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

TLDR

The paper tackles the resource‑constrained project scheduling problem, aiming to minimize project makespan. The authors present a 0‑1 linear programming formulation with exponentially many variables over feasible activity subsets, derive tighter lower bounds through relaxations, and develop a tree‑search algorithm that exploits these bounds and dominance criteria. Computational results demonstrate the exact algorithm solves hard instances that previous state‑of‑the‑art methods cannot handle. Reference: 1978.

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.