Dynamic Scheduling in a Many-Server, Multiclass System: The Role of Customer Impatience in Large Systems

Abstract

Problem definition: We study optimal scheduling of customers in service systems, such as call centers. In such systems, customers typically hang up and abandon the system if their wait for service is too long. Such abandonments are detrimental for the system, and so managers typically use scheduling as a tool to mitigate it. In this paper, we study the interplay between customer impatience and scheduling decisions when managing heterogeneous customer classes. Academic/practical relevance: Call centers constitute a large industry that has a global spending of around $300 billion and employs more than 15 million people worldwide. Our work focuses on improving call center operations, which can reduce costs and improve customer satisfaction. Mathematically, customer patience is typically modeled as exponentially distributed for tractability. Our work makes inroads into relaxing this restrictive assumption to allow modeling more realistic call center situations. Methodology: We use heavy traffic-motivated asymptotic queueing machinery that provides us the traction to successfully capture and incorporate the customer impatience distribution into the scheduling problem. In our approach, the scheduling problem reduces to a diffusion control problem, which we solve to propose near-optimal scheduling policies. Results: We propose near-optimal scheduling policies that can be implemented by call centers to improve their quality-of-service metrics. One of our main results is that, for a class of parameters, we establish sufficient conditions for both the optimality and nonoptimality of threshold policies. Managerial implications: Threshold policies are widely used for scheduling. Our work provides additional insight into whether these may be suboptimal. Our work provides an easy-to-implement alternative that can reduce customer abandonments considerably; for instance, our numerical results indicate that for a system with two customer types, the abandonment rate of one class can be lowered by 30% by using our policy relative to the best threshold policy.

Admission Control for a Capacitated Supply System with Real-Time Replenishment Information

“…The admission policy determined in the context with customers who will wait till fulfilled may not be suitable for the case where customers are of limited patience. Admission control with impatient customers in applications such as call centers have been well studied in the field of queuing theory (Ward and Kumar, 2008;Kim et al, 2018). In the field of inventory control, customers' impatience arises when backordered customers turn to other sources of supply.…”

Scheduling with Service-Time Information: The Power of Two Priority Classes

“…For example, [15] recently establish the optimality of SRPT for multi-server queues in the conventional heavy-traffic regime. In many-server heavy-traffic regime where the number of servers is sent to infinity with the arrival rate, the asymptotic optimality of cµ-type of scheduling policies may no longer hold (see, e.g., [18,19]).…”

Analysis of Complex Dynamics in Different Bargaining Systems

“…Guo et al [17] applied typical dynamic equilibrium algorithms such as the simplex gravity flow dynamics and the projected dynamical system to study the dynamic traffic equilibrium problem. Kim et al [18] studied dynamic scheduling in a service system of multilevel. Ajorlou et al [19] analyzed the optimal dynamical pricing problem in which the information of products can only be spread via words of mouth.…”