In the area of process operations, as the scale of the production increases, the mathematical complexity of the corresponding mathematical model and the time it takes to find its optimal solution increase exponentially. There are relatively few papers that have addressed the planning and scheduling problems using decentralized optimization strategies. Kelly and Zyngier (2007) presented a procedure to find a suitable way to decompose large decision-making problems and compared different decentralized approaches using hierarchical decomposition heuristics. Saharidis et al. (2006, 2008) studied the problem of production planning in deterministic and stochastic environments and compared centralized and decentralized optimization for an enterprise consisting of two production plants in series producing many different outputs with subcontracting options.

In this work, a novel decentralized strategy is proposed for large scale refinery scheduling problems. Two operating scenarios are studied - the first one corresponds to the case where simultaneous input and output flows are not allowed to occur in the storage tanks and the second one to the case where this restriction is not applied.

The proposed decentralized strategy contains two main steps. In the first step, the centralized system is decomposed following a general decomposing rule and optimal schedules are determined for each sub-problem. The main idea of the decomposition approach is that the system is decomposed at intermediate storage tanks such that the inlet and outlet stream of the tanks belong to different sub-problems. The decomposition starts with the final products or product storage tanks, and continues to include the reactors/units that are connected to them and stops when the storage tanks are reached. The products, units and storage tanks are part of the one sub-problem. Then following the input stream of each storage tank, the same procedure is used to determine the next sub-problem. If input and output stream of the storage tank are included at the same local problem then the storage tank also belongs to that local problem. The second step of the proposed approach concerns the integration of the optimal solutions of the sub-problems to achieve an optimal schedule for the entire system. The integration is based on the demand and mass balance constraints at connecting storage tanks. Since the storage tanks are connecting the sub-problems, the outflow of each of the storage tank becomes the demand for the preceding sub-problem. The material coming into the tank and the material already present in the tank should be at least equal to the material flowing out of the tank to satisfy the mass balance constraints. The mathematical formulation is based on continuous time representation and involves material balance constraints, capacity constraints, sequence constraints, assignment constraints, demand constraints and an objective function which corresponds to the minimization of makespan.

Different case studies of refinery scheduling problems are presented to illustrate the applicability and effectiveness of the decentralized strategy and the optimal solutions are compared with the ones obtained using centralized models. It is observed and proved analytically that if our decomposing rule is applied for the cases presented above, the local and global optimization give the same optimal makespan. Finally, it is important to notice that the computational effort of the proposed decentralized strategy is significantly less than the centralized approach.

Reference:

[1] J.D. Kelly and D. Zyngier (2007). Hierarchical decomposition heuristic for scheduling: Coordinated reasoning for decentralized and distributed decision-making problems. Comput. Chem. Eng.

[2] G.K. Saharidis, Y. Dallery and F. Karaesmen (2006). Centralized versus decentralized production planning. RAIRO Operations Research, 40, 113.

[3] G.K. Saharidis, V. Kouikoglou and Y. Dallery (2008). Analysis of centralized and decentralized control policies for a two-stage stochastic supply chain with subcontracting options. Submitted