Developing a mathematical model for a multi-door cross-dock scheduling problem with human factors: A modified imperialist competitive algorithm

This paper deals with optimizing the multi-door cross-docking scheduling problem for incoming and outgoing trucks. Contrary to previous studies, it first considers the simultaneous effects of learning and deteriorating on loading and unloading the jobs. A mixed-integer linear programming (MILP) model is developed for this problem, in which the basic truck scheduling problem in a cross-docking system is strongly considered as NP-hardness. Thus, in this paper, meta-heuristic algorithms namely genetic algorithm, imperialist competitive algorithm, and a new hybrid meta-heuristic algorithm, resulted from the principal component analysis (PCA) and an imperialist competitive algorithm (ICA) called PCICA are proposed and used. Finally, the numerical results obtained from meta-heuristic algorithms are examined using the relative percentage deviation and time criteria. Results show that the hybrid PCICA algorithm performs better than the other algorithms in terms of the solution quality. Computational results indicate when the learning rate increases, its decreasing effect on processing time will growth and the objective function value is improved. Finally, the sensitivity analysis also indicates when the deterioration rate is reduced, its incremental effect is decreased over time.