Optimal Work‐Rest Schedules with a Set of Fixed‐Duration Rest Periods

This paper demonstrates that the problem of optimizing the work output of an individual employee, subject to a set of fixed‐duration rest periods over a continuous time horizon, can be modeled with a quadratic programming formulation. Exogenous determination of break period durations may result from union contracts, management policies, or necessary lower bounds on break time due to transportation or other requirements. Although the new formulation is more complex than that required for previous models, an efficient solution procedure is presented which avoids the complexities of nonlinear programming. The number of iterations required for convergence is bounded from above by the number of rest periods to be scheduled and all computations are simple. An illustration of the procedure demonstrates that it may be effectively used without computer support. While this research was motivated by the fact that previous work‐rest models were not applicable to work horizons which contained a fixed‐duration meal break, the procedure can be used to obtain optimal placement for a set of fixed‐duration rest periods which may or may not include a meal break. The characteristics of optimal strategies for a set of fixed‐duration breaks proofs are shown to have implications for the design of shifts which are potentially more attractive and productive than shifts based upon typical practice. These characteristics are also compared to the general characteristics of optimal policies associated with endogenously determined break durations. This comparison provides insight into the possible consequences of exogenous determination of break durations. This paper concludes with suggestions for additional research.