The off-line group seat reservation problem

Clausen, Tommy; Hjorth, Allan Nordlunde; Nielsen, Mogens Lykkegaard; Pisinger, David

doi:10.1016/j.ejor.2010.06.037

Cited by 6 publications

(8 citation statements)

References 20 publications

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“…To the best of our knowledge, since the original publication of the problem in [6], none of the follow-up study on the Group Seat Reservation Problem has shown to be better than the original work. An online version of the seat allocation problem was first published in [3], and further analysis was made in [18].…”

Section: Previous Workmentioning

confidence: 95%

“…Using the usual terminology of the packing problems and utilising as much as possible the terminology used in [6], a train contains W seats and stops at H stations. Let N = {1, .…”

Section: Definitions Terminology and Mip Modelmentioning

confidence: 99%

“…In this paper we extend the Offline Group Seat Reservation Knapsack Problem (GSR-KP) presented in [6]. In the original formulation, a train with W seats stops in H stations.…”

Section: Introductionmentioning

confidence: 99%

“…Thus, we suggest a new GRASP procedure that solves GSR-KP and GSR-KPPS. Eventually, we adapt and improve the original instances considered in [6] adding a random profit on seats and proposing five new problems.…”

Section: Introductionmentioning

confidence: 99%

“…The third novelty is the adaptation and extension of the instances used in [6]. We introduced a new group of problems that better represents some challenging real world scenarios than the ones suggested in the original paper.…”

Section: Introductionmentioning

confidence: 99%

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The Offline Group Seat Reservation Knapsack Problem With Profit on Seats

2019

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In this paper we present the Group Seat Reservation Knapsack Problem with Profit on Seat. This is an extension of the the Offline Group Seat Reservation Knapsack Problem. In this extension we introduce a profit evaluation dependant on not only the space occupied, but also on the individual profit brought by each reserved seat. An application of the new features introduced in the proposed extension is to influence the distribution of passengers, such as assigning seats near the carriage centre for long journeys, and close to the door for short journeys. Such distribution helps to reduce the excess of dwelling time on platform. We introduce a new GRASP based algorithm that solves the original problem and the newly proposed one. In the experimental section we show that such algorithm can be useful to provide a good feasible solution very rapidly, a desirable condition in many real world systems. Another application could be to use the algorithm solution as a startup for a successive branch and bound procedure when optimality is desired. We also add a new class of problem with five test instances that represent some challenging real-world scenarios that have not been considered before. Finally, we evaluate both the existing model, the newly proposed model, and analyse the pros and cons of the proposed algorithm.

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Section: Previous Workmentioning

confidence: 95%

“…Using the usual terminology of the packing problems and utilising as much as possible the terminology used in [6], a train contains W seats and stops at H stations. Let N = {1, .…”

Section: Definitions Terminology and Mip Modelmentioning

confidence: 99%

“…In this paper we extend the Offline Group Seat Reservation Knapsack Problem (GSR-KP) presented in [6]. In the original formulation, a train with W seats stops in H stations.…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Offline Group Seat Reservation Knapsack Problem With Profit on Seats

2019

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Optimisation of seat reservations on trains to minimise transfer distances

Weicker¹

2023

Oper Res Int J

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This paper introduces a novel optimisation problem motivated by the real-world application of transferring between trains. The driving idea is to minimise the walking distances of all transferring passengers by optimising the assignment of passengers to railcarriages in the seat reservation process. The focus of this work is on formalising and modelling the problem, which has not been studied before. It aims to provide a framework for future considerations. We present three versions of the problem with increasing difficulty: one-train-one-station, one-train-many-stations, and a general problem with multiple trains and stations. Since the simplest version of the problem is a pure assignment problem in the form of minimum-cost bipartite matching, our problem modelling and algorithmic solution approach remain closely related to maxflow problems as they represent a proven method for assignment problems. However, even the one-train-many-stations problem cannot be solved by transforming it into a standard maximum-flow problem. The main result shown is the NP-hardness of the general problem.

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