Optimal Models for Meal-Break and Start-Time Flexibility in Continuous Tour Scheduling

Abstract

This paper presents a compact integer-programming model for large-scale continuous tour scheduling problems that incorporate meal-break window, start-time band, and start-time interval policies. For practical scheduling environments, generalized set-covering formulations (GSCFs) of such problems often contain hundreds of millions of integer decision variables, usually precluding identification of optimal solutions. As an alternative, we present an implicit integer-programming model that frequently has fewer than 1,500 variables and can be formulated and solved using PC-based hardware and software platforms. An empirical study using labor-requirement distributions for customer service representatives at a Motorola, Inc. call center was used to demonstrate the importance of having a model that can evaluate tradeoffs among the various scheduling policies.integer programming, implicit formulation, workforce scheduling

Telephone Call Centers: Tutorial, Review, and Research Prospects

“…For example, Aykin (1996) and Brusco and Jacobs (2000) define two sets of variables: The first defines the start time and duration of shifts; and the second defines possible break times. Additional constraints are then used to define which break times are feasible for what shifts.…”

The Impact of Scheduling and Bundling Flexibility on Sequence Effect-Based Schedules

“…Flexibility as a research question has been investigated within the context of labor scheduling, for example: start time of breaks (Bechtold & Jacobs, 1990;Brusco & Jacobs, 2000), employee cross training and resource flexibility (Daniels, Hoopes, & Mazzola, 1996;Daniels, Mazzola, & Shi, 2004;Daniels & Mazzola, 1994;Iravani, Oyen, & Sims, 2005),and using part-time workers (Mabert & Showalter, 1990).…”

A branch-and-price approach for large-scale employee tour scheduling problems

“…As another example, shifts of a tour may be allowed to start at different times each day as long as workers have enough rest time between consecutive shifts (Brusco and Jacobs 2000;Cezik et al 2001; Bard et al 2003). For an organization, it is crucial to make best use of such flexibilities to produce feasible schedules that minimize the labor cost.…”

“…Jacobs and Brusco (1996), and Brusco and Jacobs (1998) introduced overlapping start time bands and constraints limiting the number of periods where shifts can start. Later, Brusco and Jacobs (2000) combined these two models to produce the most comprehensive implicit model for continuous scenarios (24 hours per day, 7 days a week) with only one tour type. A tour type is defined by a pair of parameters [a, b] where a is the number of shifts in the tour and b is the number of periods in each shift (Mabert and Showalter 1988).…”

“…A tour type is defined by a pair of parameters [a, b] where a is the number of shifts in the tour and b is the number of periods in each shift (Mabert and Showalter 1988). Recently, Isken (2004) developed an implicit model that complements the approach of Brusco and Jacobs (2000) by allowing tours of different types.…”