The logistics problem: ZMILP=695.68,333 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: : ZMILP=12830,925 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. Grossmann2

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.

1industri@lgorithms, Toronto, Canada. 2Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, United States. 3SK-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-oils1

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: ZNLP=110102,539 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)

Clustering1 (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)

𝑥𝐿𝑦 ≤ 𝑥 ≤ 𝑥𝑈𝑦 ∀ u, arrow

mixers

splitters

𝑦𝑢 + 𝑦𝑢′ ≥ 2𝑦𝑎𝑟𝑟𝑜𝑤for u->(arrow)->u’ (links)

1

𝑥𝑢𝑈 𝑗 𝑥𝑗𝑖 ≤ 𝑦𝑢 ≤

1

𝑥𝑢𝐿 𝑗 𝑥𝑗𝑖 ∀ (i, u)

1

𝑥𝑢𝑈 𝑖 𝑥𝑗𝑖 ≤ 𝑦𝑢 ≤

1

𝑥𝑢𝐿 𝑖 𝑥𝑗𝑖 ∀ (u, j)

u = unit, perimeter and tank

The quality problem: ZNLP=701.919,400 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

𝑷 𝑴𝒂𝒙 𝒁 =

𝒕

𝒎∈𝑴𝑭𝑼

𝒑𝒓𝒊𝒄𝒆𝒎,𝒕 𝒙𝒎,𝒕 −

𝒎∈𝑴𝑪𝑫𝑼

𝒘𝒆𝒊𝒈𝒉𝒕 𝒙𝒎,𝒕𝑳𝑶𝑫 + 𝒙𝒎,𝒕

𝑼𝑷𝑫

s.t.

𝒙𝒎,𝒕+𝟏 − 𝒙𝒎,𝒕 + 𝒙𝒎,𝒕𝑳𝑶𝑫 − 𝒙𝒎,𝒕

𝑼𝑷𝑫 = 𝟎 ∀𝒎 ∈ 𝑴𝑪𝑫𝑼, 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 tanksFeed tanks

Storage tanks

Feed tanks

CDUs

Crude-Oils

blenders

in Foundations of Computer Aided Process Operations

Jan 9th 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.