Andreas Drexl

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.

Facility location models for distribution system design

The design of the distribution system is a strategic issue for almost every company. The problem of locating facilities and allocating customers covers the core topics of distribution system design. Model formulations and solution algorithms which address the issue vary widely in terms of fundamental assumptions, mathematical complexity and computational performance. This paper reviews some of the contributions to the current state-of-the-art. In particular, continuous location models, network location models, mixed-integer programming models, and applications are summarized.

Lot sizing and scheduling — Survey and extensions

This contribution summarizes recent work in the field of lot sizing and scheduling. The objective is not to give a comprehensive literature survey, but to explain differences of formal models and to provide some first readings recommendations. Our focus is on capacitated, dynamic, and deterministic cases. To underscore the importance of the research efforts, current practice is described and its shortcomings are exposed. Mathematical programming models where the planning horizon is subdivided into several discrete periods are given for both approaches that are well-established and approaches which may represent tomorrows state of the art. Two research directions are discussed in more detail: continuous time models and multi-level lot sizing and scheduling. The paper concludes with some advice for future research activities.

Multi-mode resource-constrained project scheduling by a simple, general and powerful sequencing algorithm

In this paper we present an exact solution procedure of the branch-and-bound type for solving the multi-mode resource-constrained project scheduling problem. The basic enumeration scheme is enhanced by search tree reduction schemes which highly increase the performance of the algorithm. Among the benefits of the approach are ease of description, ease of implementation, ease of generalization, and, additionally, superior performance of the exact approach as well as reasonable heuristic capabilities of the truncated version. The procedure has been coded in C and implemented on a personal computer. Using the standard project generator ProGen we have established a wide range of instances. More than 10,000 problem instances have been systematically generated to evaluate the algorithms performance. The experimental investigation illustrates: First, the effect of the bounding rules. Second, the superior performance of the exact approach and the capabilities of the truncated version; the size of the projects that can be solved to optimality has been nearly doubled. Third, the impact of the variation of several project characteristics on solution time and quality.

Semi-active, active and non-delay schedules for the resource-constrained project scheduling problem

We consider the resource-constrained project scheduling problem (RCPSP). The focus of the paper is on a formal definition of semi-active, active, and non-delay schedules. Traditionally these schedules establish basic concepts within the job shop scheduling literature. There they are usually defined in a rather informal way which does not create any substantial problems. Using these concepts in the more general RCPSP without giving a formal definition may cause serious problems. After providing a formal definition of semi-active, active, and non-delay schedules for the RCPSP we outline some of these problems occurring within the disjunctive arc concept.

An exact algorithm for project scheduling with multiple modes

We consider an extension of the classical resource-constrained project scheduling problem (RCPSP), which covers discrete resource-resource and time-resource tradeoffs. As a result a project scheduler is permitted to identify several alternatives or modes of accomplishment for each activity of the project. The solution procedure to be presented is a considerable generalization of the branch-and-bound algorithm proposed by Demeulemeester and Herroelen, which is currently the most powerful method for optimally solving the RCPSP. More precisely, we extend their concept of delay alternatives by introducing mode alternatives. The basic enumeration scheme is enhanced by dominance rules which increase the performance of the algorithm. We then report on our computational results obtained from the comparison with the most rapid procedure reported in the literature.ZusammenfassungWir betrachten eine Erweiterung des klassischen Resource-Constrained Project Scheduling Problems (RCPSP), die die Abbildung von Ressourcen-Ressourcen- und Zeit-Ressourcen-Tradeoffs ermöglicht. Damit ist der Projektplaner in der Lage, für jeden Vorgang des Projekts mehrere Ausführungsalternativen (Modi) anzugeben. Der von uns vorgestellte Algorithmus ist eine Verallgemeinerung des derzeit schnellsten Branch-and-Bound-Verfahrens für das RCPSP von Demeulemeester und Herroelen. Wir erweitern deren Konzept der Delay-Alternativen um sogenannte Modus-Alternativen. Die Enumeration wird mit Hilfe von Dominanzregeln beschleunigt. Schließlich fassen wir unsere Rechenergebnise zusammen, in denen wir unser Verfahren mit dem derzeit schnellsten aus der Literatur bekannten Algorithmus vergleichen.

NONPREEMPTIVE MULTI-MODE RESOURCE-CONSTRAINED PROJECT SCHEDULING

This paper addresses methods for formulating and solving a general class of nonpreemptive resource-constrained project scheduling problems in which job durations are discrete functions of committed renewable, nonrenewable and doubly-constrained resources (multi-mode time resource tradeoff). We present a stochastic scheduling method which solves these problems to sub-optimality in an efficient way. Computational results demonstrate that this method is highly superior to other well-known existing deterministic scheduling rules. Extensions to problems in which job-specific (demand) resource profiles are varying with time, in addition to time-varying supply resource profiles, are discussed as well.

Adaptive search for solving hard project scheduling problems

In this article we propose a new heuristic solution technique for resource‐constrained project scheduling problems. Basically, it is a hybrid of priority rule and random search techniques which employs two types of adaptations in order to determine the solution space. We enhance this general scheme by the use of a new priority rule and by lower bounding techniques. The method is evaluated by comparing it with other recently proposed heuristics on a widely used set of benchmark‐instances. Furthermore, we show that the procedure can be usefully applied to solve different hard problems within the field of project scheduling.

Project scheduling with multiple modes: A comparison of exact algorithms

This paper is devoted to a comparison of all available branch-and-bound algorithms that can be applied to solve resource-constrained project scheduling problems with multiple execution modes for each activity. After summarizing the two exact algorithms that have been suggested in the literature, we propose an alternative exact approach based on the concepts of mode and extension alternatives to solve this problem. Subsequently, we compare it to the two procedures available in the literature. Therefore, the three algorithms as well as all available bounding criteria and dominance rules are summarized in a unified framework. In addition to a theoretical comparison of the procedures, we present the results of our computational studies in order to determine the most efficient algorithm.

Inventory-based dispatching of automated guided vehicles on container terminals

This paper deals with automated guided vehicles (AGVs) which transport containers between the quay and the stack on automated container terminals. The focus is on the assignment of transportation jobs to AGVs within a terminal control system operating in real time. First, we describe a rather common problem formulation based on due times for the jobs and solve this problem both with a greedy priority rule based heuristic and with an exact algorithm. Subsequently, we present an alternative formulation of the assignment problem, which does not include due times. This formulation is based on a rough analogy to inventory management and is solved using an exact algorithm. The idea behind this alternative formulation is to avoid estimates of driving times, completion times, due times, and tardiness because such estimates are often highly unreliable in practice and do not allow for accurate planning. By means of simulation, we then analyze the different approaches. We show that the inventory-based model leads to better productivity on the terminal than the due-time-based formulation.