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Due to the special role of empty containers in the container transportation process, empty container repositioning is a focal point in the shipping industry. For this problem, highly efficient and feasible optimization models are critical in improving the benefit for shipping companies and increasing their market competitiveness. Operational decisions are affected by tactical ones. Aimed at this point, we propose a tactical and operational cooperative empty container repositioning optimization model. To cut the search space and obtain the optimal solution quickly, several initial solutions generation rules are extracted, based on business flow. Furthermore, the reachable shipping distance may change when the calling sequence is different. An algorithm which calculates the reachable shipping distance matrix between ports is presented to solve this problem. Simulated cases are used to test the proposed model and algorithm. The results show that the cases can cope with the tactical and operational cooperative empty container repositioning optimization model. Moreover, some interesting conclusions also are deduced about the relationships among number of calling ports, total profits, leasing cost, calling port fee, number of Empty Containers Repositioned (ECR), and laden containers. All these can guide and assist the various decisions to be made. According to the homepage of Symmetry, its subject areas include Mathematics, Computer Science, Theory, and Methods. Their branches include information theory, computer-aided design, and so on. The topic of our paper is to solve this engineering application problem by using a mathematical optimization model and computer methods. That is, applying mathematical theory and computer methods to make decision results for the empty container repositioning problem in the shipping industry. It has certain economic value and practical significance. Obviously, it is consistent with the theme of Symmetry.

Tactical and Operational Cooperative Empty Container Repositioning Optimization Model Based on Business Flow and Initial Solutions Generation Rules