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

Abstract

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.