Resource-Constrained Scheduling Problems

Abstract

This chapter is devoted to the description of mathematical optimization problems which arise in the context of resource-constrained project scheduling. In Section 3.1, some notations and definitions are introduced which are used throughout the forthcoming chapters. Section 3.2 presents different mathematical formulations for the fundamental resource-constrained project scheduling problem (RCPSP). Furthermore, a practically important generalization for which appropriate solution methods are described in the Chapters 4 to 6 is introduced. In Section 3.3, further possible extensions of RCPSP are examined. Finally, closely related scheduling problems are surveyed in Section 3.4. Since solution procedures for the problems presented in the latter two sections are not part of this book, references on corresponding literature are provided, respectively. Furthermore, for each reference the basic type of the solution procedure proposed, e.g., priority-rule based heuristic, tabu search or branch and bound, is stated. For brief introductions into such solution approaches, we refer to the Chapters 5 and 6. General surveys on procedures for resource allocation are contained in Davis (1966), Laue (1968), Herroelen (1972), Davis (1973), Slowinski (1977), Ritchie (1985), Domschke and Drexl (1991), Icmeli et al. (1993), Elmaghraby (1995), Özdamar and Ulusoy (1995), Herroelen et al. (1996), Kolisch and Padman (1997), and Brucker et al. (1999). Brucker et al. (1999) and Herroelen et al. (1999) both describe possible classification schemes for resource-constrained project scheduling problems.