Managing Supply in the On-Demand Economy: Flexible Workers, Full-Time Employees, or Both?

There are different workforce models in the "gig" economy. While some on-demand service providers rely strictly on either traditional employees or independent contractors, others rely on a blended workforce which melds a layer of contingent workers with a core of permanent employees. In deciding on the "right number of right people to staff at the right time", managers must appropriately weigh the pertinent tradeoffs. In this paper, we study cost-minimizing staffing decisions in service systems where the manager must decide on how many flexible (contractors) and/or fixed (full-time) agents to staff in order to effectively balance operating costs, varying customer demand patterns, and supply-side uncertainty, while not compromising on the quality of service offered to customers. We consider a queueing-theoretic framework where the number of servers is random because part of the workforce is flexible. Since the staffing problem with a random number of servers is analytically intractable, we formulate two problem relaxations, based on fluid and stochastic-fluid formulations, and establish their accuracies in large systems by relying on an asymptotic, many-server, mode of analysis. We derive the optimal staffing policy and glean insights into the appropriateness of alternative workforce models in on-demand services. We also shed light on the distinction between demand-side (customer arrival rates) and supply-side (number of servers) uncertainties in queueing systems

Fluid Approximation of a Call Center Model with Redials and Reconnects

In many call centers, callers may call multiple times. Some of the calls are re-attempts after abandonments (redials), and some are re-attempts after connected calls (reconnects). The combination of redials and reconnects has not been considered when making staffing decisions, while ignoring them will inevitably lead to under- or overestimation of call volumes, which results in improper and hence costly staffing decisions. Motivated by this, in this paper we study call centers where customers can abandon, and abandoned customers may redial, and when a customer finishes his conversation with an agent, he may reconnect. We use a fluid model to derive first order approximations for the number of customers in the redial and reconnect orbits in the heavy traffic. We show that the fluid limit of such a model is the unique solution to a system of three differential equations. Furthermore, we use the fluid limit to calculate the expected total arrival rate, which is then given as an input to the Erlang A model for the purpose of calculating service levels and abandonment rates. The performance of such a procedure is validated in the case of single intervals as well as multiple intervals with changing parameters

Optimizing Equitable Resource Allocation in Parallel Any-Scale Queues with Service Abandonment and its Application to Liver Transplant

We study the problem of equitably and efficiently allocating an arriving resource to multiple queues with customer abandonment. The problem is motivated by the cadaveric liver allocation system of the United States, which includes a large number of small-scale (in terms of yearly arrival intensities) patient waitlists with the possibility of patients abandoning (due to death) until the required service is completed (matched donor liver arrives). We model each waitlist as a GI/MI/1+GI queue, in which a virtual server receives a donor liver for the patient at the top of the waitlist, and patients may abandon while waiting or during service. To evaluate the performance of each queue, we develop a finite approximation technique as an alternative to fluid or diffusion approximations, which are inaccurate unless the queue's arrival intensity is large. This finite approximation for hundreds of queues is used within an optimization model to optimally allocate donor livers to each waitlist. A piecewise linear approximation of the optimization model is shown to provide the desired accuracy. Computational results show that solutions obtained in this way provide greater flexibility, and improve system performance when compared to solutions from the fluid models. Importantly, we find that appropriately increasing the proportion of livers allocated to waitlists with small scales or high mortality risks improves the allocation equity. This suggests a proportionately greater allocation of organs to smaller transplant centers and/or those with more vulnerable populations in an allocation policy. While our motivation is from liver allocation, the solution approach developed in this paper is applicable in other operational contexts with similar modeling frameworks.Comment: 48 Page

Estimation and monitoring of traffic intensities with application to control of stochastic systems

Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/106982/1/asmb1961.pd

Asymptotic Analysis of Service Systems with Congestion-Sensitive Customers

Many systems in services, manufacturing, and technology, feature users or customers sharing a limited number of resources, and which suffer some form of congestion when the number of users exceeds the number of resources. In such settings, queueing models are a common tool for describing the dynamics of the system and quantifying the congestion that results from the aggregated effects of individuals joining and leaving the system. Additionally, the customers themselves may be sensitive to congestion and react to the performance of the system, creating feedback and interaction between individual customer behavior and aggregate system dynamics.This dissertation focuses on the modeling and performance of service systems with congestion-sensitive customers using large-scale asymptotic analyses of queueing models. This work extends the theoretical literature on congestion-sensitive customers in queues in the settings of service differentiation and observational learning and abandonment. Chapter 2 considers the problem of a service provider facing a heterogeneous market of customers who differ based on their value for service and delay sensitivity. The service provider seeks to find the revenue maximizing level of service differentiation (offering different price-delay combinations). We show that the optimal policy places the system in heavy traffic, but at substantially different levels of congestion depending on the degree of service differentiation. Moreover, in a differentiated offering, the level of congestion will vary substantially between service classes. Chapter 3 presents a new model of customer abandonment in which congestion-sensitive customers observe the queue length, but do not know the service rate. Instead, they join the queue and observe their progress in order to estimate their wait times and make abandonment decisions. We show that an overloaded queue with observational learning and abandonment stabilizes at a queue length whose scale depends on the tail of the service time distribution. Methodologically, our asymptotic approach leverages stochastic limit theory to provide simple and intuitive results for optimizing or characterizing system performance. In particular, we use the analysis of deterministic fluid-type queues to provide a first-order characterization of the stochastic system dynamics, which is demonstrated by the convergence of the stochastic system to the fluid model. This also allows us to crisply illustrate and quantify the relative contributions of system or customer characteristics to overall system performance