Sönke Hartmann

Experimental investigation of heuristics for resource-constrained project scheduling: An update

This paper considers heuristics for the well-known resource-constrained project scheduling problem (RCPSP). It provides an update of our survey which was published in 2000. We summarize and categorize a large number of heuristics that have recently been proposed in the literature. Most of these heuristics are then evaluated in a computational study and compared on the basis of our standardized experimental design. Based on the computational results we discuss features of good heuristics. The paper closes with some remarks on our test design and a summary of the recent developments in research on heuristics for the RCPSP.

A survey of variants and extensions of the resource-constrained project scheduling problem

The resource-constrained project scheduling problem (RCPSP) consists of activities that must be scheduled subject to precedence and resource constraints such that the makespan is minimized. It has become a well-known standard problem in the context of project scheduling which has attracted numerous researchers who developed both exact and heuristic scheduling procedures. However, it is a rather basic model with assumptions that are too restrictive for many practical applications. Consequently, various extensions of the basic RCPSP have been developed. This paper gives an overview over these extensions. The extensions are classified according to the structure of the RCPSP. We summarize generalizations of the activity concept, of the precedence relations and of the resource constraints. Alternative objectives and approaches for scheduling multiple projects are discussed as well. In addition to popular variants and extensions such as multiple modes, minimal and maximal time lags, and net present value-based objectives, the paper also provides a survey of many less known concepts.

A competitive genetic algorithm for resource-constrained project scheduling

In this paper we consider the resource-constrained project scheduling problem (RCPSP) with makespan minimization as objective. We propose a new genetic algorithm approach to solve this problem. Subsequently, we compare it to two genetic algorithm concepts from the literature. While our approach makes use of a permutation based genetic encoding that contains problem-specific knowledge, the other two procedures employ a priority value based and a priority rule based representation, respectively. Then we present the results of our thorough computational study for which standard sets of project instances have been used. The outcome reveals that our procedure is the most promising genetic algorithm to solve the RCPSP. Finally, we show that our genetic algorithm yields better results than several heuristic procedures presented in the literature.

Heuristic Algorithms for the Resource-Constrained Project Scheduling Problem: Classification and Computational Analysis

The resource-constrained project scheduling problem (RCPSP) can be given as follows. A single project consists of a set J = {0,1,…, n, n +1} of activities which have to be processed. Fictitious activities 0 and n + 1 correspond to the “project start” and to the “project end”, respectively. The activities are interrelated by two kinds of constraints. First, precedence constraints force activity j not to be started before all its immediate predecessor activities comprised in the set P j have been finished. Second, performing the activities requires resources with limited capacities. We have k resource types, given by the set K = {1,…,K}. While being processed, activity j requires r j,k units of resource type k ∈ K during every period of its non-preemptable duration p j . Resource type k has a limited capacity of R k at any point in time. The parameters pj,r j,k , and R k are assumed to be deterministic; for the project start and end activities we have pj = 0 and r j,k = 0 for all k ∈ K. The objective of the RCPSP is to find precedence and resource feasible completion times for all activities such that the makespan of the project is minimized. Figure 7:1 gives an example of a project comprising n = 6 activities which have to be scheduled subject to K = 1 renewable resource type with a capacity of 4 units. A feasible schedule with an optimal makespan of 13 periods is represented in Figure 7:2.

Experimental evaluation of state-of-the-art heuristics for the resource-constrained project scheduling problem

Abstract We consider heuristic algorithms for the resource-constrained project scheduling problem. Starting with a literature survey, we summarize the basic components of heuristic approaches. We briefly describe so-called X -pass methods which are based on priority rules as well as metaheuristic algorithms. Subsequently, we present the results of our in-depth computational study. Here, we evaluate the performance of several state-of-the-art heuristics from the literature on the basis of a standard set of test instances and point out to the most promising procedures. Moreover, we analyze the behavior of the heuristics with respect to their components such as priority rules and metaheuristic strategy. Finally, we examine the impact of problem characteristics such as project size and resource scarceness on the performance.

Project Scheduling with Multiple Modes: A Genetic Algorithm

In this paper we consider the resource-constrained project scheduling problem with multiple execution modes for each activity and makespan minimization as objective. We present a new genetic algorithm approach to solve this problem. The genetic encoding is based on a precedence feasible list of activities and a mode assignment. After defining the related crossover, mutation, and selection operators, we describe a local search extension which is employed to improve the schedules found by the basic genetic algorithm. Finally, we present the results of our thorough computational study. We determine the best among several different variants of our genetic algorithm and compare it to four other heuristics that have recently been proposed in the literature. The results that have been obtained using a standard set of instances show that the new genetic algorithm outperforms the other heuristic procedures with regard to a lower average deviation from the optimal makespan.

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.

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.

A note on “hierarchical models for multi-project planning and scheduling”

Abstract We consider the multi-mode resource-constrained project scheduling problem. The focus of our analysis is on an algorithm recently proposed by Speranza and Vercellis for finding makespan minimal solutions. The correctness of the algorithm is examined. By counterexamples we illustrate that the algorithm does not generally find (existing) optimal solutions.