Characterization and Generation of a General Class of Resource-Constrained Project Scheduling Problems

Abstract

This paper addresses the issue of how to generate problem instances of controlled difficulty. It focuses on precedence- and resource-constrained (project) scheduling problems, but similar ideas may be applied to other network optimization problems. It describes a network construction procedure that takes into account a) constraints on the network topology, b) a resource factor that reflects the density of the coefficient matrix, and c) a resource strength, which measures the availability of resources. The strong impact of the chosen parametric characterization of the problems is shown via an in depth computational study. Instances for the single- and multi-mode resource-constrained project scheduling problem are benchmarked by using the state of the art (branch and bound) procedures. The results provided, demonstrate that the classical benchmark instances used by several researchers over decades belong to the subset of the very easy ones. In addition, it is shown that hard instances, being far more smaller in size than presumed in the literature, may not be solved to optimality even within a large amount of computation time.project scheduling, precedence and resource-constraints, nonpreemptive case, single-mode, multi-mode, branch and bound methods, project generator, benchmark instances

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

“…Mingozzi et al (1994) compute lb 3 using a heuristic for the weighted node packing problem. Demeulemeester and Herroelen (1995) Demeulemeester and Herroelen (1995) indicate that lb; indeed outperforms lb o and that incorporating lb; in their branch-and-bound procedure reduces the computational effort to solve the 110 problems of Patterson (1984) and the 480 problems of Kolisch et al (1992). Note that, contrary to lb 3 as calculated by Mingozzi et al (1994), the procedure above may yield an lb; which is smaller than lbo, but this constitutes no real disadvantage since lb o is calculated as well and the final value for the lower bound equals…”

“…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 .…”

Constraint propagation and decomposition techniques for highly disjunctive and highly cumulative project scheduling problems

“…For example, the precedence ratio (also known as order strength (Mastor, 1970), flexibility ratio (De Reyck and Herroelen, 1995), and density (De Reyck and Herroelen, 1995)), i.e., the ratio between the number of pairs of activities which are ordered by precedence constraints and the overall number of pairs of distinct activities, is also important (a high precedence ratio makes the problem easier). Although some researchers, e.g., (Kolisch et al, 1995), have worked on such indicators, we believe much more work is necessary to discover which indicators are appropriate for designing, selecting, or adapting constraint programming techniques with respect to the characteristics of a given problem.…”

PSPLIB - A project scheduling problem library

“…Note, the slight corruption in denoting the network complexity NC within the base parameter setting of Table 7. Again, the variable paramter combination related to a cell can be found in the Ales XYZPAR.MM, e.g., Note, once more, for standardizational purpose we have renamed the files originally presented in [17] from MM1_1.DAT,..., MM64_10.DAT to J101J..MM,..., J1064_10.MM. Contrary to the single-mode case, due to mode-coupling via resource constraints, some of the multimode instances do not have afeasible Solution (cf.…”