Batch optimal scheduling for a sugarhouse

GUILLERMO A. DURAND; DENNIS BONNÉ; STEPHEN BRIDGES; STEN BAY JØRGENSEN

Reno (EEUU)

Congreso; AIChE Annual Meeting 2001; 2001

American Institute of Chemical Engineers

A sugarhouse is one stage in the production of sugar. The purpose of the sugarhouse is to crystallize and separate sugar from the thick juice obtained in previous stages. The crystallization and the separation are carried out in batteries of batch units. A special problem in bath processing is the possible variation in task performance. The performance of a task depends, for example, on the equipment used, the chosen operating conditions, the state and the quantity of the feed and the selected external agents. Time varying conditions can make the throughput vary widely. If the processing capabilities of upstream and downstream units do not match those of the batch stage(s) then accumulation problems may arise. The most common solution is to use more than one batch unit and schedule their operation to make the overall production of the batch process as similar as possible to that of the upstream and downstream continuous stages. The scheduling has also to be planned considering the optimization of the operation in order to reach the maximum utilization of the total process plant, constrained by the batch stage sizes. Thus, batch process design and batch operation design are tightly interrelated. The scheduling basically consists of a series of decisions of whether to start or not a specified batch unit at a determined moment. This discrete time control problem and the dynamic batch-to-batch behavior of the units make the dynamic programming approach a suitable methodology for optimizing scheduling. The objective of this paper is to develop a scheduling algorithm based on dynamic programming, applied to a sugarhouse. The goal of the scheduling algorithm is to maximize the production respecting the constraints of available resources and market demand. The resulting smoother operation should ensure stable syrup quality, low sugar loss and low energy consumption. A first engineering principles dynamic model is used to investigate the dynamic scheduling solutions. The existence of an optimal static periodic solution (OSPS) to the scheduling problem has been shown. An inherent problem of dynamic programming (DP) is exponential growth in computing load. The outrolling technique is used to avoid that problem. The outrolling technique consists in the rollout of the states resulting from the DP at a specified point in time until the final time. Outrolling is initiated when DP has reached a specified number of possible states. The rollout is carried out using the OSPS, therefore a transition between this two behaviors is needed before applying the OSPS to the DP states. This produces one outrolling final state per DP state. Comparing the final objective function values, a given number of the best final states are selected. The DP algorithm continues from the starting outrolling time, but analyzing only the selected best states, until the final time or until the outrolling technique is needed again. The action of selecting states limits the number of states to be analyzed, thereby avoiding exponential growth. Once the algorithm reaches the final time, the control sequence leading to the optimal final state is constructed as normally in dynamic programming. The dynamic scheduling provides a fast optimal response to incoming disturbances and several operation scenarios, including starting and stopping, thus promising significant potential for practical implementation.