برنامه ریزی عملی برای عملیات های مرکز تماس

A practical spreadsheet-based scheduling method is developed to determine the optimal allocation of service agents to candidate tour types and start times in an inbound call center. A stationary Markovian queueing model with customer abandonment is employed to determine required staffing levels for a sequence of time intervals with varying call volumes, handling times, and relative agent availabilities. These staffing requirements populate a quadratic programming model for determining the distribution of agent tours that will maximize the fraction of offered calls beginning service within a target response time, subject to side constraints on tour type quantities. The optimal distribution is scaled to reflect the total number of scheduled agents, and a near-optimal integer solution is derived using rounding thresholds found by successive one-dimensional searches. This novel approach has been successfully implemented in large service centers at Qwest Communications and could easily be adapted to other operational environments.

Many commercial enterprises and public agencies operate centralized call centers to provide effective and responsive service for patrons. Mandelbaum [1] estimates that there are as many as 200,000 separate call centers operating in the United States, employing up to 4% of the national workforce (more than the entire agricultural sector). About 70% of the operating cost of a typical call center is attributable to personnel expense, so the economic efficiency of the operation is determined primarily by the quality of the employee scheduling process. For inbound call centers, the scheduling problem is normally characterized by a highly variable demand pattern and a requirement to assign service agents to “tours” that are constrained by labor rules. The fundamental problem is to schedule tours such that resulting time-varying staff quantities maximize the service level, or achieve a target service level at minimum cost. Efficient management of a modern call center involves decision making (and supporting modeling and analysis) on three primary time horizons: annual planning, monthly (or quarterly) scheduling, and daily execution. Annual planning deals with strategic concerns such as forecasting long-term call volume trends and associated personnel requirements, managing an employee replacement pipeline, planning for volume seasonality, and conducting an annual vacation bid. Daily execution encompasses tactical matters such as consideration of schedule change requests, monitoring of schedule compliance and center performance metrics, and responding to unpredicted fluctuations in call volume by offering discretionary time-off or overtime to appropriate agents. This article focuses on monthly scheduling, which involves confirming forecast volume and total staff quantities, adjusting for nonproductive activity requirements (estimating agent “availability”), creating a schedule, and then populating the schedule with particular employees based on seniority and preferences. We are specifically concerned with the technical task of creating an optimal schedule, which is derived as an optimal quantification of tours by type and start time. The importance of the call center scheduling problem is indicated by a large and growing body of relevant literature. Gans et al. [2] present a cogent overview, and Mandelbaum [3] provides a comprehensive bibliography. Reported application areas include retail sales [4], transportation [5], public services [6], and the telecommunications industry [7] and [8]. Solution approaches have incorporated diverse management science methods such as mathematical programming [9] and [10], analytical queueing models [11], simulation [12], dynamic programming [13], genetic algorithms [14], and other heuristic procedures [15]. Brigandi et al. [16] document deployment of a call center modeling system that delivered $750 million in increased annual profits for a diverse set of client enterprises. The system relied on simulation as the primary modeling tool, but employed queueing models to calculate staffing requirements and a network flow approach to determine workforce schedules. In this article, we apply queueing theory, quadratic programming, and a one-dimensional search algorithm to derive and evaluate optimal schedules, all within a practical spreadsheet implementation.

We have integrated queueing theory, quadratic programming, and a variable-threshold rounding algorithm to develop a practical, spreadsheet-based model for call center scheduling. The model has been successfully implemented in several repair service centers at Qwest Communications, resulting in substantial cost reductions and near elimination of service level target misses. With the new approach, we observe a 15–20% reduction in personnel requirements from those produced by previous scheduling methods. For some centers, the model has been expanded to accommodate additional tour types and varying operational practices. Hence, our experience suggests that the approach is quite flexible and could be applied to myriad call center environments including other repair services, product delivery, public services, and retail sales.