The optimal scheduling of crude-oil operations in refineries has been studied by various groups during the past decade leading to different mixed integer linear programming (MILP) or mixed integer nonlinear programming (MINLP) formulations. This paper presents a new continuous-time formulation, called single-operation sequencing (SOS) model, which can be used to solve the crude-oil operations problem introduced by Lee et al. 1 . It is different from previous formulations as it requires to postulate the number of priority-slots in which operations take place instead of specifying the number of time intervals or event points to be used in the schedule. This MINLP model is also based on the representation of a crude-oil schedule by a single sequence of transfer operations. It allows breaking symmetries involved in the problem, thus tremendously reducing the computational expenses (all instances can be solved within 2 minutes). A simple two step MILP -NLP procedure has been used to solve the non-convex MINLP model leading to an optimality gap lower than 5% in all cases.

During the last 15 years, many mathematical models have been developed in order to solve process operation scheduling problems, using discrete or continuous time representations. In this paper, we present a unified representation and modeling approach for process scheduling problems. Four different time representations are presented, compared, and applied to single-stage and multi-stage batch scheduling problems, as well as crude-oil operations scheduling problems. We introduce three solution methods that can be used to achieve global optimality or obtain near-optimal solutions depending on the stop criterion used. Computational results show that the Multi-Operation Sequencing time representation is superior to the others as it allows efficient symmetry-breaking and requires fewer priority-slots, thus leading to smaller model sizes.

The paleoclimatic variability at frequencies ranging from 10 -4 cycle per year (cpy) to 10 -3 cpy is investigated using a set of three deep-sea cores from the Indian Ocean. Three frequency bands of high paleoclimatic variability are first defined using upper and lower limits of the significant spectral power concentrations: the bands are centered around the spectral maxima located at 10.3, 4.7, and 2.5 kyr. The localisation of spectral lines is then refined by highresolution spectral analysis.Some of the resulting lines have frequencies which are close to those previously detected in other paleoclimatic records, including the precessional peak at 19 kyr. Additional lines are also in good correspondence with the response of a nonlinear climatic oscillator forced by insolation variations, including peaks at 13 kyr, 10.4 kyr and 9.4 kyr. This correspondence suggests orbital forcing. Moreover for the Indian Ocean which is influenced by the monsoon circulation, it is plausible that the precessional contribution of the forcing interact strongly with the precipitation-temperature feedback used in the model, thus emphasizing the nonlinearity of the response.

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