Fixed interval scheduling under uncertainty – A tabu search algorithm for an extended robust coloring formulation

• Fixed interval scheduling problem under uncertainty is formulated using stochastic programming.
• Risk is represented by random delays in processing times.
• Equivalent deterministic robust coloring formulations are proposed.
• Small simulated instances are solved to optimality by standard software tools.
• A tabu search algorithm suitable for larger instances is implemented.

We propose several formulations of the fixed interval scheduling problem under uncertainty, where the risk is represented by random delays in processing times. We employ various stochastic programming and robust coloring problems to deal with the uncertainty. Our main goal is to introduce equivalent deterministic reformulations of the stochastic programming problems. We show that the minimization of the expected number of overlaps is equivalent to the deterministic robust coloring problem under particular choice of the penalties. Moreover, we extend the robust coloring problem to obtain equivalence with the stochastic programming problem with the schedule reliability objective under multivariate distribution of delays represented by an Archimedean copula. We show that small simulated instances of this problem can be solved to optimality by available software tools and we propose a tabu search algorithm suitable for larger instances.