Heuristic algorithms for public sector problems

Many large scale problems which arise from real-life situations simply do not fit into classical molds and one must be satisfied with near optimal solutions as obtained by combining formal arguments with heuristic reasoning. For example practically nothing is known about nonlinear integer programs and yet one of the first problems we encountered was of this type. What was there to do? Similarly, when faced with problems of routing trucks and barges for waste disposal, it became apparent that the usual graph theoretic arguments were not directly applicable. Nevertheless, a workable approach was formulated. Analogous problems exist in airline crew scheduling, in the design of gas or sewer pipeline networks, and in legislative committee assignments. Another area which has responded well to heuristics is in the scheduling of employees who work for public services. The personnel requirements vary with each day and shift. Nevertheless, rotating schedules have been devised which meet the work demands in a satisfactory way while guaranteeing a minimum number of days off.