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

\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

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

Dynamic programming for scheduling locks in sequence

status: publishe

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

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 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

Evaluating the emission reduction potential of scheduling locks on inland waterways

Locks constitute a bottleneck along many inland waterways. We consider the problem of scheduling a system of multiple locks arranged in a sequence, a setting that occurs naturally along many inland waterways. We provide two alternative mathematical programming models and evaluate their performance. In particular, we show how ship speed can be included as a variable, which allows to consider the emissions of ships passing through the system. We then use the models to investigate the trade-off between total flow-time and emissions on instances based on realistic problem instances.status: publishe

Mathematical programming models for lock scheduling with an emission objective

We investigate the scheduling of series of consecutive locks. This setting occurs naturally along canals and waterways. Our contribution is to (i) provide two distinct mathematical programming formulations and compare them empirically, (ii) investigate the trade-off between reducing flow time and reducing emissions, and (iii) compare the results of the integrated model to those of a heuristic scheduling the locks separately. Our findings confirm that integrated scheduling of consecutive locks can reduce flow time significantly, and reveal that both model formulations have their merits when compared to each other

No-wait scheduling for locks

\u3cp\u3eWe introduce and investigate the problem of scheduling a single lock with parallel chambers. Special cases of this problem are related to interval scheduling. We focus on the existence of no-wait schedules and characterize their feasibility for a lock consisting of two chambers using new graph-theoretical concepts. We obtain a linear time algorithm for this special case. We also provide an efficient algorithm for the case where all chambers of the lock are identical. Furthermore, we describe a dynamic programming algorithm for the general case with arbitrary chambers. Finally, we indicate how our methods for the no-wait case can be applied to practical settings where waiting time is unavoidable.\u3c/p\u3