Combinatorial optimisation – tools for practical problem solving

Combinatorial optimisation problems occur whenever there is a requirement to select the best option from a finite set of alternatives. They abound in all aspects of business and industry and cover areas such as planning, scheduling, routing, location and space allocation. Such problems are renowned for being relatively simple to state but difficult to solve. This paper looks at the developments in combinatorial optimisation over the last thirty years, with particular emphasis on their practical significance, and then goes on to look at some of the issues that are pertinent to those facing such problems today.