Scheduling of mixed batch-continuous production lines

The aim of this thesis is to solve scheduling problems for mixed production lines, i.e., involving batch and continuous processes, and some resource restrictions. Discrete time mixed integer programming (MIP) formulations were initially proposed in the literature in order to solve such problems, but their drawback is the large size of formulations for solving real industrial cases. This is why continuous time MIP formulations were then proposed. Various authors did compare different types of continuous time formulations, but did not try to improve or tighten such formulations. We first study a continuous time MIP formulation in order to model the cyclic scheduling of a mixed plant composed of batch and continuous processes. By improving the initial continuous time formulation of various special cases of the general problem, we obtain a tighter model formulation for these special cases. Then, we show for all special cases of the general problem that the improved formulations give better results (quality of solutions and/or running times) than the initial one but the exact resolution of large instances remains difficult. So, we investigated MIP based heuristic methods in order to obtain good feasible solutions quickly. We show that, for some large instances, the heuristic solutions given by the exact methods (truncated Branch-and-Bound) were not better than the feasible solutions given by the MIP based heuristic methods, and the latter use less CPU solution time. Finally, in contrast to the earlier models, we consider a scheduling problem in which we model the dynamics of the process. The processing times of the batch tasks are therefore considered to be variable in this case. They are determined as the solution of the system of differential equations describing the process dynamics, and influenced by process parameters that have to be optimized. For two test cases, we compare four solution methods and we show that a piecewise linear approximation method, based on the discretization of the space of state and command variables into simplices and on the discretization of time, gives a good feasible solution offering the best compromise between quality of the approximation of the solution of the differential equations and CPU solution time.Doctorat en sciences appliquées (FSA 3)--UCL, 200