Constraint logic programming (CLP), which combines the complementary strengths of the artificial intelligence (AI) and OR approaches, is introduced as a new tool for formalizing constraint satisfaction problems that include both qualitative and quantitative constraints. CLP(R), one CLP language, is used to contrast the CLP approach with mixed integer programming (MIP). Three relative advantages of CLP over MIP are analyzed: representational efficiency for domain-specific knowledge; partial solutions; and ease of model revision. A case example of constraint satisfaction problems is implemented by MIP and CLP(R) for comparison of the two approaches. The results exhibit the representational economics of CLP with computational efficiency comparable to that of MIP.