Computers & Operations Research 35 (2008) 3284 – 3297 www.elsevier.com/locate/cor Augmenting priority rule heuristics with justification and rollout to solve the resource-constrained project scheduling problem  Ningxiong Xu a , Sally A. McKee b , Linda K. Nozick a , ∗ , Ruke Ufomata b a Civil and Environmental Engineering, Cornell University, USA b Electrical and Computer Engineering, Cornell University, USA Available online 27 February 2007 Abstract The key question addressed by the resource-constrained project scheduling problem (RCPSP) is to determine the start times for each activity such that precedence and resource constraints are satisfied while achieving some objective. Priority rule-based heuristics are widely used for large problems. Rollout and justification can be integrated with priority rule heuristics to solve the RCPSP.We develop several such procedures and examine the resulting solution quality and computational cost. We present empirical evidence that these procedures are competitive with the best solution procedures described in the literature.  2007 Elsevier Ltd. All rights reserved. Keywords: Resource-constrained project scheduling; Priority rules; Justification; Rollout procedures The key question addressed in the resource-constrained project scheduling problem (RCPSP) is to determine the start times for each activity such that precedence and resource constraints are satisfied while achieving some objective like shortest project duration or minimum resource investment. In the literature the RCPSP is commonly formulated as an integer programming problem for which the integer variables indicate the period in which an activity starts (or ends). This model has become an important management tool for many business activities. For example, production planning in make-to-order operations frequently requires the assignment of resources to small production lots, each of which has specific machining and labor needs. In these environments, the production planning problem bears considerable resemblance to the RCPSP, such as is common in construction operations or other activity-oriented situations. Many authors have developed exact solution procedures for this problem formulation (or minor variations on it) [1–3], but most of those authors have also pointed out that it is impractical to solve this integer programming problem exactly for even moderately sized instances. Computationally, the RCPSP is known to be NP-hard [4]. For problems of the size generally experienced in practice it is necessary to resort to heuristics.  This material is based upon work supported by the National Science Foundation under Grant no. 0218837. ∗ Corresponding author. Tel.: +1 607 255 6496; fax: +1 607 255 9004. E-mail addresses: nx22@cornell.edu (N. Xu), sam@csl.cornell.edu (S.A. McKee), lkn3@cornell.edu (L.K. Nozick), rou2@cornell.edu (R. Ufomata). 0305-0548/$ - see front matter  2007 Elsevier Ltd. All rights reserved. doi:10.1016/j.cor.2007.02.016