M. Sacramento Quintanilla

Justification and RCPSP: A technique that pays

Abstract The objective of this paper is to show that justification is a simple technique that can be easily incorporated in diverse algorithms for the resource-constrained project scheduling problem––improving the quality of the schedules generated without generally requiring more computing time. The results of incorporating this technique in 22 different algorithms are shown. Fifteen of the new algorithms that use double justification outperform seven of the best heuristic algorithms that do not use justification. The tests have been performed on the standard test set j120 for the RCPSP generated using ProGen.

A hybrid genetic algorithm for the resource-constrained project scheduling problem

Abstract In this paper we propose a Hybrid Genetic Algorithm (HGA) for the Resource-Constrained Project Scheduling Problem (RCPSP). HGA introduces several changes in the GA paradigm: a crossover operator specific for the RCPSP; a local improvement operator that is applied to all generated schedules; a new way to select the parents to be combined; and a two-phase strategy by which the second phase re-starts the evolution from a neighbour’s population of the best schedule found in the first phase. The computational results show that HGA is a fast and high quality algorithm that outperforms all state-of-the-art algorithms for the RCPSP known by the authors of this paper for the instance sets j60 and j120. And that it is competitive with other state-of-the-art heuristics for the instance set j30.

Resource-constrained project scheduling: A critical activity reordering heuristic

Abstract In this paper, we present a new metaheuristic algorithm for the resource-constrained project-scheduling problem. The procedure is a non-standard implementation of fundamental concepts of tabu search without explicitly using memory structures embedded in a population-based framework. The procedure makes use of a fan search strategy to intensify the search, whereas a strategic oscillation mechanism loosely related to the forward/backward technique provides the necessary diversification. Our implementation employs the topological order (TO) representation of schedules. To explore the TO vector space we introduce three types of moves, two of them based on the concept of relative criticality, and a third one based on multi-pass sampling ideas. The strategic utilisation of probabilities for move construction is another distinguishing feature of our approach. Extensive computational testing with more than 2000 problem instances shows the merit of the proposed solution method.

A Population-Based Approach to the Resource-Constrained Project Scheduling Problem

We present a population-based approach to the RCPSP. The procedure has two phases. The first phase handles the initial construction of a population of schedules and these are then evolved until high quality solutions are obtained. The evolution of the population is driven by the alternative application of an efficient improving procedure for locally improving the use of resources, and a mechanism for combining schedules that blends scatter search and path relinking characteristics. The objective of the second phase is to explore in depth those vicinities near the high quality schedules. Computational experiments on the standard j120 set, generated using ProGen, show that our algorithm produces higher quality solutions than state-of-the-art heuristics for the RCPSP in an average time of less than five seconds.

Pre-emption in resource-constrained project scheduling

The Resource-Constrained Project Scheduling Project (RCPSP), together with some of its extensions, has been widely studied. A fundamental assumption in this basic problem is that activities in progress are non-preemptable. Very little effort has been made to uncover the potential benefits of discrete activity pre-emption, and the papers dealing with this issue have reached the conclusion that it has little effect on project length when constant resource availability levels are defined. In this paper we show how three basic elements of many heuristics for the RCPSP - codification, serial SGS and double justification - can be adapted to deal with interruption. The paper is mainly focussed on problem 1_PRCPSP, a generalization of the RCPSP where a maximum of one interruption per activity is allowed. However, it is also shown how these three elements can be further adapted to deal with more general pre-emptive problems. Computational experiments on the standard j30 and j120 sets support the conclusion that pre-emption does help to decrease project length when compared to the no-interruption case. They also prove the usefulness of the justification in the presence of pre-emption. The justification is a RCPS technique that can be easily incorporated into a wide range of algorithms for the RCPSP, increasing their solution quality - maintaining the number of schedules calculated.

A tabu search approach to machine scheduling

Abstract In this paper we apply the tabu search (TS) technique to a complex machine scheduling problem. The problem can be considered as a generalization of the job-shop problem with both simple and parallel machines, job batches, setup times and release and due dates. The goal is to obtain feasible schedules by minimizing the makespan Cm,, if the problem is feasible, or to obtain a “best compromise” schedule if a full solution is not possible. The TS algorithm developed here is distinguished mainly by two aspects. Firstly, the core of the procedure is a tabu thresholding algorithm which uses a sophisticated set of moves aimed at resolving violated constraints. Secondly, the TS algorithm supplements the central tabu thresholding algorithm with two diversification strategies which are dependent on the state of the search. These strategies involve fairly major disruption of the schedules, and force significant diversification of the search. Computational experiments show that our algorithm can find high quality schedules in short running times

Scheduling projects with limited number of preemptions

A recent paper (Ballestin F, Valls V, Quintanilla S. Preemption in resource-constrained project scheduling. European Journal of Operational Research 2008;189:1136-152) revealed the potential benefits of allowing one interruption when scheduling activities in a resource-constrained project. This paper further investigates the effect of interruption on project length in more general cases. To achieve this, a new model that covers most practical applications of discrete activity preemption is proposed and a metaheuristic algorithm for the problem is developed. Computational experiments on the standard j120 and j30 sets generated using ProGen study the difference in makespan between allowing m interruptions per activity, m=0,1,2,.... In the second part of the paper the usefulness of preemption in the presence of due dates is analysed.

A Modified Tabu Thresholding Approach for the Generalised Restricted Vertex Colouring Problem

We present a modification of the Tabu Thresholding (TT) approach and apply it to the solution of the generalised restricted vertex colouring problem. Both the bounded and unbounded cases are treated. In our algorithms, the basic TT elements are supplemented with an evaluation function that depends on the best solution obtained so far, together with a mechanism which reinforces the aggressive search in the improving phase, and new diversification strategies which depend on the state of the search. The procedure is illustrated through the solution of the problem of minimising the number of workers in a heterogeneous workforce.

Pre-processing techniques for resource allocation in the heterogeneous case

The Heterogeneous Resource Allocation Problem (HRAP) deals with the allocation of resources, whose units do not all share the same characteristics, to an established plan of activities. Each activity requires one or more units of each resource which possess particular characteristics, and the objective is to find the minimum number of resource units of each type, necessary to carry out all the activities within the plan, in such a way that two activities whose processing overlaps in time do not have the same resource unit assigned. The HRAP is an NP-Complete problem and it is possible to optimally solve medium-sized HRAP instances in a reasonable time. The objective of this work is to develop pre-processing techniques that enable an HRAP to be transformed into an equivalent HRAP of smaller size, thus increasing the size of HRAPs that can be solved exactly.