The general employee scheduling problem. An integration of MS and AI

The general employee scheduling problem extends the standard shift scheduling problem by discarding key limitations such as employee homogeneity and the absence of connections across time period blocks. The resulting increased generality yields a scheduling model that applies to real world problems confronted in a wide variety of areas. The price of the increased generality is a marked increase in size and complexity over related models reported in the literature. The integer programming formulation for the general employee scheduling problem, arising in typical real world settings, contains from one million to over four million zero~ne variables. By contrast, studies of special cases reported over the past decade have focused on problems involving between 100 and 500 variables. We characterize the relationship between the general employee scheduling problem and related problems, reporting computational results for a procedure that solves these more complex problems within 98-99 % optimality and runs on a microcomputer. We view our approach as an integration of management science and artificial intelligence techniques. The benefits of such an integration are suggested by the fact that other zero~ne scheduling implementations reported in the literature, including the one awarded the Lancaster Prize in 1984, have obtained comparable approximations of optimality only for problems from two to three orders of magnitude smaller, and then only by the use of large mainframe computers.