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 hybrid shifting bottleneck procedure algorithm for the parallel-machine job-shop scheduling problem

In practice, parallel-machine job-shop scheduling (PMJSS) is very useful in the development of standard modelling approaches and generic solution techniques for many real-world scheduling problems. In this paper, based on the analysis of structural properties in an extended disjunctive graph model, a hybrid shifting bottleneck procedure (HSBP) algorithm combined with Tabu Search metaheuristic algorithm is developed to deal with the PMJSS problem. The original-version SBP algorithm for the job-shop scheduling (JSS) has been significantly improved to solve the PMJSS problem with four novelties: i) a topological-sequence algorithm is proposed to decompose the PMJSS problem into a set of single-machine scheduling (SMS) and/or parallel-machine scheduling (PMS) subproblems; ii) a modified Carlier algorithm based on the proposed lemmas and the proofs is developed to solve the SMS subproblem; iii) the Jackson rule is extended to solve the PMS subproblem; iv) a Tabu Search metaheuristic algorithm is embedded under the framework of SBP to optimise the JSS and PMJSS cases. The computational experiments show that the proposed HSBP is very efficient in solving the JSS and PMJSS problems.

Scheduling Trains with Priorities : a no-wait blocking parallel-machine job-shop scheduling model

The paper investigates train scheduling problems when prioritised trains and non-prioritised trains are simultaneously traversed in a single-line rail network. In this case, no-wait conditions arise because the prioritised trains such as express passenger trains should traverse continuously without any interruption. In comparison, non-prioritised trains such as freight trains are allowed to enter the next section immediately if possible or to remain in a section until the next section on the routing becomes available, which is thought of as a relaxation of no-wait conditions. With thorough analysis of the structural properties of the No-Wait Blocking Parallel-Machine Job-Shop-Scheduling (NWBPMJSS) problem that is originated in this research, an innovative generic constructive algorithm (called NWBPMJSS_Liu-Kozan) is proposed to construct the feasible train timetable in terms of a given order of trains. In particular, the proposed NWBPMJSS_Liu-Kozan constructive algorithm comprises several recursively-used sub-algorithms (i.e. Best-Starting-Time-Determination Procedure, Blocking-Time-Determination Procedure, Conflict-Checking Procedure, Conflict-Eliminating Procedure, Tune-up Procedure and Fine-tune Procedure) to guarantee feasibility by satisfying the blocking, no-wait, deadlock-free and conflict-free constraints. A two-stage hybrid heuristic algorithm (NWBPMJSS_Liu-Kozan-BIH) is developed by combining the NWBPMJSS_Liu-Kozan constructive algorithm and the Best-Insertion-Heuristic (BIH) algorithm to find the preferable train schedule in an efficient and economical way. Extensive computational experiments show that the proposed methodology is promising because it can be applied as a standard and fundamental toolbox for identifying, analysing, modelling and solving real-world scheduling problems.

Metaheuristics for the mixed shop scheduling problem

In this paper, three metaheuristics are proposed for solving a class of job shop, open shop, and mixed shop scheduling problems. We evaluate the performance of the proposed algorithms by means of a set of Lawrence’s benchmark instances for the job shop problem, a set of randomly generated instances for the open shop problem, and a combined job shop and open shop test data for the mixed shop problem. The computational results show that the proposed algorithms perform extremely well on all these three types of shop scheduling problems. The results also reveal that the mixed shop problem is relatively easier to solve than the job shop problem due to the fact that the scheduling procedure becomes more flexible by the inclusion of more open shop jobs in the mixed shop.

Scheduling techniques to optimise sugarcane rail transport systems

In Australia, railway systems play a vital role in transporting the sugarcane crop from farms to mills. In this paper, a novel job shop approach is proposed to create a more efficient integrated harvesting and sugarcane transport scheduling system to reduce the cost of sugarcane transport. There are several benefits that can be attained by treating the train scheduling problem as a job shop problem. Job shop is generic and suitable for all trains scheduling problems. Job shop technique prevents operating two trains on one section at the same time because it considers that the section or the machine is unique. This technique is more promising to find better solutions in reasonable computation times.

Metaheuristics for minimizing the makespan of the dynamic shop scheduling problem

For the shop scheduling problems such as flow-shop, job-shop, open-shop, mixed-shop, and group-shop, most research focuses on optimizing the makespan under static conditions and does not take into consideration dynamic disturbances such as machine breakdown and new job arrivals. We regard the shop scheduling problem under static conditions as the static shop scheduling problem, while the shop scheduling problem with dynamic disturbances as the dynamic shop scheduling problem. In this paper, we analyze the characteristics of the dynamic shop scheduling problem when machine breakdown and new job arrivals occur, and present a framework to model the dynamic shop scheduling problem as a static group-shop-type scheduling problem. Using the proposed framework, we apply a metaheuristic proposed for solving the static shop scheduling problem to a number of dynamic shop scheduling benchmark problems. The results show that the metaheuristic methodology which has been successfully applied to the static shop scheduling problems can also be applied to solve the dynamic shop scheduling problem efficiently.

A fast tabu search algorithm for the group shop scheduling problem

Three types of shop scheduling problems, the flow shop, the job shop and the open shop scheduling problems, have been widely studied in the literature. However, very few articles address the group shop scheduling problem introduced in 1997, which is a general formulation that covers the three above mentioned shop scheduling problems and the mixed shop scheduling problem. In this paper, we apply tabu search to the group shop scheduling problem and evaluate the performance of the algorithm on a set of benchmark problems. The computational results show that our tabu search algorithm is typically more efficient and faster than the other methods proposed in the literature. Furthermore, the proposed tabu search method has found some new best solutions of the benchmark instances.

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.

Modelling and solving train scheduling problems under capacity constraints

Many large coal mining operations in Australia rely heavily on the rail network to transport coal from mines to coal terminals at ports for shipment. Over the last few years, due to the fast growing demand, the coal rail network is becoming one of the worst industrial bottlenecks in Australia. As a result, this provides great incentives for pursuing better optimisation and control strategies for the operation of the whole rail transportation system under network and terminal capacity constraints. This PhD research aims to achieve a significant efficiency improvement in a coal rail network on the basis of the development of standard modelling approaches and generic solution techniques. Generally, the train scheduling problem can be modelled as a Blocking Parallel- Machine Job-Shop Scheduling (BPMJSS) problem. In a BPMJSS model for train scheduling, trains and sections respectively are synonymous with jobs and machines and an operation is regarded as the movement/traversal of a train across a section. To begin, an improved shifting bottleneck procedure algorithm combined with metaheuristics has been developed to efficiently solve the Parallel-Machine Job- Shop Scheduling (PMJSS) problems without the blocking conditions. Due to the lack of buffer space, the real-life train scheduling should consider blocking or hold-while-wait constraints, which means that a track section cannot release and must hold a train until the next section on the routing becomes available. As a consequence, the problem has been considered as BPMJSS with the blocking conditions. To develop efficient solution techniques for BPMJSS, extensive studies on the nonclassical scheduling problems regarding the various buffer conditions (i.e. blocking, no-wait, limited-buffer, unlimited-buffer and combined-buffer) have been done. In this procedure, an alternative graph as an extension of the classical disjunctive graph is developed and specially designed for the non-classical scheduling problems such as the blocking flow-shop scheduling (BFSS), no-wait flow-shop scheduling (NWFSS), and blocking job-shop scheduling (BJSS) problems. By exploring the blocking characteristics based on the alternative graph, a new algorithm called the topological-sequence algorithm is developed for solving the non-classical scheduling problems. To indicate the preeminence of the proposed algorithm, we compare it with two known algorithms (i.e. Recursive Procedure and Directed Graph) in the literature. Moreover, we define a new type of non-classical scheduling problem, called combined-buffer flow-shop scheduling (CBFSS), which covers four extreme cases: the classical FSS (FSS) with infinite buffer, the blocking FSS (BFSS) with no buffer, the no-wait FSS (NWFSS) and the limited-buffer FSS (LBFSS). After exploring the structural properties of CBFSS, we propose an innovative constructive algorithm named the LK algorithm to construct the feasible CBFSS schedule. Detailed numerical illustrations for the various cases are presented and analysed. By adjusting only the attributes in the data input, the proposed LK algorithm is generic and enables the construction of the feasible schedules for many types of non-classical scheduling problems with different buffer constraints. Inspired by the shifting bottleneck procedure algorithm for PMJSS and characteristic analysis based on the alternative graph for non-classical scheduling problems, a new constructive algorithm called the Feasibility Satisfaction Procedure (FSP) is proposed to obtain the feasible BPMJSS solution. A real-world train scheduling case is used for illustrating and comparing the PMJSS and BPMJSS models. Some real-life applications including considering the train length, upgrading the track sections, accelerating a tardy train and changing the bottleneck sections are discussed. Furthermore, the BPMJSS model is generalised to be a No-Wait Blocking Parallel- Machine Job-Shop Scheduling (NWBPMJSS) problem for scheduling the trains with priorities, in which prioritised trains such as express passenger trains are considered simultaneously with non-prioritised trains such as freight trains. In this case, no-wait conditions, which are more restrictive constraints than blocking constraints, arise when considering the prioritised trains that should traverse continuously without any interruption or any unplanned pauses because of the high cost of waiting during travel. In comparison, non-prioritised trains are allowed to enter the next section immediately if possible or to remain in a section until the next section on the routing becomes available. Based on the FSP algorithm, a more generic algorithm called the SE algorithm is developed to solve a class of train scheduling problems in terms of different conditions in train scheduling environments. To construct the feasible train schedule, the proposed SE algorithm consists of many individual modules including the feasibility-satisfaction procedure, time-determination procedure, tune-up procedure and conflict-resolve procedure algorithms. To find a good train schedule, a two-stage hybrid heuristic algorithm called the SE-BIH algorithm is developed by combining the constructive heuristic (i.e. the SE algorithm) and the local-search heuristic (i.e. the Best-Insertion- Heuristic algorithm). To optimise the train schedule, a three-stage algorithm called the SE-BIH-TS algorithm is developed by combining the tabu search (TS) metaheuristic with the SE-BIH algorithm. Finally, a case study is performed for a complex real-world coal rail network under network and terminal capacity constraints. The computational results validate that the proposed methodology would be very promising because it can be applied as a fundamental tool for modelling and solving many real-world scheduling problems.

Optimising a coal rail network under capacity constraints

This research deals with an innovative methodology for optimising the coal train scheduling problem. Based on our previously published work, generic solution techniques are developed by utilising a “toolbox” of standard well-solved standard scheduling problems. According to our analysis, the coal train scheduling problem can be basically modelled a Blocking Parallel-Machine Job-Shop Scheduling (BPMJSS) problem with some minor constraints. To construct the feasible train schedules, an innovative constructive algorithm called the SLEK algorithm is proposed. To optimise the train schedule, a three-stage hybrid algorithm called the SLEK-BIH-TS algorithm is developed based on the definition of a sophisticated neighbourhood structure under the mechanism of the Best-Insertion-Heuristic (BIH) algorithm and Tabu Search (TS) metaheuristic algorithm. A case study is performed for optimising a complex real-world coal rail system in Australia. A method to calculate the lower bound of the makespan is proposed to evaluate results. The results indicate that the proposed methodology is promising to find the optimal or near-optimal feasible train timetables of a coal rail system under network and terminal capacity constraints.

Scheduling a flow-shop with combined buffer conditions

In this paper, No-Wait, No-Buffer, Limited-Buffer, and Infinite-Buffer conditions for the flow-shop problem (FSP) have been investigated. These four different buffer conditions have been combined to generate a new class of scheduling problem, which is significant for modelling many real-world scheduling problems. A new heuristic algorithm is developed to solve this strongly NP-hard problem. Detailed numerical implementations have been analysed and promising results have been achieved.

Scheduling techniques to optimise rail operations

In Australia, railway systems play a vital role in transporting the sugarcane crop from farms to mills. The sugarcane transport system is very complex and uses daily schedules, consisting of a set of locomotives runs, to satisfy the requirements of the mill and harvesters. The total cost of sugarcane transport operations is very high; over 35% of the total cost of sugarcane production in Australia is incurred in cane transport. Efficient schedules for sugarcane transport can reduce the cost and limit the negative effects that this system can have on the raw sugar production system. There are several benefits to formulating the train scheduling problem as a blocking parallel-machine job shop scheduling (BPMJSS) problem, namely to prevent two trains passing in one section at the same time; to keep the train activities (operations) in sequence during each run (trip) by applying precedence constraints; to pass the trains on one section in the correct order (priorities of passing trains) by applying disjunctive constraints; and, to ease passing trains by solving rail conflicts by applying blocking constraints and Parallel Machine Scheduling. Therefore, the sugarcane rail operations are formulated as BPMJSS problem. A mixed integer programming and constraint programming approaches are used to describe the BPMJSS problem. The model is solved by the integration of constraint programming, mixed integer programming and search techniques. The optimality performance is tested by Optimization Programming Language (OPL) and CPLEX software on small and large size instances based on specific criteria. A real life problem is used to verify and validate the approach. Constructive heuristics and new metaheuristics including simulated annealing and tabu search are proposed to solve this complex and NP-hard scheduling problem and produce a more efficient scheduling system. Innovative hybrid and hyper metaheuristic techniques are developed and coded using C# language to improve the solutions quality and CPU time. Hybrid techniques depend on integrating heuristic and metaheuristic techniques consecutively, while hyper techniques are the complete integration between different metaheuristic techniques, heuristic techniques, or both.

Hybrid metaheuristic techniques for optimising sugarcane rail operations

Mixed integer programming and parallel-machine job shop scheduling are used to solve the sugarcane rail transport scheduling problem. Constructive heuristics and metaheuristics were developed to produce a more efficient scheduling system and so reduce operating costs. The solutions were tested on small and large size problems. High-quality solutions and improved CPU time are the result of developing new hybrid techniques which consist of different ways of integrating simulated annealing and Tabu search techniques.

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.