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Call Center Scheduling


Problem Description

Managers of service establishments, where the timing of customer demands for service is random and cyclic, commonly adjust staffing levels in an attempt to provide a uniform level of service at all times. Examples include staffing of toll plazas, airline ground services, tele-retailing, banking, telecommunications, hospitals, police patrol, and newspapers. The 800 telephone number call centers that increasingly provide a diversity of customer service and marketing functions are systems for which such staffing issues are important.

Modelling & Computational Challenges

Developing specific staffing schedules in such service systems can also be difficult, since implementations must take into account complex scheduling constraints. These include honoring employees' preferred start times, quitting times and shift lengths, adhering to legal or policy limits on the number of consecutive hours and/or days worked, restricting the patterns of days off and on duty, providing required lunch and coffee breaks, and the like. Good schedules must also reflect the economic tradeoffs that arise from shift-pay differentials, part-time pay, and overtime. A fundamental requirement is that there be enough staff on duty at all times to meet targeted service levels.

In applications described in the literature, these staffing requirements are typically determined by first dividing the workday or workweek into ''planning periods'' such as shifts, hours, quarter-hours, etc.. Then, a series of stationary queueuing models, most often M/M/S type models, is constructed, one model for each planning period. Each of these models is independently solved for the minimum number of servers needed to meet the service target in that period. We call this method of setting staffing the stationary independent period by period (SIPP) approach. The period by period staffing requirements so derived are then used to set actual workforce schedules. In some businesses, managers do this heuristically while in others these staffing requirements become the right-hand-sides of key constraints in a large optimization model that derives the actual staffing schedule.

Research at LCM

Our research evaluates the practice of the SIPP approach. Despite its very widespread use, there is reason to suspect that the SIPP approach does not always work well.  We consider Markovian queueing models with sinusoidal arrival rates and use numerical methods to evaluate this practice for parameter values corresponding to many real situations. Specifically, using the SIPP approach can result in staffing levels that do not meet specified period by period probability of delay targets during a significant fraction of the cycle. We determine the manner in which the various system parameters affect SIPP reliability and identify domains for which SIPP will be accurate. After exploring several alternatives, we propose two simple modifications of SIPP that will produce reliable staffing levels in models whose parameters span a broad range of practical situations. Our conclusions from the sinusoidal model are also tested against empirical data.

Currently, we are exploiting the usage of optimization techniques in combination with nonstationary Markovian queueing models as descriptive models for real situations that arise in the staffing of call centers and emergency departments in hospitals.

Papers & Reports

  • [1] L. Green, P. Kolesar, and J. Soares, An improved heuristic for staffing telephone call center centers with limited operating hours, Production and Operations Management, 12 (2003) 46-61
  • [2] L. Green, P. Kolesar, and J. Soares, Improving the SIPP approach for staffing service systems that have cyclic demands, Operations Research, 49 (2003) 549-564
  • [3] L. Green and J. Soares, Computing time dependent waiting time probabilities in M(t)/M/s(t) queueing systems, Manufacturing and Services Operations Management, 9(1) (2007) 54-61
  • [4] L. Green, J. Giulio, R. Green, and J. Soares, Using queueing theory to increase the effectiveness of physician staffing in the emergency department, Academic Emergency Medicine, 13(1) (2006) 61-68

Project Team

  • João Soares, LCM/CMUC
  • Linda Green, Columbia University