A tighter continuous time formulation for the cyclic scheduling of a mixed plant

Abstract In this paper, based on the cyclic scheduling formulation of Schilling and Pantelides [22], we propose a continuous time mixed integer linear programming (MILP) formulation for the cyclic scheduling of a mixed plant, i.e. a plant composed of batch and continuous tasks. The cycle duration is a variable of the model and the objective is to maximize productivity. By using strengthening techniques and the analysis of small polytopes related to the problem formulation, we strengthen the initial formulation by tightening some initial constraints and by adding valid inequalities. We show that this strengthened formulation is able to solve moderate size problems quicker than the initial one. However, for real size cases, it remains difficult to obtain the optimal solution of the scheduling problem quickly. Therefore, we introduce MILP-based heuristic methods in order to solve these larger instances, and show that they can provide quite good feasible solutions quickly

A tighter continuous time formulation for the cyclic scheduling of a mixed plant

In this paper, based on the cyclic scheduling formulation of Schilling and Pantelides [22], we propose a continuous time mixed integer linear programming (MILP) formulation for the cyclic scheduling of a mixed plant, i.e. a plant composed of batch and continuous tasks. The cycle duration is a variable of the model and the objective is to maximize productivity. By using strengthening techniques and the analysis of small polytopes related to the problem formulation, we strengthen the initial formulation by tightening some initial constraints and by adding valid inequalities. We show that this strengthened formulation is able to solve moderate size problems quicker than the initial one. However, for real size cases, it remains difficult to obtain the optimal solution of the scheduling problem quickly. Therefore, we introduce MILP-based heuristic methods in order to solve these larger instances, and show that they can provide quite good feasible solutions quickly

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

A tighter continuous time formulation for the cyclic scheduling of a mixed plant

In this paper, based on the cyclic scheduling formulation of Schilling and Pantelides [22], we propose a continuous time mixed integer linear programming (MILP) formulation for the cyclic scheduling of a mixed plant, i.e. a plant composed of batch and continuous tasks. The cycle duration is a variable of the model and the objective is to maximize productivity. By using strengthening techniques and the analysis of small polytopes related to the problem formulation, we strengthen the initial formulation by tightening some initial constraints and by adding valid inequalities. We show that this strengthened formulation is able to solve moderate size problems quicker than the initial one. However, for real size cases, it remains difficult to obtain the optimal solution of the scheduling problem quickly. Therefore, we introduce MILP-based heuristic methods in order to solve these larger instances, and show that they can provide quite good feasible solutions quickly.

Natural and anthropogenic dynamics of the coastal environment in northwestern Corsica (western Mediterranean) over the past six millennia

International audienceThe present paper provides new insights into the climatic and anthropic factors that influenced a 6000-year coastal evolution in northwestern Corsica, the third largest island of the western Mediterranean. Pollen, microcharcoal, sedimentary and geochemical analyses were carried out on a core drilled in the Crovani coastal wetland to reconstruct the regional drivers of landscape change. We show that anthropogenic and climate-induced fires favoured the development of Mediterranean maquis, dominated by Erica and Quercus ilex, from ca. 6000 to 3350 cal. BP. A change in arboreal vegetation triggered a short but intense sediment input in the Crovani pond between ca. 3350 and 3200 cal. BP. This is consistent with a coeval process of runoff recorded in several coastal sites of western Corsica and related to an arid climate change occurred in many sites of the western Mediterranean around 3200 years ago. We provide evidence of agriculture during the Late Neolithic from ca. 3900 BC, which is much earlier than any archaeological evidence previously available in this area of Corsica, followed by a progressive decline of arable farming practices. Human impact has been responsible for a degradation of the maquis only from approximately 3000 cal. BP, and it intensified in Roman times, when the area experienced the first phase of galena exploitation from the Argentella mines. Over the last 500 years, the present work evidences a major development of Castanea related to cultivation during the Genoese administration of Corsica. Our findings suggest that solar activity and the North Atlantic Oscillation had an influence on centennial-scale forest cover variations during the last 6000 years