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This study addresses the problem of determining the ship speed and bunkering ports in a ship route. All of the previous research has investigated the ship speed optimization issues by assuming that the ship navigates at constant speed or by ignoring the bunkering port decision. In this study, the problem of determining the variable speed and bunkering port is formulated mathematically with a nonlinear program in order to minimize the bunker fuel, ship time costs, and carbon tax imposed on greenhouse gas emissions. This study then provides a Lagrangian heuristic by deriving a property for a relaxed problem. The performance of the heuristic is evaluated and analysed using the data obtained from the literature, real practice and random generation.

This paper considers the problem of determining the disassembly schedule (quantity and timing) of products in order to satisfy the demand of their parts or components over a finite planning horizon. The objective is to minimize the sum of set-up, disassembly operation, and inventory holding costs. As an extension of the uncapacitated versions of the problem, we consider the resource capacity restrictions over the planning horizon. An integer program is suggested to describe the problem mathematically, and to solve the problem, a heuristic is developed using a Lagrangean relaxation technique together with a method to find a good feasible solution while considering the trade-offs among different costs. The effectiveness of the algorithm is tested on a number of randomly generated problems and the test results show that the heuristic suggested in this paper can give near optimal solutions within a short amount of computation time.

This paper focuses on an arc-welding robot scheduling problem, which is the problem of determining the sequence of welding operations while avoiding heat-caused distortion for the objective of minimizing the time required to complete a given set of welding operations. Each welding operation is specified by a weld line with two end points, each of which can be a possible starting point of the welding operation for that weld line. Because of the heat-caused distortion, there must be a certain period of time (delay) between welding operations associated with weld lines near each other. We develop several heuristic algorithms, in which heuristics for the travelling salesman problem are modified to cope with characteristics of the problem considered here. To show the performance of the heuristics suggested in this paper, computational experiments are performed on a number of randomly generated test problems and results are reported.