Abstract:We propose local search algorithms for the vehicle routing problem with soft time window constraints. The time window constraint for each customer is treated as a penalty function, which is very general in the sense that it can be non-convex and discontinuous as long as it is piecewise linear. In our algorithm, we use local search to assign customers to vehicles and to find orders of customers for vehicles to visit. It employs an advanced neighborhood, called the cyclic exchange neighborhood, in addition to standard neighborhoods for the vehicle routing problem. After fixing the order of customers for a vehicle to visit, we must determine the optimal start times of processing at customers so that the total penalty is minimized. We show that this problem can be efficiently solved by using dynamic programming, which is then incorporated in our algorithm. We then report computational results for various benchmark instances of the vehicle routing problem. The generality of time window constraints allows us to handle a wide variety of scheduling problems. As such an example, we mention in this paper an application to a production scheduling problem with inventory cost, and report computational results for real world instances.

a b s t r a c tIn this paper, we propose a capacity scaling heuristic using a column generation and row generation technique to address the multicommodity capacitated network design problem. The capacity scaling heuristic is an approximate iterative solution method for capacitated network problems based on changing arc capacities, which depend on flow volumes on the arcs. By combining a column and row generation technique and a strong formulation including forcing constraints, this heuristic derives high quality results, and computational effort can be reduced considerably. The capacity scaling heuristic offers one of the best current results among approximate solution algorithms designed to address the multicommodity capacitated network design problem.

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Ship scheduling problem is an important operational level planning problem in maritime logistics. In this paper, we show how we designed and developed a mathematical model for real-world tanker scheduling problem in Japan. Tanker operators own their fleet of tankers and make their schedules for the next several weeks for meeting customers' demands. However, due to the high uncertainty of the ship operations and unexpected changes of demands, the schedules has to be revised frequently. Our methodology allows the operators to determine schedules that minimize the operational cost in a few minutes. These solutions provides cost improvements for tanker operators, as measured by reduction of 5-16%.