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We propose a two-phase algorithm for solving the manufacturer's pallet loading problem (MPLP). A new integer linear programming model is developed to obtain the maximum number of items that could be packed onto a pallet in the first phase. The solution obtained in the first phase is then adopted to generate a layout pattern for the MPLP with a constraint programming model in the second phase. The computational results indicate that this algorithm can solve difficult instances to the optimality within reasonable computational times.Keywords -Pallet loading problem, cutting and packing, mathematical programming, supply chain management II. A TWO-PHASE ALGORITHM FOR MPLP First Phase: A New Integer LP Model for MPLPBeasley's 0-1 model [16] considered positions of rectangles in the two-dimensional space. In this paper, we

The berth allocation problem is an optimization problem concerning seaside operations at container terminals. This study investigates the dynamic and continuous berth allocation problem (BAP), whose objective is to minimize the total weighted service time and the deviation cost from vessels' preferred position. The problem is formulated as a mixed integer programming model. Due to that the BAP is NP-hard, two efficient and effective simulated annealing (SA) algorithms are proposed to locate vessels along the quay. The first SA assigns vessels to available positions along the quay from the left to the right, while the second assigns vessels from both sides. Both small and large-scale instances in the literature are tested to evaluate the effectiveness of the proposed SA algorithms using the optimization software Gurobi and heuristic algorithms from the literature. The results indicate that the proposed SAs can provide optimal solutions in small-scale instances and updates the best solutions in large-scale instances. The improvement over other comparing heuristics is statistically significant.

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