In this paper, we focus on the makespan minimization on restricted preemptive unrelated parallel machines scheduling under uncertain processing times. We propose to investigate the problem under discrete scenario representation of uncertain processing times and to use min-max objective to generate a schedule minimizing the worst-case makespan over all the scenarios. We show that the robust assignment counterpart of the deterministic formulation provides a lower bound of the worst-case makespan and we propose a Mixed Integer Linear Program that computes the robust schedule minimizing the worst-case makespan under the set of discrete scenarios with restricted number of preemptions. Moreover, we prove that this robust schedule is equivalent to the optimal schedule of the artificial worst-case scenario. Thus, it is too conservative. To reduce the conservativeness, we propose an improved robust formulation under which the sequence is scenario dependent.

This paper describes the design of Bob++, a framework for implementing sequential and/or parallel search algorithms. To our knowledge, the Bob++ is among the rare frameworks that allow implementation of various search methods (B&B, D&C (divide-and-conquer), DP (dynamic programming), A*) for general COPs and run the application on any architecture (sequential/SMP machines, clusters/grids) with minimum modification in the source code. The Bob++ is based on the notion of global priority queue that encapsulates sequential data structures and load balancing strategies. This makes transparent the parallelizations of the search algorithms. To parallelize Bob++ library, we integrated it on Athapascan parallel programming interface which is a C++ library developed by the INRIA Apache project