Loading containers on double-stack cars: Multi-objective optimization models and solution algorithms for improved safety and reduced maintenance cost

To improve safety measures of loading containers on double-stack rail cars, this paper develops a multi-objective optimization model that focuses on a number of practical requirements such as the center-of-gravity height of a loaded car and load balance considerations. A lexicographic goal programming approach is then used to address different priorities for potentially conflicting objectives and constraints. To minimize the center-of-gravity height, a linear-fractional programming technique is adopted in this study to transform the corresponding generalized mixed integer fractional problem into a sequence of mixed integer linear subproblems. A tabu search algorithm is proposed to get the close-to-optimal solutions of the large-scale double-stack car loading problems. Based on a set of matching and assigning rules, this paper further presents a two-stage heuristic algorithm for solving large-scale double-stack car loading problems. A real-world case study is used to examine the efficiency and effectiveness of the proposed optimization and heuristic procedures.