Study On The Problem Of Labor Force Planning For Multi-skill Call Centers

Call centers is becoming an indispensable part in daily life. As an effective way toenhance competence, it is widely used in business, and to this end, call centers mustprovide high-quality service, which means enough agents are needed to guarantee thatmost calls get service in a short period of time. On the other hand, however, labor costusually accounts for over 60% of the total cost, and call centers should schedule asfew agents as possible in order to save cost and achieve high utilization rate.Therefore, the study of how to utilize the labor force efficiently is of great importancefor call centers.The labor force planning problem for call centers is generally solved in 3 steps: 1)forecast the call volume; 2) calculate the agent-shifts needed; 3) work out theschedule for the agents. This dissertation focuses on the problems introduced in the2nd step, which we refer to as scheduling problem.Earlier call centers mostly were single-skill call centers (SSCC), which providesingle service. But more and more enterprises start to provide various services. As aconsequence, nowadays most call centers are multi-skill call centers (MSCC). Varietyof skills induces the problem of routing.This dissertation is about the research we did on the scheduling and routingproblem for MSCC.1) SchedulingThe complexity of the scheduling problem relies largely on the number of skillsof the call centers. For SSCC, the scheduling problem is simpler, whose research has along history, and fruitful results have already been obtained. For MSCC, the diversityof skills leads to the diversity of agents, which makes the scheduling problem muchharder to attack. The diversity of agents creates new dimension for the problem: thenumber of each kind of agents needs to be solved. The diversity both of agents and ofskills introduces the problem of routing. The effect of routing policy has to beconsidered while solving the scheduling problem. The research on this topic is just inits primitive stage, and only limited results have been obtained.Two models for the MSCC scheduling problem are proposed in this dissertation:the Divide Scheduling Model and the Polyhedral Set Approximation Model. In eachperiod, the time a multi-skill agent spends on each skill varies according to the variation of factors like call load and the composition of working staff. Based on thisobservation, in the Divide Scheduling Model a multi-skill agent is decomposed into a(convex) combination of single-skill agents, which varies at each period. In this way,the flexibility of a multi-skill agent is fully taken advantage of. The Polyhedral SetApproximation Model studies the problem from a quite different angle. For eachperiod, there exists a set of feasible solutions. Although it is usually not practical tofind the set, yet it is possible to construct some simpler sets to approximate it.Polyhedral set is one of them.The two proposed models take the same approach to handle the routing problem.An approximation is found first, without taking into consideration the routing policies,which is hard to analyze. The approximation is then verified via simulation, andadjustment is done according to the result. If the approximation is close to theoptimum, fewer times of simulation are needed to arrive at a good solution.2) RoutingThe routing problem is a newly-introduced problem for MSCC. It is divided intotwo parts: agent selection problem and call selection problem. The former decideswhich agent is supposed to handle the newly-arrived call while the latter picks thenext call to be handled from the waiting queue for the agent who has just finishedhis/her current task. Under certain circumstances, the routing policy has a huge impacton the scheduling problem, especially when the number of agents is close to theminimum required for the specified service level. Efficient routing policy leads tohigh utilization rate. Overflow routing policy is the one often used in practice. Itassigns different priorities to different candidates of routing and always selects theone with the highest priority.This dissertation presents a preliminary discussion on the problem of overflowrouting. We studied the problem with the help of simulation and proposed severaldynamic routing policies. Some part of the system status is considered by the policies.This dissertation brings new ideas to the literature, including:1) Two new models for scheduling. The Divide Scheduling Model is used inpractice after optimization. We believe that the Polyhedral Set Approximation Modelis also a practical model because of its lower and tunable complexity.2) A new approach for scheduling. All the current scheduling models takerouting policy as an input. The proposed Divide Scheduling Model takes a newapproach, the intermedia result obtained by the model contains information of how to divide multi-skill agents, which is very instructive for designing the routing policy.3) Dynamic overflow routing policies. We found that the CS policy has a muchgreater impact for the service level than the AS policy. We also proposed severaldynamic routing policies.