MultiOperations TimeSlots Model for CrudeOil Operations Scheduling

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Multi-Operations Time-Slots Model for Crude-Oil
Operations Scheduling

• Sylvain Mouret1, Ignacio Grosmann1, Pierre
  Pestiaux2
• 1Carnegie Mellon University
• 2Total SA
• 18th European Symposium on Computer Aided Process
  Engineering
• Lyon, France

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Outline

• Problem statement
• Proposed approach
• Basic Idea
• MINLP model
• Search procedure
• Results and comparisons
• Sensitivity to the number of time-slots
• Comparison with other algorithms
• Larger instances
• Conclusion and future work

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A typical oil refinery

• Crude-oil refining into useful petroleum
  products
• LPG, gasoline, diesel fuel, kerosene, heating
  oil,
• 3 phases
• Crude-oil unloading and blending
• Fractionation and reaction processes
• Product blending and shipping

Standard refinery system. (Méndez et al., 2005)
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- Crude-oil Blending Operations Scheduling
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Crude-oil scheduling problem (Lee al., 1996)

• Scheduling horizon 0,H
• 4 types of resources
• Crude-oil marine vessels
• Storage tanks
• Charging tanks
• Crude Distillation Units (CDUs)
• 3 types of operations
• Unloading Vessel unloading to storage tanks
• Transfer Transfer from storage tanks to
  charging tanks
• Distillation Distillation of charging tanks

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Crude-oil scheduling problem (Lee al., 1996)

• Given
• Refinery configuration
• Logistics constraints
• Initial tanks inventory and composition
• Vessels arrival time, inventory level and
  composition
• Distillation specifications and demands
  (planning decisions)
• Determine
• Required operations
• Timing decisions
• Transfer volumes
• Minimize
• Cost of distilled crude-oil mixtures

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Example of crude-oil operation schedule

• Common logistics constraints
• Only one docking station available for vessel
  unloadings
• No simultaneous inlet and outlet operations on
  tanks
• Crude distillation units can only be charged by
  one tank
• Continuous distillation

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Multi-Operation Time Slots Basic idea

• Continuous time model
• Basic steps
• Define the set of transfer operations
• Postulate the number of time slots
• Define a priority order on the set of time slots
• Assign exactly one operation to each time slot
  and determine the timing and volume decisions
• MINLP model
• Binary variables assignment variables
• Continuous variables time, volume and level
  variables

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Multi-Operation Time Slots Example (case study)
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Multi-Operation Time Slots - Sets and Variables

• Ordered set of time slots
• Set of operations
• Assignment variables
• Operation v is assigned to time slot i iff
• Exactly one operation for each time slot
• Time variables
• Start time
• End time

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Multi-Operation Time SlotsNon-overlapping
constraints

• For each ordered pair of slots i lt j and
• for each pair of non-overlapping operations v
  and w
• For example,
• Vessel unloadings 1 and 2
• Distillation transfers 7 and 8

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Multi-Operation Time SlotsTank inventory and
composition constraints

• Tanks
• Crude-oil types
• Volume variables
• Level variables
• Tank inventory constraints
• Tank composition constraints

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Multi-Operation Time SlotsOther constraints

• Continuous distillation
• Flowrate limitations
• Scheduling constraints
• Vessels availability time window
• Precedence constraints
• Distillation specification
• Objective function

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Search procedure MILP-NLP decomposition

• Master problem find optimal solution of the MILP
  relaxation
• Solution may not satisfy the nonlinear
  composition constraints
• Fix assignment variables
• Slave problem find optimal solution for the
  resulting NLP (with nonlinear composition
  constraints)

MILP minimize objective s.t. all
constraint except composition constraint
Fix assignment variables Ziv
NLP minimize objective s.t. all constraint
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Effect of the number of time slots (case study)

• MILP-NLP decomposition tested on case-study with
  5 to 13 time slots
• Size of the MINLP for 13 time-slots
• 1215 binary variables, 1086 continuous variables,
  2979 constraints
• Feasible schedule obtained with 9 slots Optimal
  schedule obtained with 10 slots
• MILP solver Xpress 17.10, NLP solver CONOPT 3

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Comparison with other algorithms (case study)

• Number of time slots 13
• Algorithms used
• MILP-NLP decomposition Xpress (MILP), CONOPT
  (NLP)
• MINLP solvers DICOPT, SBB, AlphaECP, BARON
  (global optimizer)

? Order of magnitude reduction for CPU time
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Larger instances

• 4 examples from Lee al. (1996)
• MILP solver Xpress 17.10
• NLP solver CONOPT 3
• Problem 3 shows a gap of 5.5 between the MILP
  and the NLP solutions

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Conclusion and Future Work

• Conclusions
• New MINLP continuous-time formulation for the
  crude-oil operations scheduling problem
• Handles logistics constraints and minimization
  of crude-oil costs
• MILP-NLP decomposition algorithm compares well
  to MINLP solvers
• Future work
• Include symmetry-breaking constraints and
  operating rules
• Hybrid optimization Contraint Programming as a
  symmetry-breaking branching tool
• Practical case-study
• Improve the MILP-NLP decomposition
• Take into account stochastic parameters (vessels
  arrival time)

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Multi-Operation Time SlotsA schedule as a word

• A schedule can be represented as a sequence of
  operations corresponding to the sequence of
  time-slots
• For example, the following schedule is
  represented by the sequence 7683513762

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Multi-Operation Time SlotsSymmetry breaking and
operating rules

• Multiple assignments may lead to the same
  schedule
• For example, slots 1 and 2 can be exchanged
• Refinery specific operating rules can be applied
• For example, distillation sequences can be defined

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Multi-Operation Time SlotsSymmetry breaking

• The possible sequences of operations are
  represented by a regular language (Regular
  Constraint by Côté et al., 2007)
• Case study has 2 refinery states distillation 7
  or 8
• During distillation 7
• Overall

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Scheduling formulations

• Fixed Time Grid
• Kondili et al. (1993), Shah et al. (1993),
  Pantelides (1994)
• Crude-oil scheduling Shah (1996), Lee et al.
  (1996)
• Variable Time Grid
• Zhang and Sargent (1996), Schilling and
  Pantelides (1996)
• Crude-oil scheduling Moro and Pinto (2004)
• Single-Operation Time Slots (event point
  formulation)
• Ierapetritou and Floudas (1998)
• Crude-oil scheduling Jia et al. (2003)
• Multi-Operation Time Slots

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Scheduling formulations

• Fixed Time Grid
• Variable Time Grid
• Single-Operation Time Slots (event point
  formulation)
• Multi-Operation Time Slots

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Fixed Time Grid formulation

• Discretization of the time horizon into n
  fixed-length adjacent time slots
• Identical MILP-NLP decomposition
• Example 4 from Lee al. (1996), optimal
  solution 107.45

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Quality of the solution Human heuristics

• Solution found by a human operator (trial and
  error)
• 2 vessels, 2 storage tanks, 2 charging tanks, 1
  CDU, 8 days
• Total costs 137,930

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Quality of the solution MINLP solution

• Solution found by the MILP-NLP decomposition
  approach
• 2 vessels, 2 storage tanks, 2 charging tanks, 1
  CDU, 8 days
• Total costs 120,250 (14.7 decrease)

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Quality of the solution Main differences
Human operator solution
MINLP solution

• Different sequence of distillations
• Unloading are done earlier in human operator
  solution
• Transfers take longer in human operator solution
• Leads to 14.7 decrease of total costs

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