A note on exact algorithms and heuristics for generation of V- and [formula omitted]-shaped sequences

Abstract

We present two groups of algorithms for generation of V- and Λ-shaped sequences, and discuss their applications in scheduling. The first group includes two recursive exact algorithms which generate all V- and Λ-shaped sequences composed of the elements of a given set. The second group includes two heuristics which generate suboptimal V-shaped schedules for a single machine time-dependent scheduling problem with deteriorating jobs. The results of extensive computational experiments with C++, C# and Python implementations of these algorithms show that the exact algorithms can be used to solve single machine scheduling problems with V- or Λ-shaped optimal schedules, while the heuristics generate very good suboptimal schedules for the time-dependent scheduling problem.