The Weighted Fair Sequences Problem

Scheduling problems on which constraints are imposed with regard to the temporal distances between successive executions of the same task have numerous applications, ranging from task scheduling in real-time systems to automobile production on a mixed-model assembly line. This paper introduces a new NP-hard optimization problem belonging to this class of problems, namely the Weighted Fair Sequences Problem (WFSP). We present a mathematical formulation for the WFSP based on mixed-integer linear programming (MILP) as well as a series of cuts to improve its resolution via exact methods. Finally, we propose a heuristic solution method that works with much less variables of the WFSP formulation. The reported computational experiments show that, for a given time horizon, the proposed MILP-based heuristic increases the size of WFSP instances that can be tackled in practice. Moreover, its results should be considered as optimal whether a presented conjecture on the WFSP problem is proved true in the future.