Robust Load-Balanced Configuration With Fixed Costs For The Parallel Multi-Purpose Machines Problem

The problem which is presented here concerns the configuration of a Parallel Multi-Purpose Machines workshop. To configure this workshop means to qualify each machine for a subset of products. This configuration has to be chosen in order to satisfy the demand while checking the load-balancing of machines. Moreover, the addressed problem is a multicriteria optimization problem. In fact on the one hand, as the demand is strongly subject to uncertainties the configuration has to be robust: a performance of load-balancing despite demand uncertainties must be guaranteed. Thus, the configuration must be the most robust as possible. On the other hand, to configure the workshop involves some costs (regarded as proportional to the number of qualifications of machines) which must be minimized. In this article a method of Branch and Bound type is proposed and experimented to determine the configuration which is the most robust against demand uncertainties but which does not exceed a maximum number of qualified machines