Program Does Not Equal Program: Constraint Programming and Its Relationship to Mathematical Programming

Arising from research in the computer science community, constraint programming is a fairly new technique for solving optimization problems. For those familiar with mathematical programming, a number of language barriers make it difficult to understand the concepts of constraint programming. In this short tutorial on constraint programming, we explain how it relates to familiar mathematical programming concepts and how constraint programming and mathematical programming technologies are complementary. We assume a minimal background in linear and integer programming. G eorge Dantzig [1963] invented the simplex method for linear programming in 1947 and first described it in a paper entitled " Programming in a linear structure " [Dantzig 1948, 1949]. Fifty years later, linear programming is now a strategic technique used by thousands of businesses trying to optimize their global operations. In the mid-1980s, researchers developed constraint programming as a computer science technique by combining developments in the artificial intelligence community with the development of new computer programming languages. Fifteen years later, constraint programming is now being seen as an important technique that complements traditional mathematical programming technologies as businesses continue to look for ways to optimize their business operations. Developed independently as a technique within the computer science literature, constraint programming is now getting attention from the operations research com