George B. Dantzig, 90, a mathematician who devised a formula that revolutionized planning, scheduling, network design and other complex functions integral to modern-day business, industry and government, died May 13 at his home in Palo Alto, Calif. The cause of death, according to his daughter, was complications from diabetes and cardiovascular disease.

Dr. Dantzig was known as the father of linear programming and as the inventor of the "simplex method," an algorithm for solving linear programming problems.

"He really created the field," said Irvin Lustig, an operations research software consultant who was Dr. Dantzig's student at Stanford University.

Dr. Dantzig's seminal work allows the airline industry, for example, to schedule crews and make fleet assignments. It's the tool that shipping companies use to determine how many planes they need and where their delivery trucks should be deployed. The oil industry long has used linear programming in refinery planning, as it determines how much of its raw product should become different grades of gasoline and how much should be used for petroleum-based byproducts. It's used in manufacturing, revenue management, telecommunications, advertising, architecture, circuit design and countless other areas.

"The virtually simultaneous development of linear programming and computers led to an explosion of applications, especially in the industrial sector," Stanford University Professor Arthur F. Veinott Jr. said in a statement. "For the first time in history, managers were given a powerful and practical method of formulating and comparing extremely large numbers of interdependent alternative courses of action to find one that was optimal."

George Bernard Dantzig was born in Portland, Ore., in 1914. His father, Tobias Dantzig, was a Russian mathematician who had gone to Paris to study with Henri Poincare, the renowned French mathematician and philosopher of science. Tobias Dantzig married Anja Ourisson, a student at the Sorbonne who also was studying mathematics, and the couple immigrated to the United States.

In the early 1920s, the Dantzig family moved to Baltimore and then to Washington, where Anja Dantzig became a linguist at the Library of Congress and her husband taught mathematics at the University of Maryland. Their son attended Powell Junior High School and Central High School, where he was fascinated by geometry. His father nurtured his interest by challenging him with complex geometry problems -- thousands of them.

Dr. Dantzig received his bachelor's degree in mathematics and physics from the University of Maryland in 1936 and his master's degree in mathematics from the University of Michigan in 1937.

Although he enjoyed statistics, abstract mathematics bored him. Abandoning academia, he moved back to Washington in 1937 and took a job with the Bureau of Labor Statistics.

In 1939, he resumed his studies at the University of California at Berkeley, studying statistics under mathematician Jerzy Neyman. An incident during his first year at Berkeley became a math-world legend.

As Dr. Dantzig recalled years later, he arrived late for class one day and saw two problems on the blackboard that he assumed were homework assignments. He copied them down, took them home and solved them after a few days. "The problems seemed to be a little harder to do than usual," he said.

On a Sunday morning six weeks later, an excited Neyman banged on his student's front door, eager to tell him that the homework problems he had solved were two of the most famous unsolved problems in statistics.

"That was the first inkling I had that there was anything special about them," Dr. Dantzig recalled.

From 1941 to 1946, he was the civilian head of the combat analysis branch of the Air Force's Headquarters Statistical Control. His task was to find a way of managing "hundreds of thousands of different kinds of material goods and perhaps fifty thousand specialties of people," seemingly intractable problems that spurred his search for a mathematical model for what would become linear programming.

He received his doctorate from Berkeley in 1946 and returned to Washington, where he became a mathematical adviser at the Defense Department, charged with mechanizing the planning process. Based partly on his earlier work with aircraft supply flow, he worked out the simplex algorithm.

In 1952, he became a research mathematician with the Rand Corp. and began implementing linear programming on computers. In 1960, he became a professor at Berkeley and chairman of the Operations Research Center, and in 1966, professor of operations research and computer science at Stanford University. He remained at Stanford until his retirement in the mid-1990s.

Survivors include his wife of 68 years, Anne Dantzig of Palo Alto; three children, David Dantzig of Cleveland, Paul Dantzig of New York and Jessica Klass of Berkeley; three grandchildren; and two great-grandchildren.

His daughter noted that as an influential teacher for many years, her father had two families -- his own and the hundreds of students who studied and worked with him throughout his long career.

He won numerous awards for his groundbreaking work, including the National Medal of Science in 1975.

He was the author of the pioneering book "Linear Programming and Extensions" (1963), updated in 1997 and 2003, and he co-authored "Compact City" (1973). He had been working on a science fiction novel in recent years, "In His Own Image," about a plague that wipes out mankind.

By Joe Holley Washington Post Staff Writer Thursday, May 19, 2005

© 2005 The Washington Post Company

Dr. Dantzig was known as the father of linear programming and as the inventor of the "simplex method," an algorithm for solving linear programming problems.

"He really created the field," said Irvin Lustig, an operations research software consultant who was Dr. Dantzig's student at Stanford University.

Dr. Dantzig's seminal work allows the airline industry, for example, to schedule crews and make fleet assignments. It's the tool that shipping companies use to determine how many planes they need and where their delivery trucks should be deployed. The oil industry long has used linear programming in refinery planning, as it determines how much of its raw product should become different grades of gasoline and how much should be used for petroleum-based byproducts. It's used in manufacturing, revenue management, telecommunications, advertising, architecture, circuit design and countless other areas.

"The virtually simultaneous development of linear programming and computers led to an explosion of applications, especially in the industrial sector," Stanford University Professor Arthur F. Veinott Jr. said in a statement. "For the first time in history, managers were given a powerful and practical method of formulating and comparing extremely large numbers of interdependent alternative courses of action to find one that was optimal."

George Bernard Dantzig was born in Portland, Ore., in 1914. His father, Tobias Dantzig, was a Russian mathematician who had gone to Paris to study with Henri Poincare, the renowned French mathematician and philosopher of science. Tobias Dantzig married Anja Ourisson, a student at the Sorbonne who also was studying mathematics, and the couple immigrated to the United States.

In the early 1920s, the Dantzig family moved to Baltimore and then to Washington, where Anja Dantzig became a linguist at the Library of Congress and her husband taught mathematics at the University of Maryland. Their son attended Powell Junior High School and Central High School, where he was fascinated by geometry. His father nurtured his interest by challenging him with complex geometry problems -- thousands of them.

Dr. Dantzig received his bachelor's degree in mathematics and physics from the University of Maryland in 1936 and his master's degree in mathematics from the University of Michigan in 1937.

Although he enjoyed statistics, abstract mathematics bored him. Abandoning academia, he moved back to Washington in 1937 and took a job with the Bureau of Labor Statistics.

In 1939, he resumed his studies at the University of California at Berkeley, studying statistics under mathematician Jerzy Neyman. An incident during his first year at Berkeley became a math-world legend.

As Dr. Dantzig recalled years later, he arrived late for class one day and saw two problems on the blackboard that he assumed were homework assignments. He copied them down, took them home and solved them after a few days. "The problems seemed to be a little harder to do than usual," he said.

On a Sunday morning six weeks later, an excited Neyman banged on his student's front door, eager to tell him that the homework problems he had solved were two of the most famous unsolved problems in statistics.

"That was the first inkling I had that there was anything special about them," Dr. Dantzig recalled.

From 1941 to 1946, he was the civilian head of the combat analysis branch of the Air Force's Headquarters Statistical Control. His task was to find a way of managing "hundreds of thousands of different kinds of material goods and perhaps fifty thousand specialties of people," seemingly intractable problems that spurred his search for a mathematical model for what would become linear programming.

He received his doctorate from Berkeley in 1946 and returned to Washington, where he became a mathematical adviser at the Defense Department, charged with mechanizing the planning process. Based partly on his earlier work with aircraft supply flow, he worked out the simplex algorithm.

In 1952, he became a research mathematician with the Rand Corp. and began implementing linear programming on computers. In 1960, he became a professor at Berkeley and chairman of the Operations Research Center, and in 1966, professor of operations research and computer science at Stanford University. He remained at Stanford until his retirement in the mid-1990s.

Survivors include his wife of 68 years, Anne Dantzig of Palo Alto; three children, David Dantzig of Cleveland, Paul Dantzig of New York and Jessica Klass of Berkeley; three grandchildren; and two great-grandchildren.

His daughter noted that as an influential teacher for many years, her father had two families -- his own and the hundreds of students who studied and worked with him throughout his long career.

He won numerous awards for his groundbreaking work, including the National Medal of Science in 1975.

He was the author of the pioneering book "Linear Programming and Extensions" (1963), updated in 1997 and 2003, and he co-authored "Compact City" (1973). He had been working on a science fiction novel in recent years, "In His Own Image," about a plague that wipes out mankind.

By Joe Holley Washington Post Staff Writer Thursday, May 19, 2005

© 2005 The Washington Post Company