Modeling And Solving For The Ship Stowage Problem Of Mixed-steel Product

The ship stowage plan is to determine the loading locations and loading sequence of steel products to be loaded onto the ship,with consideration of shipping destinations,ship stability,loading regulations and so on.A reasonable stowage plan is able to improve loading efficiency and reduce the reshuffles in the unloading process.In this paper,a dynamic mixed shipping stowage problem of steel product is addressed to improve the efficiency of quay logistics and reduce logistics costs.In this paper,a dynamic mixed stowage planning problem is extracted from the shipping process of steel products.For deterministic scenario of this problem,an integer programming model is established,and a differential evolution algorithm is proposed to solve the problem.For the dynamic scenario,due to the exponential growth of the scale with an increasing number of products,an approximate dynamic programming(ADP)algorithm is employed to solve the problem.The main contents of this paper are summarized as follows:(1)For the deterministic scenario,all loading plans are released at the same time,and the static ship mixed stowage planning problem is to determine the loading locations and sequence for products,while satisfies the constraints including loading combined materials,ship stability and loading regulations.For this problem,an integer programming model is established to minimize the completion time of crane operation,the number of reshuffles and the destination dispersion of coils.Due to the fact that the standard optimization software CPLEX cannot obtain optimal solutions for large scale instances within a reasonable time,a hybrid two-level differential evolution algorithm is proposed with guiding mutation strategy and individual dependent parameter setting.Experiments are conducted with instances from engineering application.The numerical results demonstrated the computational efficiency of the proposed model and the algorithm.(2)For the dynamic scenario,the objective of dynamic ship mixed stowage problem is to minimize the total completion time of crane operation.In the condition that loading plans are released dynamically,the stowage plan is to determine the loading locations of products considering the constraints including mixed loading,ship stability,loading regulations and so on.In view of the dynamic characteristics and the scale of the problem is exponentially expanding with the increase of product number,an approximate dynamic programming algorithm is designed based on the expected total crane handling time.The numerical results demonstrate that the proposed approximate dynamic programming algorithm can effectively solve the dynamic mixed loading ship stowage problem in practice.(3)Based on the proposed model and solution method,a ship stowage decision support system is developed.For the cases that plans are released at one time and dynamically,the system calls the solution methods for static and dynamic problems to generate the optimization plan and also gives the evaluation result of the scheme.Modules that cooperate manual adjustments are also embedded to improve the robustness of the system.