Backup Solutions for the Refueling Problem in Foreign Transportation: A Case Study in Mexico

In this paper, we addressed an optimization problem in the bus transportation industry from two points of view. Firstly, we used an integer linear optimization model to describe the problem, and we solved it via a mathematical solver and a genetic algorithm. The problem to be solved is to minimize the recharged fuel cost necessary to complete a trip on a passenger bus from a Mexican company. Among the assumptions of the problem, we have that the bus can only restore fuel at the stops of the trip, the price of gasoline varies at each stop, and the amount of fuel in the tank always has to be greater or equal to a certain reserve amount and less or equal to the tank's total capacity. It is shown that, under certain conditions, the problem always has a solution since we can choose the strategy of recharging in each city until the tank is full, and in this way, we can reach the next city and complete the trip; however, this approach is far from giving an optimal solution. The integer linear optimization problem arises as a minimization problem with 3n + 1 constraints, where n represents the number of designated stations that form the trip to be made. In the genetic algorithm approach, the amount of gasoline in the tank was represented as individuals, and suitable mutation and crossover operators were proposed for the problem until a solution yielded good results for the cost function. In the approach with integer linear programming, it was possible to obtain optimal solutions for large instances of the problem in a very short time. Regarding the genetic algorithm, it was possible to get suitable approximations of the optimal points and generate backup solutions for the problem.