The Cost of Consecutivity in the (5, 7) Cyclic Staffing Problem

Abstract

The (5, 7) cyclic staffing problem is the problem of finding the least number of workers assigned to a 7 day cyclic schedule, so that sufficient workers are present during day i to meet requirement b _i and each person works a shift of 5 consecutive days and is idle for the other 2. In this paper we derive an expression for the minimal workforce size in the problem in terms of the b _i's. This result is interesting because it shows the extra number of workers needed by insisting that each person's idle days are consecutive.