Erwin Pesch

Resource-constrained project scheduling : Notation, classification, models, and methods

Abstract Project scheduling is concerned with single-item or small batch production where scarce resources have to be allocated to dependent activities over time. Applications can be found in diverse industries such as construction engineering, software development, etc. Also, project scheduling is increasingly important for make-to-order companies where the capacities have been cut down in order to meet lean management concepts. Likewise, project scheduling is very attractive for researchers, because the models in this area are rich and, hence, difficult to solve. For instance, the resource-constrained project scheduling problem contains the job shop scheduling problem as a special case. So far, no classification scheme exists which is compatible with what is commonly accepted in machine scheduling. Also, a variety of symbols are used by project scheduling researchers in order to denote one and the same subject. Hence, there is a gap between machine scheduling on the one hand and project scheduling on the other with respect to both, viz. a common notation and a classification scheme. As a matter of fact, in project scheduling, an ever growing number of papers is going to be published and it becomes more and more difficult for the scientific community to keep track of what is really new and relevant. One purpose of our paper is to close this gap. That is, we provide a classification scheme, i.e. a description of the resource environment, the activity characteristics, and the objective function, respectively, which is compatible with machine scheduling and which allows to classify the most important models dealt with so far. Also, we propose a unifying notation. The second purpose of this paper is to review some of the recent developments. More specifically, we review exact and heuristic algorithms for the single-mode and the multi-mode case, for the time–cost tradeoff problem, for problems with minimum and maximum time lags, for problems with other objectives than makespan minimization and, last but not least, for problems with stochastic activity durations.

The Job Shop Scheduling Problem: Conventional and new Solution Techniques

A job shop consists of a set of different machines that perform operations on jobs. Each job has a specified processing order through the machines, i.e. a job is composed of an ordered list of operations each of which is determined by the machine required and the processing time on it. There are no precedence constraints among operations of different jobs. Operations can not be interrupted (non-preemption) and each machine can handle only one job at a time. Consequently, each job can be performed on only one machine at a time. The operation sequences on the machines are unknown and have to be determined in order to minimize the makespan, i. e. the time required to complete all jobs.

A branch-and-bound algorithm for the resource-constrained project scheduling problem

Abstract. We describe a time-oriented branch-and-bound algorithm for the resource-constrained project scheduling problem which explores the set of active schedules by enumerating possible activity start times. The algorithm uses constraint-propagation techniques that exploit the temporal and resource constraints of the problem in order to reduce the search space. Computational experiments with large, systematically generated benchmark test sets, ranging in size from thirty to one hundred and twenty activities per problem instance, show that the algorithm scales well and is competitive with other exact solution approaches. The computational results show that the most difficult problems occur when scarce resource supply and the structure of the resource demand cause a problem to be highly disjunctive.

Fast Clustering Algorithms

This paper considers the problem of partitioning the vertices of a weighted complete graph into cliques of unbounded size and number, such that the sum of the edge weights of all cliques is maximized. The problem is known as the clique-partitioning problem and arises as a clustering problem in qualitative data analysis. A simple greedy algorithm is extended to an ejection chain heuristic leading to optimal solutions in all practical test problems known from literature. The heuristic is used to compute an initial lower bound as well as to guide branching in a branch and bound algorithm which is superior to present exact methods. Empirical data for all three algorithms are reported. INFORMS Journal on Computing, ISSN 1091-9856, was published as ORSA Journal on Computing from 1989 to 1995 under ISSN 0899-1499.

A Survey on Container Processing in Railway Yards

In spite of extraordinary support programs initiated by the European Union and other national authorities, the percentage of overall freight traffic moved by train is in steady decline. This development is driven by the fact that macro-economic benefits of rail traffic, such as relief of overloaded road networks and reduced environmental impacts, are countervailed by severe disadvantages from the perspective of the shipper, e.g., low average delivery speed and general lack of reliability. Attracting a higher share of freight traffic on rail requires a more efficient freight handling in railway yards, which includes technical innovations as well as the development of suited decision support systems. This paper reviews container processing in railway yards from an operational research perspective and analyzes basic decision problems for the two most important yard types, namely conventional rail-road and modern rail-rail transshipment yards. Existing literature is reviewed and open research challenges are identified.

Shunting yard operations: Theoretical aspects and applications ☆

Almost ever since freight has been transported via rail, shunting yards (also called classification or marshaling yards) are operated in order to separate freight trains and reassemble new trains. The efficient use of shunting yards has a deep impact on the efficiency and reliability of rail freight services. Thus, much research on shunting yards has been published, starting from the 1950s. Lately, several publications mostly focusing on the sorting procedures have livened up research on shunting yards. This paper reviews the literature on the operational processes at shunting yards over the last 40years and discusses the operational challenges of freight transshipment. The approaches are classified according to different sorting strategies which allows an easy access to the models for both, researchers and practitioners. The paper concludes with an overview on future research challenges.

Constraint propogation techniques for the disjunctive scheduling problem

Abstract Constraint propagation is an elementary method for reducing the search space of combinatorial search and optimization problems which has become more and more important in the last decades. The basic idea of constraint propagation is to detect and remove inconsistent variable assignments that cannot participate in any feasible solution through the repeated analysis and evaluation of the variables, domains and constraints describing a specific problem instance. The contribution of this paper is twofold. The first contribution is a description of efficient constraint propagation methods also known as consistency tests for the disjunctive scheduling problem (DSP) which is a generalization of the classical job shop scheduling problem (JSP). Applying an elementary constraint based approach involving a limited number of search variables, we will derive consistency tests that ensure 3 -b-consistency. We will further present and analyze both new and classical consistency tests which to some extent are generalizations of the aforementioned consistency tests involving a higher number of variables, but still can be implemented efficiently with a polynomial time complexity. Further, the concepts of energetic reasoning and shaving are analyzed and discussed. The other contribution is a classification of the consistency tests derived according to the domain reduction achieved. The particular strength of using consistency tests is based on their repeated application, so that the knowledge derived is propagated, i.e., reused for acquiring additional knowledge. The deduction of this knowledge can be described as the computation of a fixed point. Since this fixed point depends upon the order of the application of the tests, we first derive a necessary condition for its uniqueness. We then develop a concept of dominance which enables the comparison of different consistency tests as well as a simple method for proving dominance. An extensive comparison of all consistency tests is given. Quite surprisingly, we will find out that some apparently stronger consistency tests are subsumed by apparently weaker ones. At the same time an open question regarding the effectiveness of energetic reasoning is answered.

TSP ejection chains

Abstract We identify ejection chain methods for the traveling salesman problem based on a special reference structure for generating constructions related to alternating paths. Computational tests show that the method performs very effectively, obtaining generally better solutions than improved versions of the Lin-Kernighan method within the same time frame. Our approach, which currently has a simple tabu search guidance component at a local level, also has the potential to be combined in more advanced ways with metaheuristics such as genetic algorithms, simulated annealing and tabu search.

The disjunctive graph machine representation of the job shop scheduling problem

Abstract The disjunctive graph is one of the most popular models used for describing instances of the job shop scheduling problem, which has been very intensively explored. In this paper, a new time and memory efficient representation of the disjunctive graph is proposed. It has the form of a graph matrix and combines advantages of a few classical graph representations, enabling easy operating on the problem data. Computational experiments have proved higher efficiency of the proposed approach over the classical ones.

A Survey of Interval Capacity Consistency Tests for Time- and Resource-Constrained Scheduling

Interval capacity consistency tests consider the resource capacities available and required within certain time intervals. The goal of the tests is to draw conclusions that allow to rule out inadmissible activity start times or sequences. The tests can be effectively used to reduce the search space of difficult time- and resource-constrained scheduling problems. They have successfully been applied in algorithms for solving idealised problems such as the classical job shop scheduling problem (JSP) or the resource-constrained project scheduling problem (RCPSP) as well as for solving industrial scheduling problems. For instance, it seems fair to say that the advances in modern branch and bound algorithms for the JSP that have been made in the last decade can to a large extent be attributed to the effect of interval consistency tests, some of which are also known under the names of immediate selection, edge finding, and energetic reasoning. The tests can also serve to derive tight lower bounds for makespan minimisation problems.