INFORMS Open Forum

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

Hello Ken,

As a MSBA student who is just trying to implement linear programming in the school project, I find your post really helpful and informative.
I can't agree with you more regarding your perspective on LP/MILP, especially in the modern world where companies are focusing on optimization. Thank you for sharing your insights and thoughts, and the links you attached are very resourceful too, the post definitely helped me gain more clarity about the linear programming and its application.

In terms of the implementation of linear programming, I am wondering is there any suggested/common practice to evaluate the model performance, or how would you validate a linear programming model with high complexity, thank you!

Tien (Candice) Her

UC Davis
San Francisco CA

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

Hi, Tien.  In LP/MILP for the real world the devil is always in the coefficients. How accurately do we know the numbers? And we are assuming linear dependence on the coefficients, how accurate is that in the business situation?  It's often hard to gather data on that. Just like with linear regression on real data.  The good thing: we absolutely understand the comparative statics, mathematically. The bad thing: the models are based on wrong assumptions if the comparative statics don't fit the situation.

Hello Ken,

As a MSBA student who is just trying to implement linear programming in the school project, I find your post really helpful and informative.
I can't agree with you more regarding your perspective on LP/MILP, especially in the modern world where companies are focusing on optimization. Thank you for sharing your insights and thoughts, and the links you attached are very resourceful too, the post definitely helped me gain more clarity about the linear programming and its application.

In terms of the implementation of linear programming, I am wondering is there any suggested/common practice to evaluate the model performance, or how would you validate a linear programming model with high complexity, thank you!

Tien (Candice) Her

UC Davis
San Francisco CA

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

Great questions from Tien and Shayan.  Great response from Bruce.  John Milne and I (and others) use the term industrial strength optimization (ISO) - I haven't give much thought lately how to describe it.  We might think about ISO can fall into three areas: solve time, formulation, and tuning / robustness.  These are the costs Bruce was describing.  There is some basic sanity checking.

some code/reporting that checks material are balanced, demand is balanced.
Capacity utilization
How well is demand being met
At Arkieva and at IBM we wrote and use softpegging reports

This is just off the top of my head.

ISO would be a good topic for an INFORMS session.  Generally one learns this through apprenticeship in the trenches.

Again my apologies for a poor response.   My email is kfordyce@arkieva.com

Hi, Tien.  In LP/MILP for the real world the devil is always in the coefficients. How accurately do we know the numbers? And we are assuming linear dependence on the coefficients, how accurate is that in the business situation?  It's often hard to gather data on that. Just like with linear regression on real data.  The good thing: we absolutely understand the comparative statics, mathematically. The bad thing: the models are based on wrong assumptions if the comparative statics don't fit the situation.

Hello Ken,

As a MSBA student who is just trying to implement linear programming in the school project, I find your post really helpful and informative.
I can't agree with you more regarding your perspective on LP/MILP, especially in the modern world where companies are focusing on optimization. Thank you for sharing your insights and thoughts, and the links you attached are very resourceful too, the post definitely helped me gain more clarity about the linear programming and its application.

In terms of the implementation of linear programming, I am wondering is there any suggested/common practice to evaluate the model performance, or how would you validate a linear programming model with high complexity, thank you!

Tien (Candice) Her

UC Davis
San Francisco CA

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

------------------------------
Ken Fordyce
director analytics without borders
Arkieva
Wilmington DE
------------------------------

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

------------------------------
Ken Fordyce
director analytics without borders
Arkieva
Wilmington DE
------------------------------

------------------------------
"Yuxin ""Raychel""" Yi
UC Davis
San Francisco CA

Original Message:
Sent: 01-16-2024 14:41
From: Ken Fordyce
Subject: Why care about LP – linear programming?

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

------------------------------
Ken Fordyce
director analytics without borders
Arkieva
Wilmington DE
------------------------------

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

Hello Ken,

I'm a MSBA student who encounters linear programming-related problems when applying them to real business world. Thanks for sharing about linear programming! I'm curious about how to speed up the time it takes to solve a linear programming model when dealing with a lot of data. Is there any modification we need to do with the model itself? Thank you!

Abby Chen

UC Davis

San Francisco

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

You asked:
> I'm curious about how to speed up the time it takes to solve a linear programming model when dealing with a lot of data.

The leading commercial solvers (Gurobi, IBM ILOG CPLEX, FICO Xpress-MP) all have fast implementations of multiple algorithms (primal and dual simplex, barrier/interior point) for linear programming. Experienced LP practitioners have seen instances where there is more computation time spent in assembling an instance for the solver than it takes to actually solve the problem.  I once heard about a case where it took 30 minutes to put all the data together into a model and pass it into the solver, and the solver solved the problem in less than a minute!  These kinds of things can be due to a number of issues, including, but not limited to:

• Using a modeling language like AMPL, OPL or Mosel.  These are not designed to efficiently process "a lot of data".
  
• Writing code in Python, Java or any programming language that is inefficient in its processing of "a lot of data".
  
• Inefficient code (e.g., poorly written SQL) for retrieving "a lot of data" from a database.
• Ingesting "a lot of data" that you think is needed to solve the problem, when much less data is really needed.
  
• Not taking advantage of data sparsity that is usually present in "a lot of data".

Finally, a poorly written model might cause the performance of the solver to not be that great.  This is less true with LP, more so with mixed integer programming (MIP).  With LP, it sometimes happens because the data presented to the model is poorly scaled or has other poor numeric characteristics.

"Speeding up the time" from a solver is as much about how well you organize and process your data, and how well you convert it into a representation that is suitable for the solver to give you acceptable performance.

Hello Ken,

I'm a MSBA student who encounters linear programming-related problems when applying them to real business world. Thanks for sharing about linear programming! I'm curious about how to speed up the time it takes to solve a linear programming model when dealing with a lot of data. Is there any modification we need to do with the model itself? Thank you!

Abby Chen

UC Davis

San Francisco

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

You asked:
> I'm curious about how to speed up the time it takes to solve a linear programming model when dealing with a lot of data.

The leading commercial solvers (Gurobi, IBM ILOG CPLEX, FICO Xpress-MP) all have fast implementations of multiple algorithms (primal and dual simplex, barrier/interior point) for linear programming. Experienced LP practitioners have seen instances where there is more computation time spent in assembling an instance for the solver than it takes to actually solve the problem.  I once heard about a case where it took 30 minutes to put all the data together into a model and pass it into the solver, and the solver solved the problem in less than a minute!  These kinds of things can be due to a number of issues, including, but not limited to:

• Using a modeling language like AMPL, OPL or Mosel.  These are not designed to efficiently process "a lot of data".
  
• Writing code in Python, Java or any programming language that is inefficient in its processing of "a lot of data".
  
• Inefficient code (e.g., poorly written SQL) for retrieving "a lot of data" from a database.
• Ingesting "a lot of data" that you think is needed to solve the problem, when much less data is really needed.
  
• Not taking advantage of data sparsity that is usually present in "a lot of data".

Finally, a poorly written model might cause the performance of the solver to not be that great.  This is less true with LP, more so with mixed integer programming (MIP).  With LP, it sometimes happens because the data presented to the model is poorly scaled or has other poor numeric characteristics.

"Speeding up the time" from a solver is as much about how well you organize and process your data, and how well you convert it into a representation that is suitable for the solver to give you acceptable performance.

Hello Ken,

I'm a MSBA student who encounters linear programming-related problems when applying them to real business world. Thanks for sharing about linear programming! I'm curious about how to speed up the time it takes to solve a linear programming model when dealing with a lot of data. Is there any modification we need to do with the model itself? Thank you!

Abby Chen

UC Davis

San Francisco

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

I would take some issue with Irv Lustig's statement that modeling languages and programming language APIs are not designed or able to process a lot of data. Any widely used modeling language or solver API will have efficient data processing as one of its design goals. So if you have reason to choose one of these (or are already using one) then it would make sense to investigate the other points in Irv's list of issues, before concluding that your data processing needs are so great that you need to consider (or switch to) a different software solution.

You asked:
> I'm curious about how to speed up the time it takes to solve a linear programming model when dealing with a lot of data.

The leading commercial solvers (Gurobi, IBM ILOG CPLEX, FICO Xpress-MP) all have fast implementations of multiple algorithms (primal and dual simplex, barrier/interior point) for linear programming. Experienced LP practitioners have seen instances where there is more computation time spent in assembling an instance for the solver than it takes to actually solve the problem.  I once heard about a case where it took 30 minutes to put all the data together into a model and pass it into the solver, and the solver solved the problem in less than a minute!  These kinds of things can be due to a number of issues, including, but not limited to:

• Using a modeling language like AMPL, OPL or Mosel.  These are not designed to efficiently process "a lot of data".
  
• Writing code in Python, Java or any programming language that is inefficient in its processing of "a lot of data".
  
• Inefficient code (e.g., poorly written SQL) for retrieving "a lot of data" from a database.
• Ingesting "a lot of data" that you think is needed to solve the problem, when much less data is really needed.
  
• Not taking advantage of data sparsity that is usually present in "a lot of data".

Finally, a poorly written model might cause the performance of the solver to not be that great.  This is less true with LP, more so with mixed integer programming (MIP).  With LP, it sometimes happens because the data presented to the model is poorly scaled or has other poor numeric characteristics.

"Speeding up the time" from a solver is as much about how well you organize and process your data, and how well you convert it into a representation that is suitable for the solver to give you acceptable performance.

Hello Ken,

I'm a MSBA student who encounters linear programming-related problems when applying them to real business world. Thanks for sharing about linear programming! I'm curious about how to speed up the time it takes to solve a linear programming model when dealing with a lot of data. Is there any modification we need to do with the model itself? Thank you!

Abby Chen

UC Davis

San Francisco

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

Hello Ken,

I'm a MSBA student who encounters linear programming-related problems when applying them to real business world. Thanks for sharing about linear programming! I'm curious about how to speed up the time it takes to solve a linear programming model when dealing with a lot of data. Is there any modification we need to do with the model itself? Thank you!

Abby Chen

UC Davis

San Francisco

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

Hello Ken,

I'm a MSBA student who encounters linear programming-related problems when applying them to real business world. Thanks for sharing about linear programming! I'm curious about how to speed up the time it takes to solve a linear programming model when dealing with a lot of data. Is there any modification we need to do with the model itself? Thank you!

Abby Chen

UC Davis

San Francisco

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

------------------------------

Richard Liu

UC Davis
San Francisco CA
------------------------------

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

Hello Ken,

It's a pleasure to meet you! I'm currently pursuing my Master's in Business Analytics (MSBA), and have been learning about linear regression from this program. For me, it is amazing how lots of data can help to predict many things and I am personally fascinated by it.

However, at the same time, applying these concepts in real-life scenarios could prove to be more challenging than in an academic environment. The complexity of real-world data and situations seems to be a significant step up from classroom examples.

I noticed in your post that linear programming is extensively utilized in supply chain management. Could you please share insights into other industries or sectors where linear programming is also prevalently applied? I'm keen to understand its broader practical applications.

Thank you for your time and insights!

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/

I recently caught two interviews with Bob Bixby on the web.  I jotted down a short summary – "LP Lessons from Bixby"  to share.  The two presentations contained a ton of helpful material. 

Why care about LP – linear programming?

For SCM professions LP is of the principal modeling methods or solvers used in the supply chain management activity Supply or Central Planning.  The Central Planning Engine (CPE) is a computational model that determines which products should be produced when and where to best meet demand and business policies – it intelligently matches assets with demand.  In linear programming the relationships between production decisions, consumption of assets, purchase of raw material, assigning inventory to meet demand, and movement of inventory and WIP are represented in linear equations.  In LP the values for the decision variables can be any value greater than or equal to ZERO.  I might decide to produce 10.5 batches of cookies and 12.8 rolls.  In mixed integer linear programming (MILP) some of the decisions variables must be integer.  We might require the number of cookies produced to be an integer value.  Binary or 0/1 integers are used to capture logical conditions.  For example, on any given day the bakery can produce cookies or rolls, but not both.

For Data Scientists, LP is a particularly powerful way to model complex relationships and find an intelligent solution.  For example, linear statistical models (regression) can be formulated and solved as an LP easily incorporating complex preferences – for example the number of independent variables allowed in the model is limited to three or place a limit on each "B" parameter. 

Why Bob Bixby?

Bob was one of the fathers of modern linear programming (LP) and mixed integer linear programming (MILP) transforming it from occasionally helpful to a mainstay of modern analytics.  Bob is clear many others made huge contributions, but his imprint is on most modern solvers including two of the leading commercial solvers: CPLEX and GUROBI.

Where are the Bixby lessons found?

Optimization: Past, Present, Future https://www.youtube.com/watch?v=_R8-nt5NyiE

A recent interview found at https://youtu.be/47BZgFhEFJ8

I urge everyone to listen to this material, it is packed full of valuable and interesting information.  

My View of Highlights

1.     LP/MILP is a computational science – yes theory is helpful, but the in-depth work on real world problems is a key to moving forward.  Bob's example of degeneracy makes this clear.  This is similar to medicine and especially surgery.

2.     LP is now a solved problem.  There are well established algorithms and implementations such that very large problems can be solved quickly, and smallish problems can be solved very fast.  This dramatically opens opportunities for organizations to use this computational solver.  

3.     The growth has been and is in MILP.  Catch this section in both videos.  Growth in the ability to solve MILP and the application of MILP.  However, MILP remains "hard" (can take a long time) to solve.  

a.     Today many central planning applications have an integer component.  There are situations where "integer component" is not critical to the value of the model and solving faster is more important. This is sometimes difficult for a planner to grasp; humans think in integers.

4.     LP/MILP is an AI technology.

Some links the reader might find helpful are:

Short-Interval Detailed Production Scheduling in 300mm Semiconductor Manufacturing using Mixed Integer and Constraint Programming by Bixby, Burda, and Miller.

Linear Programming Techniques in Regression Analysis, E. A. Kiountouzis, Journal of the Royal Statistical Society. Series C (Applied Statistics), Vol. 22, No. 1 (1973), pp. 69-73 (5 pages)

https://www.jstor.org/stable/2346304

Revealing the Mystery of Linear Programming – workhorse of modern supply chain management and emerging data science technology

https://www.linkedin.com/in/ken-fordyce-bb07b010/recent-activity/documents/