a novel transition identification mechanism for the diesel blending and distribution scheduling problem using the discrete time representation with two time-scales granularity

ABSTRACT Transitions between tasks arise in many different scheduling problems. Sometimes transitions are undesired because they incur costs; sometimes they are undesired because they require setup time, and sometimes both. In one way or the other, frequently, transitions need to be identified and penalized in order for their frequency to be minimized. The present work is concerned with the study of alternative optimization formulations to address transitions with the blending and distribution scheduling of oil derivatives. Our study starts by revisiting a model proposed in the literature that was built considering a very short time horizon (24 h). Next, improvements concerning the transition constraints are evaluated and a new approach is proposed with the purpose of extending model applicability to cases where longer time horizons are of interest. The new proposed mechanism of evaluating transitions relies on aggregating the detailed discrete time scale (hours) to a higher and less detailed level (days). Transitions are then evaluated on the lower level of aggregation with the benefit of reducing the number of required constraints. It must also be emphasized that the proposed model is built on the basis of a set of heuristics that have direct impact on solution and solution time. Results attained for a four-day time horizon demonstrate cost savings on the order of 32% when compared with four sequenced schedules of a one-day time horizon each. Savings are mainly obtained as a consequence of the reduction of the predicted number of transitions.