Branch-and-Bound Algorithms for Stochastic Resource-Constrained Project Scheduling

We study branch-and-bound algorithms for resource-constrained project scheduling where processing times of jobs are random. The objective is to find a so-called scheduling policy which minimizes the project makespan in expectation. The proposed procedures are based upon four classes of scheduling policies which differ considerably with respect to their computational tractability as well as with respect to the optimum costs that can be achieved within the respective class. The purpose of the paper is twofold. First, we establish results on the trade-off between computational efficiency and solution quality for each of the considered classes of policies and evaluate their practical applicability for scheduling stochastic resource-constrained projects. Second, we develop and apply various ingredients such as dominance rules and lower bounds that turn out to be useful within the computation. In order to comprehensively study these issues we have implemented five different branch-and-bound algorithms and explore their computational behavior on 1440 test instances

On the Representation of Resource Constraints in Project Scheduling

In project scheduling, resource constraints are usually defined via resource consumption and -availability. Many algorithmic approaches, however, are based on the concept of minimal forbidden sets to represent the resource constraints. Jobs of a forbidden set can be scheduled simultaneously with respect to the precedence constraints, however, they consume more resources than available. Forbidden sets are usually not given explicitly, and by definition even the number of inclusion-minimal forbidden sets may be exponential in the number of jobs. In this paper, we propose a simple branch-and-bound type algorithm to efficiently compute and represent all minimal forbidden sets for a given instance. We evaluate the algorithm on well established test sets of the project scheduling problem library PSPLIB. In addition, we exhibit intimite relations between the different representations of resource constraints and threshold hypergraphs

A Note on Scheduling Problems with Irregular Starting Time Costs

In [9], Maniezzo and Mingozzi study a project scheduling problem with irregular starting time costs. Starting from the assumption that its computational complexity status is open, they develop a branch-and-bound procedure, and identify special cases that are solvable in polynomial time. In this note, we review three previously established, related results which show that the general problem is solvable in polynomial time

Scheduling with AND/OR precedence constraints

In many scheduling applications it is required that the processing of some job must be postponed until some other job, which can be chosen from a pre-given set of alternatives, has been completed. The traditional concept of precedence constraints fails to model such restrictions. Therefore, the concept has been generalized to so-called AND/OR precedence constraints which can cope with this kind of requirement