Routing Trains through railway stations: model formulation and algorithms

In this paper we consider the problem of routing trains through railway stations. This problem occurs as a subproblem in a project which the authors are carrying out in cooperation with the Dutch railways. The project involves the analysis of future infrastructural capacity requirements in the Dutch railway network, Part of this project is the automatic generation and evaluation of timetables. To generate a timetable a hierarchical approach is followed: at the upper level in the hierarchy a tentative timetable is generated, taking into account the specific scheduling problems of the trains at the railway stations at an aggregate level. At the lower level in the hierarchy it is checked whether the tentative timetable is feasible with respect to the safety rules and the connection requirements at the stations. To carry out this consistency cheek, detailed schedules for the trains at the railway yards have to be generated. In this paper we present a mathematical model formulation for this detailed scheduling problem, based on the Node Packing Problem (NPP). Furthermore, we describe a solution procedure for the problem, based on a branch-and-cut approach. The approach is tested in an empirical study with data from the station of Zwolle in The Netherlands

Parameterized complexity of machine scheduling: 15 open problems

Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 open questions in this area whose resolution we expect to lead to the discovery of new approaches and techniques both in scheduling and parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc

A branch-and-price algorithm for a hierarchical crew scheduling problem.

We describe a real-life problem arising at a crane rental company. This problem is a generalization of the basic crew scheduling problem given in Mingozzi et al. and Beasley and Cao. We formulate the problem as an integer programming problem and establish ties with the integer multicommodity flow problem and the hierarchical interval scheduling problem. After establishing the complexity of the problem we propose a branch-and-price algorithm to solve it. We test this algorithm on a limited number of real-life instances.Scheduling;

Customer Engagement Plans for Peak Load Reduction in Residential Smart Grids

In this paper, we propose and study the effectiveness of customer engagement plans that clearly specify the amount of intervention in customer's load settings by the grid operator for peak load reduction. We suggest two different types of plans, including Constant Deviation Plans (CDPs) and Proportional Deviation Plans (PDPs). We define an adjustable reference temperature for both CDPs and PDPs to limit the output temperature of each thermostat load and to control the number of devices eligible to participate in Demand Response Program (DRP). We model thermostat loads as power throttling devices and design algorithms to evaluate the impact of power throttling states and plan parameters on peak load reduction. Based on the simulation results, we recommend PDPs to the customers of a residential community with variable thermostat set point preferences, while CDPs are suitable for customers with similar thermostat set point preferences. If thermostat loads have multiple power throttling states, customer engagement plans with less temperature deviations from thermostat set points are recommended. Contrary to classical ON/OFF control, higher temperature deviations are required to achieve similar amount of peak load reduction. Several other interesting tradeoffs and useful guidelines for designing mutually beneficial incentives for both the grid operator and customers can also be identified

A mazing 2+ε approximation for unsplittable flow on a path

We study the problem of unsplittable flow on a path (UFP), which arises naturally in many applications such as bandwidth allocation, job scheduling, and caching. Here we are given a path with nonnegative edge capacities and a set of tasks, which are characterized by a subpath, a demand, and a profit. The goal is to find the most profitable subset of tasks whose total demand does not violate the edge capacities. Not surprisingly, this problem has received a lot of attention in the research community. If the demand of each task is at most a small-enough fraction δ of the capacity along its subpath (δ-small tasks), then it has been known for a long time [Chekuri et al., ICALP 2003] how to compute a solution of value arbitrarily close to the optimum via LP rounding. However, much remains unknown for the complementary case, that is, when the demand of each task is at least some fraction δ > 0 of the smallest capacity of its subpath (δ-large tasks). For this setting, a constant factor approximation is known, improving on an earlier logarithmic approximation [Bonsma et al., FOCS 2011]. In this article, we present a polynomial-time approximation scheme (PTAS) for δ-large tasks, for any constant δ > 0. Key to this result is a complex geometrically inspired dynamic program. Each task is represented as a segment underneath the capacity curve, and we identify a proper maze-like structure so that each corridor of the maze is crossed by only O(1) tasks in the optimal solution. The maze has a tree topology, which guides our dynamic program. Our result implies a 2 + ε approximation for UFP, for any constant ε > 0, improving on the previously best 7 + ε approximation by Bonsma et al. We remark that our improved approximation algorithm matches the best known approximation ratio for the considerably easier special case of uniform edge capacities

License class design: complexity and algorithms

In this paper a generalization of the Fixed Job Scheduling Problem (FSP) is considered, which appears in the aircraft maintenance process at an airport. A number of jobs have to be carried out, where the main attributes of a job are a fixed start time, a fixed finish time and an aircraft type. For carrying out these jobs a number of engineers are available. An engineer is allowed to carry out a specific job only if he has a license for the corresponding aircraft type. Furthermore, the jobs must be carried out in a non-preemptive way and each engineer can be carrying out at most one job at the same time. Within this setting natural questions to be answered ask for the minimum number of engineers required for carrying out all jobs or, more generally, for the minimum total costs for hiring engineers. In this paper a complete classification of the computational complexity of two classes of mathematical problems related to these practical questions is given. Furthermore, it is shown that the polynomially solvable cases of these problems can be solved by a combination of Linear Programming and Network Flow algorithms

Departure Management with Robust Gate Allocation

International audienceThe Airport Collaborative Decision Making (A-CDM) concept yields concrete and promising solutions for airports, in terms of traffic punctuality and predictability, with possible delay, noise and pollution reduction. A key feature of A-CDM is the Departure Management (DMAN): runway takeoff sequences can be anticipated such that a significant part of the delay can be shifted at the gate, engines off, without penalizing the remaining traffic. During this process, an increase in the gate occupancy for delayed departures is unavoidable, therefore the airport layout must provide enough gates and their allocation must be robust enough w.r.t. departures delay. In this paper, we introduce a method to estimate the gate delays due to the DMAN pre-departure scheduling, then we propose a robust gate allocation algorithm and assess its performance with current and increased traffic at Paris-Charles-de-Gaulle international airport. Results show a significant reduction in the number of gate conflicts, when comparing such a robust gate allocation to current practice