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.     

Single machine scheduling with batch-dependent setup times

We address a single-machine batch scheduling problem. The setup times (incurred whenever starting a new batch) are assumed to be a function of the number of batches processed previously, i.e., batch-dependent. The objective is minimum total flow-time. We focus on the case of identical processing time jobs. Given the number of jobs and the setup times, we have to determine the optimal number of batches and their (integer) size. An efficient (O(n)) solution procedure is introduced.     

The periodicity and robustness in a single-track train scheduling problem

The most important operating problem in any railway industry is to produce robust train timetables with minimum delays. The train scheduling problem is defined as an application of job shop scheduling which is considered to be one of the most interesting research topics. This paper deals with scheduling different types of trains in a single railway track. The authors have focused on the robust and periodic aspects of produced timetables. This paper is also concerned with some applicable constraints, such as the acceleration and deceleration times, station capacity and headway constraints. The periodic timetable for railways is modeled based on the periodic event scheduling problem (PESP). Furthermore, a fuzzy approach is used to reach a tradeoff among the total train delays, the robustness of schedules, and the time interval between departures of trains from the same origins. To solve large-scale problems, a meta-heuristic algorithm based on simulated annealing (SA) is utilized and validated using some numerical examples on a periodic robust train scheduling problem. Finally, a robustness measure is defined in order to assure the effectiveness of the proposed SA to find robust solutions.     

Single machine scheduling with past-sequence-dependent setup times and deteriorating jobs

This paper considers single machine scheduling problems with setup times and deteriorating jobs. The setup times are proportional to the length of the already processed jobs, that is, the setup times are past-sequence-dependent (p-s-d). It is assumed that the job processing times are defined by functions dependent on their starting times. The following objectives are considered: the makespan, the total completion time, and the sum of earliness, tardiness, and due-window starting time and size penalties. We propose polynomial time algorithms to solve these problems.     

Task-resource scheduling problem

Cloud computing is a new and rapidly emerging computing paradigm where applications,data and IT services are provided over the Internet.The task-resource management is the key role in cloud computing systems.Task-resource scheduling problems are premier which relate to the efficiency of the whole cloud computing facilities.Task-resource scheduling problem is NPcomplete.In this paper,we consider an approach to solve this problem optimally.This approach is based on constructing a logical model for the problem.Using this model,we can apply algorithms for the satisfiability problem(SAT) to solve the task-resource scheduling problem.Also,this model allows us to create a testbed for particle swarm optimization algorithms for scheduling workflows.     

Robust scheduling on a single machine to minimize total flow time

In a real-world manufacturing environment featuring a variety of uncertainties, production schedules for manufacturing systems often cannot be executed exactly as they are developed. In these environments, schedule robustness that guarantees the best worst-case performance is a more appropriate criterion in developing schedules, although most existing studies have developed optimal schedules with respect to a deterministic or stochastic scheduling model. This study concerns robust single machine scheduling with uncertain job processing times and sequence-dependent family setup times explicitly represented by interval data. The objective is to obtain robust sequences of job families and jobs within each family that minimize the absolute deviation of total flow time from the optimal solution under the worst-case scenario. We prove that the robust single machine scheduling problem of interest is NP-hard. This problem is reformulated as a robust constrained shortest path problem and solved by a simulated annealing-based algorithmic framework that embeds a generalized label correcting method. The results of numerical experiments demonstrate that the proposed heuristic is effective and efficient for determining robust schedules. In addition, we explore the impact of degree of uncertainty on the performance measures and examine the tradeoff between robustness and optimality.     

A branch-and-cut algorithm for a production scheduling problem with sequence-dependent and time-dependent setup times

This paper introduces and compares three different formulations of a production scheduling problem with sequence-dependent and time-dependent setup times on a single machine. The setup is divided into two parts: one that can be performed at any time and another one that is restricted to be performed outside of a given time interval. As a result, the setup time between two jobs is a function of the completion time of the first job. The problem can be formulated as a time-dependent traveling salesman problem, where the travel time between two nodes is a function of the departure time from the first node. We show that the resulting formulation can be strengthened to provide better linear programming relaxation lower bounds. We also introduce several families of valid inequalities which are used within a branch-and-cut algorithm. Computational experiments show that this algorithm can solve some instances with up to 50 jobs within reasonable computing times.     

Preemptive open shop scheduling with multiprocessors: polynomial cases and applications

This paper addresses a multiprocessor generalization of the preemptive open-shop scheduling problem. The set of processors is partitioned into two groups and the operations of the jobs may require either single processors in either group or simultaneously all processors from the same group. We consider two variants depending on whether preemptions are allowed at any fractional time points or only at integer time points. We reduce the former problem to solving a linear program in strongly polynomial time, while a restricted version of the second problem is solved by rounding techniques. Applications to course scheduling and hypergraph edge coloring are also discussed.     

一类具有资源约束和恶化效应的单机成组排序问题

讨论具有连续资源的单机成组排序问题.这一模型中同一组内的工件不允许分开加工,各工件组的安装时间是所消耗资源的非负减少连续函数.工件的加工时问是开工时问的严格减少函数.针对满足资源消耗总量限制条件下极小化最大完工时问的问题.以及在满足最大完工时间限制条件下极小化资源消耗总量的问题,讨论了最优排序的某些特征,分别给出了求解最优资源分配的方法.最后通过数值例子表明了所提出方法的正确性和有效性.     

A note on a single-machine lot scheduling problem with indivisible orders

In this paper, a lot scheduling problem on a single machine with indivisible orders is studied. The objective is to minimize the total completion time of all orders. We show that the problem is NP-hard in the strong sense. Then, a binary integer programming approach and four simple heuristics are proposed to solve the problem. The binary integer programming approach with running time limit is considered as one heuristic method. As compared to a lower bound, the average performances of the heuristic method are really good and better than those of the four simple heuristics.     

Three scheduling problems with deteriorating jobs to minimize the total completion time

In this paper, three scheduling problems with deteriorating jobs to minimize the total completion time on a single machine are investigated. By a deteriorating job, we mean that the processing time of the job is a function of its execution start time. The three problems correspond to three different decreasing linear functions, whose increasing counterparts have been studied in the literature. Some basic properties of the three problems are proved. Based on these properties, two of the problems are solved in O(nlogn) time, where n is the number of jobs. A pseudopolynomial time algorithm is constructed to solve the third problem using dynamic programming. Finally, a comparison between the problems with job processing times being decreasing and increasing linear functions of their start times is presented, which shows that the decreasing and increasing linear models of job processing times seem to be closely related to each other.     

Approximation results for a bicriteria job scheduling problem on a single machine without preemption

We study the problem of minimizing the average weighted completion time on a single machine under the additional constraint that the sum of completion times does not exceed a given bound B(1|∑Cj?B|∑wjCj) for which we propose a (2,1)-approximation algorithm. We also address the problem 1|∑cjCj?B|∑wjCj for which we present a (2,2)-approximation algorithm. After showing that the problem of minimizing two different sums of weighted completion times is intractable, we present an algorithm which computes a (2(1+?),1) (respectively (2(1+?),2))-approximate Pareto curve for the problem 1‖(∑Cj,∑wjCj) (respectively 1‖(∑cjCj,∑wjCj)).     

A study of hybrid evolutionary algorithms for single machine scheduling problem with sequence-dependent setup times

We present a systematic comparison of hybrid evolutionary algorithms (HEAs), which independently use six combinations of three crossover operators and two population updating strategies, for solving the single machine scheduling problem with sequence-dependent setup times. Experiments show the competitive performance of the combination of the linear order crossover operator and the similarity-and-quality based population updating strategy. Applying the selected HEA to solve 120 public benchmark instances of the single machine scheduling problem with sequence-dependent setup times to minimize the total weighted tardiness widely used in the literature, we achieve highly competitive results compared with the exact algorithm and other state-of-the-art metaheuristic algorithms in the literature. Meanwhile, we apply the selected HEA in its original form to deal with the unweighted 64 public benchmark instances. Our HEA is able to improve the previous best known results for one instance and match the optimal or the best known results for the remaining 63 instances in a reasonable time.     

Two machine flow shop scheduling problem with weighted WIP costs

This paper considers two new machine flow shop scheduling problems where the objective is to minimize the total WIP (work-in-process) cost. In this type of problems, the unit time WIP cost increases or decreases as a job passes through a series of stages in the production process.     

Single machine scheduling problems with resource dependent release times

We consider two single machine scheduling problems with resource dependent release times that can be controlled by a non-increasing convex resource consumption function. In the first problem, the objective is to minimize the total resource consumption with a constraint on the sum of job completion times. We show that a recognition version of the problem is NP-complete. In the second problem, the objective is to minimize the weighted total resource consumption and sum of job completion times with an initial release time greater than the total processing times. We provide some optimality conditions and show that the problem is polynomially solvable.     

A tabu search heuristic for a sequence-dependent and time-dependent scheduling problem on a single machine

This paper introduces a tabu search heuristic for a production scheduling problem with sequence-dependent and time-dependent setup times on a single machine. The problem consists in scheduling a set of dependent jobs, where the transition between two jobs comprises an unrestricted setup that can be performed at any time, and a restricted setup that must be performed outside of a given time interval which repeats daily in the same position. The setup time between two jobs is thus a function of the completion time of the first job. The tabu search heuristic relies on shift and swap moves, and a surrogate objective function is used to speed-up the neighborhood evaluation. Computational experiments show that the proposed heuristic consistently finds better solutions in less computation time than a recent branch-and-cut algorithm. Furthermore, on instances where the branch-and-cut algorithm cannot find the optimal solution, the heuristic always identifies a better solution.     

Algorithms for multiprocessor scheduling with two job lengths and allocation restrictions

A variant of the High Multiplicity Multiprocessor Scheduling Problem with C job lengths is considered, in which jobs can be processed only by machines not greater than a given index. When C=2, polynomial algorithms are proposed, for the feasibility version of the problem and for maximizing the number of scheduled jobs.     

The economic lot scheduling problem: A pure genetic search approach

The economic lot scheduling problem (ELSP) is the challenge of accommodating several products to be produced on a single machine in a cyclical pattern. A solution involves determining the repetitive production schedule for N$N$ products with a goal of minimizing the total of setup and holding costs. We develop the genetic lot scheduling (GLS) procedure. This method combines an extended solution structure with a new item scheduling approach, allowing a greater number of potential schedules to be considered while being the first to explicitly state the assignment of products to periods as part of the solution structure. We maintain efficient solution feasibility determination, a problematic part of ELSP solution generation and a weakness of several other methods, by employing simple but effective sequencing rules that create “nested” schedules. We create a binary chromosomal representation of the new problem formulation and utilize a genetic algorithm to efficiently search for low cost ELSP solutions. The procedure is applied to a benchmark problem suite from the literature, including Bomberger's stamping problem [Bomberger, A dynamic programming approach to a lot scheduling problem. Management Science 1966; 12:778–84], a problem that has been under investigation since the mid 1960's. The genetic lot scheduling procedure produces impressive results, including the best solutions obtained to date on some problems.     

A genetic algorithm for railway scheduling with environmental considerations

A genetic algorithm is a randomized optimization technique that draws its inspiration from the biological sciences. Specifically, it uses the idea that genetics determines the evolution of any species in the natural world. Integer strings are used to encode an optimization problem and these strings are subject to combinatorial operations called reproduction, crossover and mutation, which improve these strings and cause them to ‘evolve’ to an optimal or nearly optimal solution. In this paper, the general machinations of genetic algorithms are described and a performance-enhanced algorithm is proposed for solving the important practical problem of railway scheduling. The problem under consideration involves moving a number of trains carrying mineral deposits across a long haul railway line with both single and double tracks in either direction. Collisions can only be avoided in sections of the line with double tracks. Constraints reflecting practical requirements to reduce environmental impacts from mineral transport, such as avoidance of loaded trains traversing populated areas during certain time slots, have to be satisfied. This is an NP-hard problem, which usually requires enumerative, as opposed to constructive, algorithms. For this reason, an ‘educated’ random search procedure like the genetic algorithm is an alternative and effective technique. The genetic algorithm is given difficult test problems to solve and the algorithm was able to generate feasible solutions in all cases.