An Exact Algorithm for the Resource-Constrained Project Scheduling Problem Based on a New Mathematical Formulation

Abstract

In this paper we consider the Project Scheduling Problem with resource constraints, where the objective is to minimize the project makespan. We present a new 0-1 linear programming formulation of the problem that requires an exponential number of variables, corresponding to all feasible subsets of activities that can be simultaneously executed without violating resource or precedence constraints. Different relaxations of the above formulation are used to derive new lower bounds, which dominate the value of the longest path on the precedence graph and are tighter than the bound proposed by Stinson et al. (1978). A tree search algorithm, based on the above formulation, that uses new lower bounds and dominance criteria is also presented. Computational results indicate that the exact algorithm can solve hard instances that cannot be solved by the best algorithms reported in the literature.Project Scheduling, Branch-and-Bound Methods, Networks/Graphs, Lower Bounds

GRASP for set packing problems

“…Kim [12] represented a ship scheduling problem as an SPP and used LINDO software to solve it. Mingozzi et al [13] used an SPP formulation to calculate the bounds for a Resource Constrained Project Scheduling Problem using a greedy method. Rossi [14] considered an SPP formulation for a ground holding problem and solved it exactly with a Branch & Cut method.…”

“…• The values of items (c i ) are uniformly distributed in the interval [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] (weighted) or fixed to 1 (unicost).…”

A branch-and-bound procedure for the resource-constrained project scheduling problem with generalized precedence relations

“…Recently, Mingozzi et al (1994) Stinson et al (1978) on the 110 RCPSP instances assembled by Patterson (1984) and the 480 randomly generated RCPSP instances of Kolisch et al (1992). Mingozzi et al (1994) have also developed a new branch-and-bound procedure for the RCPSP based on this new mathematical formulation, which incorporates the most promising new lower bound lb 3 .…”

“…Mingozzi et al (1994) have also developed a new branch-and-bound procedure for the RCPSP based on this new mathematical formulation, which incorporates the most promising new lower bound lb 3 . Mingozzi et al (1994) compute lb 3 using a heuristic for the weighted node packing problem.…”

Activity Prioritization Under Resource Constraints Using a Utility Index Method

“…A solution to RCSP can be sought through a number of possible methodologies. A very common approach is to utilize implicit enumeration and backtracking (the methods used by most commercially available exact solvers) such as branch and bound methods, as proposed in Brucker and Knust [2], *Address correspondence to this author at the Department of Civil and Environmental Engineering, University of Cyprus, Nicosia 1678, Cyprus; Tel: +357-22892270; Fax: +357-22892295; E-mails: SCHRISTO@UCY.AC.CY or SC163@HOTMAIL.COM Demeulemeester and Herroelen [3], Mingozzi et al [4], Crawford [5], and Garey et al [6]. Other methods utilize intelligent branching and evaluation techniques such as mathematical programming [7], dynamic programming [8], zero-one programming [9], or artificial agent techniques such as genetic algorithms [10] and ant colony optimization [11][12][13].…”