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.

This work presents a stochastic multiperiod model for representing a petroleum refinery. Uncertainty is taken into account in parameters such as demands, product sale prices and crude oil prices. In the present work, uncertainty is considered as a set of discrete scenarios, each representing a possible shifting of market expectations. Every environment is weighted through an expected probability of occurrence. Previous work revealed that the computational effort of uncertain multiperiod refinery production planning models grows exponentially with the number of time periods and scenarios. Therefore, in order to reduce the computational effort over uncertain long-planning horizons, special techniques must be employed. The proposal is to apply Lagrangean Decomposition, which exploits the block-diagonal structure of the problem, to reduce solution time by decomposing the model on a temporal basis. Solution of the proposed algorithm showed a significant reduction in computational effort with respect to the full-scale outer approximation solver.