Abstract
The paper examines the complexity of assigning multiple breaks to shifts in the context of large-scale tour scheduling. A mixed-integer programming (MIP) model is presented that includes shift and days-off scheduling along with break assignments for a multi-skilled workforce. To achieve tractability, a two-stage decomposition procedure is proposed that separates the tour scheduling problem (TShP) from the break assignment problem (BAP). The former MIP is first solved to determine the shifts and days off for the workforce that minimize labor and shortages costs over the planning horizon. The results are used as input to a second MIP that optimally places the breaks to minimize the costs of working hours and uncovered periods. Three implicit BAP formulations are investigated. To better understand the literature and the models previously developed, a 3-field break classification scheme is introduced. The first field characterizes the number of breaks permitted per shift, the second specifies whether the length of the breaks is fixed or variable, and the third limits their position in a shift. A complexity analysis of the resulting 12 BAPs along with a few special cases is also included. Most problems are shown to be strongly NP-hard. Computations are presented for a wide variety of scenarios for both the TShP and the BAP using data provided by a European airport ground handler company. In all, over 500 instances were investigated using high and low demand fluctuation curves and the various break and shift flexibility options. The results indicate that increasing flexibility in break regulations can make a significant difference in coverage, but the degree depends on the underlying structure of the demand curve as well as on the types of shifts permitted. Formulations with the most flexible shift and break regulations reduced undercoverage by up to 16.68% compared to the most common scenarios in which shifts are limited to a single lunch break.
Highlights
In most personnel scheduling problems, workforce demand is a function of the number of required tasks per period and, depending on the application, can have extremely high variance
Much has been written about the first option, there is a noticeable absence in the literature when it comes to analyzing different break regulations, especially in the context of tour scheduling
Since the need for break assignments is common in many shift and tour scheduling problems, we classify and analyze the complexity of various break assignment problem (BAP) found in the lit
Summary
In most personnel scheduling problems, workforce demand is a function of the number of required tasks per period and, depending on the application, can have extremely high variance. Ground handling as well as many other personnel scheduling problems requires the explicit assignment of shifts and days off to individual employees rather than to a generic workforce. For applications where breaks are assigned dynamically over the day, e.g., for fast food, ground handling, and mail processing operations, the decomposition approach provides an upper bound on costs In such environments, the break assignment model can be used in a rolling horizon manner to support reactive planning. A heuristic decomposition procedure for scheduling a hierarchical workforce that can accommodate all permissible break placements in a shift (the heuristic supports reactive planning of breaks in response to unforeseen changes in hourly demand) that has successfully been applied at a major European ground handling service company. We close with some insights and observations on the proposed methodology
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