyclical planning horizon running 14 days. The objective of this exercise is to minimize the total fuel costs fixed and operational for a given set of locomotives, trains and yards. In addition, there are numerous constraints relating to refueling, locomotive tank capacity, refueling truck capacity etc. This problem has similarity to the network flow problem. We formulate this problem as a Mixed Integer Program (MIP) and present our experience in the following sections.