The logistics problem: Z MILP =695.6 8,333 continuous + 3,508 binary variables 3,957 equality and 15,810 inequality constraints Non-Zeros: 59,225 ; Degrees-of-freedom: 7,884 CPU(s): 176.0 seconds / 8 threads in CPLEX 12.6. The logistics problem: : Z MILP =128 30,925 continuous and 29,490 binary variables 6,613 equality and 79,079 inequality constraints (degrees-of-freedom = 53,802) CPU: 128.8 seconds using 8 threads in CPLEX 12.6. Jeffrey D. Kelly , 1 Brenno C. Menezes, 2 Faramroze Engineer, 3 Ignacio E. Grossmann 2 Crude-Oil Blend Scheduling Optimization of an Industrial-Sized Refinery: a Discrete-time Benchmark Goal : solve a discrete-time formulation for optimization of scheduling in crude-oil refineries considering both the logistics details practiced in industry in an MILP problem and the process feed diet and quality calculations in an NLP model. Figure 1. Crude-oil refining scheduling: from crude-oils to fuels. 1 industri@lgorithms, Toronto, Canada. 2 Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, United States. 3 SK-Innovation, Seoul, South Korea. 2. BC Menezes, JD Kelly, IE Grossmann, Comput Aided Chem Eng, 37, 2015. Figure 2. Proposed Reductions and PDH Algorithm Proposed Algorithm: The quantity-logic-quality phenomena is decomposed considering first the logistics model (MILP) and, secondly, the quality problem with in an NLP model by fixing the logic results from the logistics problem. 2 A pre-scheduling reduction to cluster similar quality crude-oils 1 decreases the discrete search space in the possible superstructure of assignments. SK Example: UOPSS modeling, pre-solving, and parallel processing solved a discrete-time formulation with 7 days/2h-step (84 periods) for a highly complex refinery (34 crude, 24 storage tanks, 11 feed tanks, 5 CDUs in 9 modes). 1. JD Kelly, BC Menezes, IE Grossmann, F Engineer, 2017, FOCAPO. Future Work: the next steps are planned for further development • Factors in bulk qualities (LP) between Storage and Feed Tanks in the MILP • Wide-Scheduling: from Crude-Oil Unloading to Delivery of Fuels • Initialization, Synchronization, Real-time Scheduling with Parameter Feedback The quality problem: Z NLP =110 102,539 continuous variables 58,019 equality and 768 inequality constraints (degrees-of-freedom = 44,520) CPU: 103.3 seconds in the IMPL’ SLP engine linked to CPLEX 12.6. Crude blend scheduling (MILP+NLP) (this work) Clustering 1 (MILP) Figure 4. Crude-Oil Blend Scheduling: illustrative example. x = continuous variables (flow f) y = binary variables (setup su) unit perimeter (sink, source) tank in-port (i) out-port (j) arrow (mode does not apply) x = continuous variables (flow f) (shape+mode) ≤ ≤ ∀ u, arrow mixers splitters + ′ ≥2 for u->(arrow)->u’ (links) 1 ≤ ≤ 1 ∀ (i, u) 1 ≤ ≤ 1 ∀ (u, j) u = unit, perimeter and tank The quality problem: Z NLP =701.9 19,400 continuous variables 14,862 equality and 696 inequality constraint Non-Zeros: 26,430 ; Degrees-of-freedom: 4,538 CPU(s): 16.8 seconds in the IMPL’ SLP engine linked to CPLEX 12.6. MILP-NLP gap: 0.09% with only one PDH iteration. MILP-NLP gap: from 5% to 3.5% with two PDH iterations. Figure 5. Proposed Reductions and PDH Algorithm Then, stream yields of crude distillation units (CDU), for the feed tank composition found in the quality calculation, are updated iteratively in the following logistics problem until their convergence is achieved. Both local and global MILP results of the logistics model are solved in the NLP programs of the quality and an ad-hoc criteria selects to continue those among a score of the MILP+NLP pairs of solutions. Figure 3. PDH search for MILP+NLP optimal solutions = ∈ , , − ∈ , + , s.t. ,+ − , + , − , =∀∈ , Formulation : Structural Programming Language in IMPL using the UOPSS (unit-operation-port-state superstructure). The objective maximizes the gross margin from fuels revenues subtracting the performance of the CDU throughputs, giving by the deviation from the quantity in the previous time-period against the current time-period, minimizing the 1- norm or linear deviation of the flow in consecutive time-periods. Storage tanks Feed tanks Storage tanks Feed tanks CDUs Crude-Oils blenders in Foundations of Computer Aided Process Operations Jan 9 th 2017, Tucson, United States Conclusion : • a phenomenological decomposition of logistics (MILP) and quality (NLP) is applied to solve industrial-sized problems to feasibility with a demonstration of the theory in practice. • Computing Skills in IMPL handles huge NLPs: techniques as reverse polish notation, derivatives using complex numbers, derivatives by groups with same pattern, SLP linking with MILP solvers, among others.