Mathematical programming models for scheduling locks in sequence

We investigate the scheduling of series of consecutive locks. This setting occurs naturally along canals and waterways. We describe a problem that generalizes different models that have been studied in literature. Our contribution is to (i) provide two distinct mathematical programming formulations, and compare them empirically, (ii) show how these models allow for minimizing emission by having the speed of a ship as a decision variable, (iii) to compare, on realistic instances, the optimum solution found by solving the models with the outcome of a decentralized heuristic

Scheduling locks on inland waterways.

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Scheduling parallel batching machines in a sequence

Motivated by the application of scheduling a sequence of locks along a waterway, we consider a scheduling problem where multiple parallel batching machines are arranged in a sequence and process jobs that travel along this sequence. We investigate the computational complexity of this problem. More specifically, we show that minimizing the sum of completion times is strongly NP-hard, even for two identical machines and when all jobs travel in the same direction. A second NP-hardness result is obtained for a different special case where jobs all travel at an identical speed. Additionally, we introduce a class of so-called synchronized schedules, and investigate special cases where the existence of an optimum solution which is synchronized can be guaranteed. Finally, we reinforce the claim that bi-directional travel contributes fundamentally to the computational complexity of this problem by describing a polynomial time procedure for a setting with identical machines and where all jobs travel in the same direction at equal speed.nrpages: 43status: publishe

Scheduling parallel batching machines in a sequence

\u3cp\u3eMotivated by the application of scheduling a sequence of locks along a waterway, we consider a scheduling problem where multiple parallel batching machines are arranged in a sequence and process jobs that travel along this sequence. We investigate the computational complexity of this problem. More specifically, we show that minimizing the sum of completion times is strongly NP-hard, even for two identical machines and when all jobs travel in the same direction. A second NP-hardness result is obtained for a different special case where jobs all travel at an identical speed. Additionally, we introduce a class of so-called synchronized schedules and investigate special cases where the existence of an optimum solution which is synchronized can be guaranteed. Finally, we reinforce the claim that bidirectional travel contributes fundamentally to the computational complexity of this problem by describing a polynomial time procedure for a setting with identical machines and where all jobs travel in the same direction at equal speed.\u3c/p\u3

Dynamic programming for scheduling locks in sequence

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Scheduling parallel batching machines in a sequence

© 2018, Springer Science+Business Media, LLC, part of Springer Nature. Motivated by the application of scheduling a sequence of locks along a waterway, we consider a scheduling problem where multiple parallel batching machines are arranged in a sequence and process jobs that travel along this sequence. We investigate the computational complexity of this problem. More specifically, we show that minimizing the sum of completion times is strongly NP-hard, even for two identical machines and when all jobs travel in the same direction. A second NP-hardness result is obtained for a different special case where jobs all travel at an identical speed. Additionally, we introduce a class of so-called synchronized schedules and investigate special cases where the existence of an optimum solution which is synchronized can be guaranteed. Finally, we reinforce the claim that bidirectional travel contributes fundamentally to the computational complexity of this problem by describing a polynomial time procedure for a setting with identical machines and where all jobs travel in the same direction at equal speed.status: publishe