Shi Qiang Liu

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.

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 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.

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 (TS) metaheuristic algorithm is developed to deal with the PMJSS problem. The original-version shifting bottleneck procedure (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 in a set of single-machine scheduling (SMS) and/or parallel-machine scheduling 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 TS 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.

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.

A hybrid metaheuristic algorithm to optimise a real-world robotic cell

In this paper, a real-world robotic cell is investigated by transforming it into a special job shop with a set of stationary robots for manufacturing the parts of a product (i.e., operations of a job) at multiple operational stages. In addition, this robotic cell contains a particular mobile robot to transport the parts among stationary robots inside the cell as well as a depot (for initialising the production) and a stockpile (for stocking the complete products) outside the cell. Thus, a new scheduling problem called Blocking Job Shop Scheduling problem with Robotic Transportation (BJSSRT) is proposed. A numerical example is presented to illustrate the characteristics and complexity of BJSSRT. According to the problem properties, four types of robotic movements are defined for a mobile robot in an operations execution: processing-purpose, depot-purpose, return-purpose and stocking-purpose. By satisfying complex feasibility conditions, an innovative graph-based constructive algorithm is developed to produce a good feasible BJSSRT schedule. Embedded with the constructive algorithm, a hybrid Tabu Search and Threshold Accepting metaheuristic algorithm is developed to find a near-optimal solution in an efficient way. The proposed BJSSRT methodology has practical benefits in modelling the automated production system using stationary and mobile robots, especially in manufacturing and mining industries.

An operational-level multi-stage mine production timetabling model for optimally synchronising drilling, blasting and excavating operations

Abstract This paper proposes a new multi-stage mine production timetabling (MMPT) model to optimise open-pit mine production operations including drilling, blasting and excavating under real-time mining constraints. The MMPT problem is formulated as a mixed integer programming model and can be optimally solved for small-size MMPT instances by IBM ILOG-CPLEX. Due to NP-hardness, an improved shifting bottleneck procedure algorithm based on the extended disjunctive graph is developed to solve large-size MMPT instances in an effective and efficient way. Extensive computational experiments are presented to validate the proposed algorithm that is able to efficiently obtain the near-optimal operational timetable of mining equipment units.

Job shop scheduling with a combination of four buffering constraints

In this paper, a new scheduling problem is investigated in order to optimise a more generalised Job Shop Scheduling system with a Combination of four Buffering constraints (i.e. no-wait, no-buffer, limited-buffer and infinite-buffer) called CBJSS. In practice, the CBJSS is significant in modelling and analysing many real-world scheduling systems in chemical, food, manufacturing, railway, health care and aviation industries. Critical problem properties are thoroughly analysed in terms of the Gantt charts. Based on these properties, an applicable mixed integer programming model is formulated and an efficient heuristic algorithm is developed. Computational experiments show that the proposed heuristic algorithm is satisfactory for solving the CBJSS in real time.

An integrated approach to optimise sugarcane rail operations

An innovative mathematical model is presented to optimise a cane transport system.An integrated depth-first-search algorithm with constraint programming is presented.A hybrid metaheuristic technique is developed for finding more accurate solutions with less CPU time. In Australia, the railway system plays a vital role in transporting the sugarcane crop from farms to mills. The sugarcane transport system is complex as it routines a daily schedule, which consists of a set of train runs to satisfy the requirements of the mills and harvesters. A constrain programming approach is used to formulate this complicated system. Metaheuristic techniques and constraint programming are hybridised as an efficient solution approach. Thus, a better sugarcane transport scheduling system is achieved to maximise the throughput of sugarcane transport. A numerical investigation is presented and demonstrates that high-quality solutions are obtainable for industry-scale applications in a reasonable time.