Statistical and Economic Evaluation of Time Series Models for Forecasting Arrivals at Call Centers

Call centers' managers are interested in obtaining accurate point and distributional forecasts of call arrivals in order to achieve an optimal balance between service quality and operating costs. We present a strategy for selecting forecast models of call arrivals which is based on three pillars: (i) flexibility of the loss function; (ii) statistical evaluation of forecast accuracy; (iii) economic evaluation of forecast performance using money metrics. We implement fourteen time series models and seven forecast combination schemes on three series of daily call arrivals. Although we focus mainly on point forecasts, we also analyze density forecast evaluation. We show that second moments modeling is important both for point and density forecasting and that the simple Seasonal Random Walk model is always outperformed by more general specifications. Our results suggest that call center managers should invest in the use of forecast models which describe both first and second moments of call arrivals

Statistical Analysis of a Telephone Call Center: A Queueing-Science Perspective

A call center is a service network in which agents provide telephone-based services. Customers that seek these services are delayed in tele-queues. This paper summarizes an analysis of a unique record of call center operations. The data comprise a complete operational history of a small banking call center, call by call, over a full year. Taking the perspective of queueing theory, we decompose the service process into three fundamental components: arrivals, customer abandonment behavior and service durations. Each component involves different basic mathematical structures and requires a different style of statistical analysis. Some of the key empirical results are sketched, along with descriptions of the varied techniques required. Several statistical techniques are developed for analysis of the basic components. One of these is a test that a point process is a Poisson process. Another involves estimation of the mean function in a nonparametric regression with lognormal errors. A new graphical technique is introduced for nonparametric hazard rate estimation with censored data. Models are developed and implemented for forecasting of Poisson arrival rates. We then survey how the characteristics deduced from the statistical analyses form the building blocks for theoretically interesting and practically useful mathematical models for call center operations. Key Words: call centers, queueing theory, lognormal distribution, inhomogeneous Poisson process, censored data, human patience, prediction of Poisson rates, Khintchine-Pollaczek formula, service times, arrival rate, abandonment rate, multiserver queues.

Ambulance Emergency Response Optimization in Developing Countries

The lack of emergency medical transportation is viewed as the main barrier to the access of emergency medical care in low and middle-income countries (LMICs). In this paper, we present a robust optimization approach to optimize both the location and routing of emergency response vehicles, accounting for uncertainty in travel times and spatial demand characteristic of LMICs. We traveled to Dhaka, Bangladesh, the sixth largest and third most densely populated city in the world, to conduct field research resulting in the collection of two unique datasets that inform our approach. This data is leveraged to develop machine learning methodologies to estimate demand for emergency medical services in a LMIC setting and to predict the travel time between any two locations in the road network for different times of day and days of the week. We combine our robust optimization and machine learning frameworks with real data to provide an in-depth investigation into three policy-related questions. First, we demonstrate that outpost locations optimized for weekday rush hour lead to good performance for all times of day and days of the week. Second, we find that significant improvements in emergency response times can be achieved by re-locating a small number of outposts and that the performance of the current system could be replicated using only 30% of the resources. Lastly, we show that a fleet of small motorcycle-based ambulances has the potential to significantly outperform traditional ambulance vans. In particular, they are able to capture three times more demand while reducing the median response time by 42% due to increased routing flexibility offered by nimble vehicles on a larger road network. Our results provide practical insights for emergency response optimization that can be leveraged by hospital-based and private ambulance providers in Dhaka and other urban centers in LMICs

A regret model applied to the maximum coverage location problem with queue discipline

This article discusses issues related to the location and allocation problems where is intended to demonstrate, through the random number generation, the influence of congestion of such systems in the final solutions. It is presented an algorithm that, in addition to the GRASP, incorporates the Regret with the pminmax method to evaluate the heuristic solution obtained in regard to its robustness for different scenarios. To the well know Maximum Coverage Location Problem from Church and Revelle [1] an alternative perspective is added in which the choice behavior of the server does not only depend on the elapsed time from the demand point looking to the center, but also includes the waiting time for service conditioned by a waiting queue.N/

The Impact of Information Technology on Emergency Health Care Outcomes

This paper analyzes the productivity of technology and job design in emergency response systems, or 911 systems.' During the 1990s, many 911 systems adopted Enhanced 911' (E911), where information technology is used to link automatic caller identification to a database of address and location information. A potential benefit to E911 is improved timeliness of the emergency response. We evaluate the returns to E911 in the context of a panel dataset of Pennsylvania counties during 1994-1996, when almost half of the 67 counties experienced a change in technology. We measure productivity using an index of health status of cardiac patients at the time of ambulance arrival, where the index should be improved by timely response. We also consider the direct effect of E911 on several patient outcomes, including mortality within the first hours following the incident and the total hospital charges incurred by the patient. Our main finding is that E911 increases the short-term survival rates for patients with cardiac diagnoses by about 1%, from a level of 96.2%. We also provide evidence that E911 reduces hospital charges. Finally, we analyze the effect of job design, in particular the use of Emergency Medical Dispatching' (EMD), where call-takers gather medical information, provide medical instructions over the telephone, and prioritize the allocation of ambulance and paramedic services. Controlling for EMD adoption does not affect our results about E911, and we find that EMD and E911 do not have significant interactions in determining outcomes (that is, they are neither substitutes nor complements).

A regret model applied to the maximum capture location problem

This article addresses issues related to location and allocation problems. Herein, we intend to demonstrate the influence of congestion, through the random number generation, of such systems in final solutions. An algorithm is presented which, in addition to the GRASP, incorporates the Regret with the pminmax method to evaluate the heuristic solution obtained with regard to its robustness for different scenarios. Taking as our point of departure the Maximum Capture Location Problem proposed by Church and Revelle [1, 26], an alternative perspective is added in which the choice behavior of the server does not depend only on the elapsed time from the demand point looking to the center, but includes also the service waiting time.N/

A Simulation of the ECSS Help Desk with the Erlang A Model

During steady states, the Level 1 help desk might expect about 500 to 600 calls per month. That is about 0.39 to 0.46 calls per user per month, which represents the workload once ECSS is established and most of the users have already received training for the system. The optimal level for this workload is about 12 agents to operate the entire 24 hour period. At this level, the Level 1 help desk would minimize the amount of customers that renege from the system to about 15 to 22 percent and still maintain acceptable utilization percentages of about 52% to 59% while keeping the average wait time under a minute. The Level 2 help desk will experience similar environments like the Level 1 help desk. The major differences are that the Level 2 help desk would see lower call volumes since only about 40% of Level 1 calls are passed on the Level 2; and that the Level 2 help desk will have a longer average service rate. The simulation shows that the optimal staffing level is about 12. The simulation shows average wait times about 1 to 2.6 minutes, utilization from 47% to 60%, and 12% to 33% of customers that would renege