Combinatorial optimization: Current successes and directions for the future

Our ability to solve large, important combinatorial optimization problems has improved dramatically in the past decade. The availability of reliable software, extremely fast and inexpensive hardware and high-level languages that make the modeling of complex problems much faster have led to a much greater demand for optimization tools. This paper highlights the major breakthroughs and then describes some very exciting future opportunities. Previously, large research projects required major data collection efforts, expensive mainframes and substantial analyst manpower. Now, we can solve much larger problems on personal computers, much of the necessary data is routinely collected and tools exist to speed up both the modeling and the post-optimality analysis. With the information-technology revolution taking place currently, we now have the opportunity to have our tools embedded into supply-chain systems that determine production and distribution schedules, process-design and location-allocation decisions. These tools can be used industry-wide with only minor modifications being done by each user.