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