Decision Sciences Journal
Volume 27, Number 3
Summer 1996
A Stochastic Goal Program for Employee Scheduling
Fred F. Easton
Robert H. Brethen Operations Management Institute, School of
Management, Syracuse University, Syracuse, NY 13244-2130
Donald F. Rossin
School of Management, University of Michigan-Dearborn, Dearborn, MI
48128-1491
ABSTRACT
Deterministic goal programs for employee scheduling decisions
attempt to minimize expected operating costs by assigning the ideal
number of employees to each feasible schedule. For each period in
the planning horizon, managers must first determine the amount of
labor that should be scheduled for duty. These requirements are
often established with marginal analysis techniques, which use
estimates for incremental labor costs and shortage expenses.
Typically, each period in the planning horizon is evaluated as an
independent epoch. An implicit assumption is that individual
employees can be assigned to schedules with as little as a single
period of work. If this assumption violates local work rules, the
labor requirements parameters for the deterministic goal program
may be suboptimal.
As we show in this research, this well-known limitation can lead
to costly staffing and scheduling errors. We propose an employee
scheduling model that overcomes this limitation by integrating the
labor requirements and scheduling decisions. Instead of a single,
externally determined staffing goal for each period, the model uses
a probability distribution for the quantity of labor required. The
model is free to choose an appropriate staffing level for each
period, eliminating the need for a separate goal-setting procedure.
In most cases this results in better, less costly decisions. In
addition, the proposed model easily accommodates both linear and
nonlinear under- and overstaffing penalties. We use simple examples
to demonstrate many of these advantages and to illustrate the key
techniques necessary to implement our model. We also assess its
performance in a study of more than 1,700 simulated stochastic
employee scheduling problems.
Subject Areas: Goal Programming, Labor and Staff
Planning, and Service Operations.
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