A heuristic method for analyzing driver scheduling problem

A heuristic approach, ZEST for ESTimator, is developed to analyze bus driver scheduling problems and produce an estimate of the number of drivers required for a bus schedule. Based on the observation that the maximum number of drivers is needed in the morning and afternoon peaks, ZEST divides the driver scheduling problem into morning and afternoon subproblems, solves each subproblem separately, and, finally, combines the solutions. The key techniques in ZEST derive from manual scheduling operations that examine the critical decision points in a bus schedule that are vital for a good driver schedule and use these decision points to develop chains of meal breaks that dovetail one driver's meal break with another driver's. ZEST can be used as a standalone estimator of driver duties or as a component of other driver scheduling approaches.     

Optimizing railway crew schedules with fairness preferences

Railway crew scheduling deals with generating duties for train drivers to cover all train movements of a given timetable while taking into account a set of work regulations. The objective is to minimize the overall costs associated with a crew schedule, which includes workforce costs and hotel costs. A cost minimal schedule often contains duties that are unpopular to train drivers, and these unpopular duties are often unevenly distributed among crew depots. At the company that motivated our research, for example, train drivers dislike duties that start in the early morning hours. Currently, some crew depots operate large numbers of these unpopular duties, while others do not have any unpopular duties at all. The train drivers perceive this situation as unfair. They prefer schedules with fewer and more evenly distributed unpopular duties across crew depots. In this paper, we define and measure unpopularity and (un)fairness in a railway crew scheduling context. We integrate fairness conditions into a column generation-based solution algorithm and analyze the effect of increased fairness on cost. We also show how increased fairness affects the unpopularity of a schedule. Our method has been applied to test instances at a large European railway freight carrier. Compared to a standard approach that penalizes only the number of unpopular duties in a schedule, we were able to significantly improve schedule fairness with only marginal increases in schedule cost.     

A robust two-phase heuristic algorithm for the truck scheduling problem in a resource-constrained crossdock

This paper studies truck scheduling in a resource-constrained crossdock. The problem decides on the sequence of incoming and outgoing trucks at the dock doors of the crossdocking terminal, subject to the availability of crossdock resources including dock doors and material handling systems. The resources are assumed non-preemptive making it necessary to address the feasibility of the problem before its optimality as it might be entrapped in deadlock and no feasible solution is produced. The paper thus aims at developing an algorithmic approach capable of establishing solution feasibility for truck scheduling problem instances of various types and difficulty levels which at the same time can be readily implemented in an industrial setting. The proposed approach is a two-phase heuristic algorithm where in the first phase, a heuristic search is deployed to construct a feasible sequence of trucks for the assignment to dock doors and in the second, a rule-based heuristic is used to assign each sequenced truck to a proper dock door, subject to a limited number of forklifts, such that significant savings in the truck schedule length are achieved. Extensive experiments are conducted to evaluate the efficiency of the algorithm in terms of deadlock avoidance and solution quality. The evaluation is carried out against the solutions generated by the exact mathematical model of the problem and a constructive heuristic developed for a similar truck scheduling problem. Experimental results demonstrate that the proposed algorithm is robust in avoiding deadlock and generates feasible solutions for the instances where the other two approaches cannot. Furthermore, significant improvement in the solution quality is achieved by augmenting the algorithm to a re-starting heuristic.     

Combined task and message scheduling in distributed real-timesystems

The paper presents an algorithm for offline scheduling of communicating tasks with precedence and exclusion constraints in distributed hard real time systems. Tasks are assumed to communicate via message passing based on a time bounded communication paradigm, such as the real time channel (D.D. Kandlur et al., 1994). The algorithm uses a branch-and-bound (B & B) technique to search for a task schedule by minimizing maximum task lateness (defined as the difference between task completion time and task deadline), and exploits the interplay between task and message scheduling to improve the quality of solution. It generates a complete schedule at each vertex in the search tree, and can be made to yield a feasible schedule (found before reaching an optimal solution), or proceed until an optimal task schedule is found. We have conducted an extensive simulation study to evaluate the performance of the proposed algorithm. The algorithm is shown to scale well with respect to system size and degree of intertask interactions. It also offers good performance for workloads with a wide range of CPU utilizations and application concurrency. For larger systems and higher loads, we introduce a greedy heuristic that is faster but has no optimality properties. We have also extended the algorithm to a more general resource-constraint model, thus widening its application domain     

A pre-run-time scheduling algorithm for object-based distributed real-time systems

The most important goal in hard real-time systems is to guarantee that all timing constraints are satisfied. Even though object-based techniques (which contain reusable software components) are used to manage the complexity in the software development process of such systems, execution efficiency may have to be sacrificed, due to the large number of procedure calls and contention for accessing software components. These issues are addressed by the following parallelizing techniques: (a) converting potentially inefficient procedure calls to a source of concurrency via asynchronous remote procedure calls (ARPC) (b) replicating (or cloning) software components to reduce the contention. The existing object-based scheduling algorithms construct an initial schedule and apply incremental parallelization techniques to modify the initial schedule till a feasible schedule is generated. But these algorithms are applicable for scheduling only multiple independent tasks. This paper describes a pre-run-time scheduling algorithm for a set of periodic object-based tasks having precedence constraints among them. The algorithm allocates the components of object-based periodic real-time tasks to the sites of a distributed system based on a clustering heuristic which takes into account the ARPC parallelism and load balancing, and schedules them on respective sites. The algorithm also finds a schedule for communication channel(s). Further, it clones the components of object-based periodic tasks, if contention occurs in accessing them. In addition to the above (periodicity and precedence) constraints, the tasks handled by our algorithm can have resource constraints among them. The experimental evaluation of the algorithm shows that the combination of the proposed clustering heuristic and cloning enhances schedulability.     

A dynamic driver management scheme for less-than-truckload carriers

This paper describes a scheme for the dynamic management of linehaul drivers developed for a large US less-than-truckload (LTL) carrier. Virtually all scheduling problems faced by transportation service providers are complicated by time-constrained vehicle operators that can be renewed only after resting. LTL driver scheduling is further complicated by the fact that trucking moves, unlike passenger airline flights or train dispatches, are not pre-scheduled. The technology developed in this paper combines greedy search with enumeration of time-feasible driver duties, and is capable of generating in a matter of minutes cost-effective driver schedules covering 15,000–20,000 loads and satisfying a variety of real-life driver constraints. Computational results justify the algorithmic design choices made in the development of the scheme, and a comparison with real-world dispatch data indicates that the technology produces driver schedules of very high quality.     

Pharmacy duty scheduling problem

In this study, we define the pharmacy duty scheduling problem, which requires a subset of pharmacies to be on duty on national holidays, at weekends, and at nights, in order to be able to satisfy the emergency medicine needs. We model the pharmacy duty scheduling problem as a multiperiod p‐median problem with special side constraints, and analyze the computational complexity. We propose a Tabu Search heuristic and develop lower bound (LB) algorithms. We test the performance of mathematical models, Tabu Search heuristic, and the LBs on randomly generated instances. We analyze the current system in ?zmir, the third largest city in Turkey, with a population of 3.5 million, and apply solution methods. Our results show that the proposed Tabu Search algorithm suggests improvements on the current system.     

A decomposition based hybrid heuristic algorithm for the joint passenger and freight train scheduling problem

We study the joint problem of scheduling passenger and freight trains for complex railway networks, where the objective is to minimize the tardiness of passenger trains at station stops and the delay of freight trains. We model the problem as a mixed integer program and propose a two-step decomposition heuristic to solve the problem. The heuristic first vertically decomposes the train schedules into a passenger train scheduling phase and then a freight train scheduling phase. In the freight train scheduling phase, we use a train-based decomposition to iteratively schedule each freight train. Experimental results show the efficiency and quality of the proposed heuristic algorithm on real world size problems.     

A constraint satisfaction neural network and heuristic combined approach for concurrent activities scheduling

Scheduling activities in concurrent product development process is of great sig-nificance to shorten developements lead time and minimize the cost.Moreover,it can eliminate the unnecessary redesign periods and guarantee that serial activities can be executed as concurrently as possible,This paper presents a constraint satisfaction neural network and heuristic combined approach for concurrent activities scheduling.In the combined approack,the neural network is used to obtain a feasible starting time of all the activities based on sequence constraints ,the heuristic algorithm is used to obtain a feasible solution of the scheduling problem based on resource constrainsts.The feasible scheduling solution is obtained by a gradient optimization function .Sim-ulations have shown that the proposed combined approach is efficient and fasible with respect to concurrent activities scheduling.     

A Constraint Satisfaction Neural Network and Heuristic Combined Approach for Concurrent Activities Scheduling

Scheduling activities in concurrent product development process is of great significance to shorten development lead time and minimize the cost. Moreover, it can eliminate the unnecessary redesign periods and guarantee that serial activities can be executed as concurrently as possible. This paper presents a constraint satisfaction neural network and heuristic combined approach for concurrent activities scheduling. In the combined approach, the neural network is used to obtain a feasible starting time of all the activities based on sequence constraints, the heuristic algorithm is used to obtain a feasible solution of the scheduling problem based on resource constraints. The feasible scheduling solution is obtained by a gradient optimization function. Simulations have shown that the proposed combined approach is efficient and feasible with respect to concurrent activities scheduling.     

Learning and backtracking in non-preemptive scheduling of tasks under timing constraints

We propose two novel heuristic search techniques to address the problem of scheduling tasks under hard timing constraints on a single processor architecture. The underlying problem is NP-hard in the strong sense and it is a fundamental challenge in feedback-control theory and automated cybernetics. The proposed techniques are a learning-based approaches and they take much less memory space. A partial feasible schedule is maintained and extended over a repeated problem solving trials, previously assigned priorities are refined according to the gained information about the problem to lead the convergence to a complete feasible schedule if one exists. First, we present the learning in hard-real-time with single learning (LHRTS-SL) algorithm where a single learning function is utilized, then we discuss its drawback and we propose the LHRTS with double learning algorithm in which a second learning function is integrated to cope up with LHRTS-SL drawback. Experimental results show the efficiency of the proposed techniques in terms of success ratio when used to schedule randomly generated problem instances.     

Efficient scheduling algorithms for real-time multiprocessorsystems

Efficient scheduling algorithms based on heuristic functions are developed for scheduling a set of tasks on a multiprocessor system. The tasks are characterized by worst-case computation times, deadlines, and resources requirements. Starting with an empty partial schedule, each step of the search extends the current partial schedule by including one of the tasks yet to be scheduled. The heuristic functions used in the algorithm actively direct the search for a feasible schedule, i.e. they help choose the task that extends the current partial schedule. Two scheduling algorithms are evaluated by simulation. To extend the current partial schedule, one of the algorithms considers, at each step of the search, all the tasks that are yet to be scheduled as candidates. The second focuses its attention on a small subset of tasks with the shortest deadlines. The second algorithm is shown to be very effective when the maximum allowable scheduling overhead is fixed. This algorithm is hence appropriate for dynamic scheduling in real-time systems     

带约束的清洁排班问题模型及其求解

保洁服务公司的清洁任务往往具有不同级别、不同时长和不同周期等特点,缺乏通用清洁排班问题模型,现阶段主要依赖人工排班方案,存在耗时费力且排班质量不稳定等问题.因此提出了属于NP难问题的带约束的清洁排班问题的数学模型,并使用模拟退火算法(SA)、蜂群算法(BCO)、蚁群算法(ACO)和粒子群优化算法(PSO)对该模型进行求...     

Dispatching rule selection using artificial neural networks for dynamic planning and scheduling

To schedule a job shop, the first task is to select an appropriate scheduling algorithm or rule. Because of the complexity of scheduling problems, no general algorithm sufficient for solving all scheduling problems has yet been developed. Most job-shop scheduling systems offer alternative algorithms for different situations, and experienced human schedulers are needed to select the best dispatching rule in these systems. This paper proposes a new algorithm for job-shop scheduling problems. This algorithm consists of three stages. First, computer simulation techniques are used to evaluate the efficiency of heuristic rules in different scheduling situations. Second, the simulation results are used to train a neural network in order to capture the knowledge which can be used to select the most efficient heuristic rule for each scheduling situation. Finally, the trained neural network is used as a dispatching rule selector in the real-time scheduling process. Research results have shown great potential in using a neural network to replace human schedulers in selecting an appropriate approach for real-time scheduling. This research is part of an ongoing project of developing a real-time planning and scheduling system.     

CCTD：一种通信限制下的Fork-Join任务调度算法

现代并行系统的复杂调度问题可以转化为Fork-join图的任务调度问题.然而在实际计算环境中,两个处理节点之间的通信大多以独占方式进行,现有的大多数任务调度算法往往忽略了对通信信道独占性的考虑.提出了一种带通信限制的Fork-join图调度算法CCTD.该算法引入了实际环境中的通信独占性限制,同时保证了Fork-join图的基于复制的优化调度,而且尽可能地减少了对处理器占用.实验结果表明,CCTD算法是一种适应性强的、高效的Fork-join图调度算法.     

The train driver recovery problem—A set partitioning based model and solution method

The need to recover a train driver schedule occurs during major disruptions in the daily railway operations. Based on data from the Danish passenger railway operator DSB S-tog A/S, a solution method to the train driver recovery problem (TDRP) is developed. The TDRP is formulated as a set partitioning problem. We define a disruption neighbourhood by identifying a small set of drivers and train tasks directly affected by the disruption. Based on the disruption neighbourhood, the TDRP model is formed and solved. If the TDRP solution provides a feasible recovery for the drivers within the disruption neighbourhood, we consider that the problem is solved. However, if a feasible solution is not found, the disruption neighbourhood is expanded by adding further drivers or increasing the recovery time period. Fractional solutions to the LP relaxation of the TDRP are resolved with a constraint branching strategy using the depth-first search of the Branch & Bound tree. The LP relaxation of the TDRP possesses strong integer properties. We present test scenarios generated from the historical real-life operations data of DSB S-tog A/S. The numerical results show that all but one tested instances produce integer solutions to the LP relaxation of the TDRP and solutions are found within a few seconds.     

A graph coloring model for a feasibility problem in monthly crew scheduling with preferential bidding

We consider a monthly crew scheduling problem with preferential bidding in the airline industry. We propose a new methodology based on a graph coloring model and a tabu search algorithm for determining if the problem contains at least one feasible solution. We then show how to combine the proposed approach with a heuristic sequential scheduling method that uses column generation and branch-and-bound techniques.     

Project-driven planning and scheduling support for virtual manufacturing

The paper addresses the issue of decision-making support for small and medium-size enterprises operating within a virtual project-driven enterprise environment. The problem considered here can be defined in terms of finding a feasible schedule that satisfies the constraints imposed by the work-order duration, the price, and the time-constrained resource availability. The problem belongs to the class of multi-mode case problems of project scheduling, where finding a feasible solution is NP-hard. A heuristic method for process planning and scheduling is proposed. The method is based on a critical path approach and the branch and bound search scheme. It has been implemented in a web-enabled interactive software package, and is illustrated using the example of a virtual construction enterprise. Received: February 2005 / Accepted: January 2006     

A nonpreemptive real-time scheduler with recovery from transient faults and its implementation

Real-time systems (RTS) are those whose correctness depends on satisfying the required functional as well as the required temporal properties. Due to the criticality of such systems, recovery from faults is an essential part of a RTS. In many systems, such as those supporting space applications, single event upsets (SEUs) are the prevalent type of faults; SEUs are transient faults and affect a single task at a time. We present a scheme to guarantee that the execution of real-time tasks can tolerate SEUs and intermittent faults assuming any queue-based scheduling technique. Three algorithms are presented to solve the problem of adding fault tolerance to a queue of real-time tasks by reserving sufficient slack in a schedule so that recovery can be carried out before the task deadline without compromising guarantees given to other tasks. The first algorithm is a dynamic programming optimal solution, the second is a linear-time heuristic for scheduling dynamic tasks, and the third algorithm comprises extensions to address queues with gaps between tasks (gaps are caused by precedence, resource, or timing constraints). We show through simulations that the heuristics closely approximate the optimal algorithm. Finally, we describe the implementation of the modified admission control algorithm, non-preemptive scheduler, and recovery mechanism in the FT-RT-Mach operating system.     

The impact of reserve duties on the robustness of a personnel shift roster: An empirical investigation

In personnel scheduling, a duty roster is typically constructed under the assumption of a deterministic model. However, organisations operate in a stochastic environment and the conjectures made about the demand for staff and the availability of employees may prove to be insufficient to represent reality. In order to anticipate these unexpected events, we investigate the impact of introducing reserve duties in the medium-term personnel shift roster. Reserve duties are scheduled by enforcing specific staffing requirements and/or time-related constraints that consider reserve duties only. We propose a three-step methodology that imitates the workforce management process to evaluate the delivered robustness in terms of the actual performance. After a personnel roster is constructed, unexpected events are simulated and an optimisation model determines the required adjustments to balance supply and demand. Detailed computational experiments are presented to provide managerial insights into different strategies to schedule reserve duties.