A bi-objective truck scheduling problem in a cross-docking center with probability of breakdown for trucks

•We consider possibility of breakdown for trucks in cross-docking truck scheduling.•We assume that trucks may be broken based on a Poisson distribution function.•We mathematically model the problem.•We employ a complete enumeration method to obtain optimum results.•We employ multi-objective meta-heuristics to solve large-scale problems.

This paper addresses a truck scheduling problem in a cross-docking center, in which trucks may confront breakdowns during their service times. In fact, the number of breakdowns in one unit of time for each truck follows a Poisson distribution function. On the other hand, customers are promised to receive required items in a pre-determined time; so, a due date is assigned to each outbound truck. Thus, a bi-objective linear mathematical model is developed inspired by models in the body of the respective literature. A complete enumeration method is employed to find optimum solutions subject to the complexity of large-scale problems, and we modify three multi-objective meta-heuristics; namely, Non-dominated Sorting Genetic Algorithm II (NSGA-II), Multi-Objective Simulated Annealing (MOSA) and Multi-Objective Differential Evolutionary (MODE). In addition, a Response Surface Methodology (RSM) as a statistical tool is used to find an appropriate amount of factors associated with the forgoing meta-heuristics. Finally, the performances of the proposed meta-heuristics are measured and compared with each other.