Exponential time algorithms for just-in-time scheduling problems with common due date and symmetric weights

Abstract

This paper focuses on the solution, by exact exponential-time algorithms, of just-in-time scheduling problems when jobs have symmetric earliness/tardiness weights and share a non restrictive common due date. For the single machine problem, a Sort & Search algorithm is proposed with worst-case time and space complexities in $$\mathcal {O}^*(1.4143^n)$$. This algorithm relies on an original modeling of the problem. For the case of parallel machines, an algorithm integrating a dynamic programming algorithm across subsets and machines and the above Sort & Search algorithm is proposed with worst-case time and space complexities in $$\mathcal {O}^*(3^n)$$. To the best of our knowledge, these are the first worst-case complexity results obtained for non regular criteria in scheduling.