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Integrated Scheduling and Dynamic Optimization ofBatch Processes Using State Equipment Networks
Yisu Nie1 Lorenz T. Biegler1 John M. Wassick2
1Center for Advanced Process Decision-makingDepartment of Chemical Engineering
Carnegie Mellon University
2The Dow Chemical Company
October 13, 2011
Yisu Nie (Carnegie Mellon University) EWO meeting October 13, 2011 1 / 8
IntroductionBackground and motivation
The current status quo of batch scheduling and operationsI Batch process scheduling: recipe-based approaches
F Decoupled scheduling and unit operationsF Dow’s practice: Discrete-time resource-task network 1
+ Easy (linear) models for scheduling− Poor process flexibility− Loss of process profitability
I Dynamic optimization of batch operations: few experiencesF Investigated mostly in single machine environment
Integration of scheduling and dynamic optimizationI Adding value to existing assetsI Improving plant reliability
1J.M. Wassick and J. Ferrio. Extending the resource task network for industrial applications. Computers and Chemical
Engineering, 2011
Yisu Nie (Carnegie Mellon University) EWO meeting October 13, 2011 2 / 8
IntroductionBackground and motivation
The current status quo of batch scheduling and operationsI Batch process scheduling: recipe-based approaches
F Decoupled scheduling and unit operationsF Dow’s practice: Discrete-time resource-task network 1
+ Easy (linear) models for scheduling− Poor process flexibility− Loss of process profitability
I Dynamic optimization of batch operations: few experiencesF Investigated mostly in single machine environment
Integration of scheduling and dynamic optimizationI Adding value to existing assetsI Improving plant reliability
1J.M. Wassick and J. Ferrio. Extending the resource task network for industrial applications. Computers and Chemical
Engineering, 2011
Yisu Nie (Carnegie Mellon University) EWO meeting October 13, 2011 2 / 8
IntroductionBackground and motivation
The current status quo of batch scheduling and operationsI Batch process scheduling: recipe-based approaches
F Decoupled scheduling and unit operationsF Dow’s practice: Discrete-time resource-task network 1
+ Easy (linear) models for scheduling− Poor process flexibility− Loss of process profitability
I Dynamic optimization of batch operations: few experiencesF Investigated mostly in single machine environment
Integration of scheduling and dynamic optimizationI Adding value to existing assetsI Improving plant reliability
1J.M. Wassick and J. Ferrio. Extending the resource task network for industrial applications. Computers and Chemical
Engineering, 2011
Yisu Nie (Carnegie Mellon University) EWO meeting October 13, 2011 2 / 8
IntroductionProblem description
GivenI A batch plant with existing equipmentI A time horizon to make productsI Dynamic models of process operations
DetermineI The optimal production scheduleI The optimal equipment control strategy
Via1 Process representation using the state
equipment network(SEN)2 Mathematical optimization formulation
Yisu Nie (Carnegie Mellon University) EWO meeting October 13, 2011 3 / 8
Solution StrategyIntegrated optimization based on the SEN
The SEN represents the process system as a directed graphconnecting two kinds of nodes
Material Feed, intermediate and final products
Equipment Process units carrying out operations
The integrated formulation
Objective function Max Profit = Product sales - Material cost - Operating cost
Constraints I Scheduling considerationsAssignment constraints, material balance, capacity constraints, timing
constraintsI Unit operation
Dynamic first-principle models, limits on controls and statesI Material quality measurement
Material blending, quality requirementsI Auxiliary tightening constraints
Tightening timing constraints, mass balance of process units
Yisu Nie (Carnegie Mellon University) EWO meeting October 13, 2011 4 / 8
Solution StrategyIntegrated optimization based on the SEN
The SEN represents the process system as a directed graphconnecting two kinds of nodes
Material Feed, intermediate and final products
Equipment Process units carrying out operations
The integrated formulation
Objective function Max Profit = Product sales - Material cost - Operating cost
Constraints I Scheduling considerationsAssignment constraints, material balance, capacity constraints, timing
constraintsI Unit operation
Dynamic first-principle models, limits on controls and statesI Material quality measurement
Material blending, quality requirementsI Auxiliary tightening constraints
Tightening timing constraints, mass balance of process units
Yisu Nie (Carnegie Mellon University) EWO meeting October 13, 2011 4 / 8
Case StudyA jobshop batch plant
Equipment units and products manufactured in the plantHeater×1 Reactor×2 Filter×2 Distillation
Column×1Packaging
Line×2
FeedA
Prod1
Prod3
Prod2
30(MU/ton)
50(MU/ton)
20(MU/ton)
5(MU/ton)
Maximizing the net profit within a 10-hour time horizon
ModelStatistics
Type Var.(Discrete) # Nonlinear Var. # Cons. #
Recipe-based MILP 676(90) 0 1079Integrated MINLP 4978(90) 2292 12507
ModelSolution
Profit(MU) CPU time (s) Node(Best) # Gap(%)
Recipe-based 1374 0.366 288(199) 0.0Integrated 1935 9564 5000(1602) 67.9
MILP solved by CPLEX, MINLP solved by SBB(CONOPT)
Yisu Nie (Carnegie Mellon University) EWO meeting October 13, 2011 5 / 8
Case StudyA jobshop batch plant
Equipment units and products manufactured in the plantHeater×1 Reactor×2 Filter×2 Distillation
Column×1Packaging
Line×2
FeedA
Prod1
Prod3
Prod2
30(MU/ton)
50(MU/ton)
20(MU/ton)
5(MU/ton)
Maximizing the net profit within a 10-hour time horizon
ModelStatistics
Type Var.(Discrete) # Nonlinear Var. # Cons. #
Recipe-based MILP 676(90) 0 1079Integrated MINLP 4978(90) 2292 12507
ModelSolution
Profit(MU) CPU time (s) Node(Best) # Gap(%)
Recipe-based 1374 0.366 288(199) 0.0Integrated 1935 9564 5000(1602) 67.9
MILP solved by CPLEX, MINLP solved by SBB(CONOPT)
Yisu Nie (Carnegie Mellon University) EWO meeting October 13, 2011 5 / 8
Case StudyOptimal production schedules in Gantt charts
Recipe-based approach
Line2
Line1
Column
Filter2
Filter1
Reactor2
Reactor1
Heater
0 2 4 6 8 10
Time(hr)
80.00 80.00
35.00 35.00 35.00
34.36 45.00 45.00
69.36
80.00 80.00
60.00 60.00
37.02 25.00
39.48 50.84
HeatingReaction1Reaction2Filtration1Filtration2
Distillation1Distillation2Packaging1Packaging2Packaging3
Integrated approach
Line2
Line1
Column
Filter2
Filter1
Reactor2
Reactor1
Heater
0 2 4 6 8 10
Time(hr)
73.63 62.83 40.00
34.91 28.74 17.83 35.00
34.04 44.89 45.00
68.94
73.63 57.83 40.00
60.00 58.46 45.43
40.26 33.18
38.01 30.00
HeatingReaction1Reaction2Filtration1Filtration2
Distillation1Distillation2Packaging1Packaging2Packaging3
Numbers inside slots are batch sizes
Yisu Nie (Carnegie Mellon University) EWO meeting October 13, 2011 6 / 8
Case StudyOptimal operating profiles for batch units
Optimal temperature profiles of Reactor 1
4 5 6 7 8 9
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6 1.8
Sca
led
tem
p
Time(hr)
Event slot 1: Reaction 1Recipe
Integrated
0.4 0.6 0.8
1 1.2
2 2.2 2.4 2.6 2.8 3 3.2 3.4 3.6
Sca
led
tem
p
Time(hr)
Event slot 2: Reaction 2
0.4 0.6 0.8
1 1.2
3.8 4 4.2 4.4 4.6 4.8 5 5.2 5.4
Sca
led
tem
p
Time(hr)
Event slot 3: Reaction 2
0.6 0.9 1.2 1.5 1.8
5.6 5.8 6 6.2 6.4 6.6 6.8 7 7.2
Sca
led
tem
p
Time(hr)
Event slot 4: Reaction 2
Dynamic profiles also obtained for Reactor 2 and Distillation Column
Yisu Nie (Carnegie Mellon University) EWO meeting October 13, 2011 7 / 8
Conclusions and Acknowledgments
Concluding remarksI The state equipment network representation of batch processesI An optimization formulation for the integration of scheduling and
dynamic optimization
Future work
Off-line→On-lineI Alternative scheduling formulationsI Data-driven dynamic models
Thank you
I am glad to take questions...
Yisu Nie (Carnegie Mellon University) EWO meeting October 13, 2011 8 / 8
Conclusions and Acknowledgments
Concluding remarksI The state equipment network representation of batch processesI An optimization formulation for the integration of scheduling and
dynamic optimization
Future work
Off-line→On-lineI Alternative scheduling formulationsI Data-driven dynamic models
Thank you
I am glad to take questions...
Yisu Nie (Carnegie Mellon University) EWO meeting October 13, 2011 8 / 8
Conclusions and Acknowledgments
Concluding remarksI The state equipment network representation of batch processesI An optimization formulation for the integration of scheduling and
dynamic optimization
Future work
Off-line→On-lineI Alternative scheduling formulationsI Data-driven dynamic models
Thank you
I am glad to take questions...
Yisu Nie (Carnegie Mellon University) EWO meeting October 13, 2011 8 / 8