A hybrid network flow tabu search heuristic for the minimum shift design problem

The minimum shift design problem (MSD) is a scheduling problem that commonly arises in workforce management activities. Given a collection of shifts and workforce requirements, the problem consists in finding a minimum cardinality set of work shifts, and the number of workers to assign to each shift, in order to meet (or minimize the deviation from) prespecified staff requirements. This problem reduces to a special case of the minimum edge-cost flow problem (MECF ) for which a logarithmic hardness of approximation lower bound can be shown. We propose a two-stage heuristic for MSD. The first stage, inspired by the relation between the MSD and MECF problems, is based on a greedy heuristic that relies on a mincost max-flow (MCMF ) subroutine. The second stage is a composite tabu search procedure based on the interleaving of different neighborhood definitions. We compare our heuristic with