Scheduling trains as a blocking parallel-machine job shop scheduling problem

In this paper, the train scheduling problem is modelled as a blocking parallel-machine job shop scheduling (BPMJSS) problem. In the model, trains, single-track sections and multiple-track sections, respectively, are synonymous with jobs, single machines and parallel machines, and an operation is regarded as the movement/traversal of a train across a section. Due to the lack of buffer space, the real-life case should consider blocking or hold-while-wait constraints, which means that a track section cannot release and must hold the train until next section on the routing becomes available. Based on literature review and our analysis, it is very hard to find a feasible complete schedule directly for BPMJSS problems. Firstly, a parallel-machine job-shop-scheduling (PMJSS) problem is solved by an improved shifting bottleneck procedure (SBP) algorithm without considering blocking conditions. Inspired by the proposed SBP algorithm, feasibility satisfaction procedure (FSP) algorithm is developed to solve and analyse the BPMJSS problem, by an alternative graph model that is an extension of the classical disjunctive graph models. The proposed algorithms have been implemented and validated using real-world data from Queensland Rail. Sensitivity analysis has been applied by considering train length, upgrading track sections, increasing train speed and changing bottleneck sections. The outcomes show that the proposed methodology would be a very useful tool for the real-life train scheduling problems

A robust reactive scheduling model for intensive care units

The ICU is an integral part of any hospital and is under great load from patient arrivals as well as resource limitations. Scheduling of patients in the ICU is complicated by the two general types; elective surgery and emergency arrivals. This complicated situation is handled by creating a tentative initial schedule and then reacting to uncertain arrivals as they occur. For most hospitals there is little or no flexibility in the number of beds that are available for use now or in the future. We propose an integer programming model to handle a parallel machine reacting system for scheduled and unscheduled arrivals.

Rostering ambulance services

This paper developed a model for rostering ambulance crew in order to maximise the coverage throughout a planning horizon and minimise the number of ambulance crew. Rostering Ambulance Services is a complex task, which considers a large number of conflicting rules related to various aspects such as limits on the number of consecutive work hours, the number of shifts worked by each ambulance staff and restrictions on the type of shifts assigned. The two-stage models are developed using nonlinear integer programming technique to determine the following sub-problems: the shift start times; the number of staff required to work for each shift; and a balanced schedule of ambulance staff. At the first stage, the first two sub-problems have been solved. At the second stage, the third sub-problem has been solved using the first stage outputs. Computational experiments with real data are conducted and the results of the models are presented.

Online scheduling in the operating theatre

Online scheduling is considered in this paper for the Operating Theatre. Robust elective schedules are determined in the offline environment prior to the day of surgery for the online environment. Changes to the offline schedule during project implementation are minimized using an online scheduling model that operates in real-time. The model aims to minimise cancellations of pre-scheduled elective patients whilst also allowing for additional scheduling of emergency cases, time permitting, which may arise during the schedules implementation. Surgical durations are modelled with a lognormal distribution. The single theatre case is solved and the computationally complex multiple theatre case, which is left for future work, is discussed.

Techniques for inserting additional trains into existing timetables

In this paper techniques for scheduling additional train services (SATS) are considered as is train scheduling involving general time window constraints, fixed operations, maintenance activities and periods of section unavailability. The SATS problem is important because additional services must often be given access to the railway and subsequently integrated into current timetables. The SATS problem therefore considers the competition for railway infrastructure between new services and existing services belonging to the same or different operators. The SATS problem is characterised as a hybrid job shop scheduling problem with time window constraints. To solve this problem constructive algorithm and metaheuristic scheduling techniques that operate upon a disjunctive graph model of train operations are utilised. From numerical investigations the proposed framework and associated techniques are tested and shown to be effective.

A sequencing approach for creating new train timetables

Train scheduling is a complex and time consuming task of vital importance. To schedule trains more accurately and efficiently than permitted by current techniques a novel hybrid job shop approach has been proposed and implemented. Unique characteristics of train scheduling are first incorporated into a disjunctive graph model of train operations. A constructive algorithm that utilises this model is then developed. The constructive algorithm is a general procedure that constructs a schedule using insertion, backtracking and dynamic route selection mechanisms. It provides a significant search capability and is valid for any objective criteria. Simulated Annealing and Local Search meta-heuristic improvement algorithms are also adapted and extended. An important feature of these approaches is a new compound perturbation operator that consists of many unitary moves that allows trains to be shifted feasibly and more easily within the solution. A numerical investigation and case study is provided and demonstrates that high quality solutions are obtainable on real sized applications.