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

An Integrated Approach to Seismic Event Location: 1. Evaluating How Method of Location Affects the Volume of Groups of Hypocenters

When seismic events occur in spatially compact clusters, the volume and geometric characteristics of these clusters often provides information about the relative effectiveness of different location methods, or about physical processes occurring within the hypocentral region. This report defines and explains how to determine the convex polyhedron of minimum volume (CPMV) surrounding a set of points. We evaluate both single-event and joint hypocenter determination (JHD) relocations for three rather different clusters of seismic events: 1) nuclear explosions from Mururoa relocated using P and PKP phases reported by the ISC, 2) intermediate depth earthquakes near Bucaramanga, Colombia, relocated using P and PKP phases reported by the ISC, and 3) shallow earthquakes near Vanuatu (formerly, the New Hebrides), relocated using P and S phases from a local station network. This analysis demonstrates that different location methods markedly affect the volume of the CPMV, however, volumes for JHD relations are �not always smaller than volumes for single-event relocations.Phillips Laboratory, Directorate of Geophysics, Air Force Material Command, Hanscom Air Force Base, MassachusettsInstitute for Geophysic

Rare-event analysis of mixed Poisson random variables, and applications in staffing

A common assumption when modeling queuing systems is that arrivals behave like a Poisson process with constant parameter. In practice, however, call arrivals are often observed to be significantly overdispersed. This motivates that in this paper we consider a mixed Poisson arrival process with arrival rates that are resampled every $N^{a}$ time units, where $a> 0$ and $N$ a scaling parameter. In the first part of the paper we analyse the asymptotic tail distribution of this doubly stochastic arrival process. That is, for large $N$ and i.i.d. arrival rates $X_1, \dots, X_N$, we focus on the evaluation of $P_N(A)$, the probability that the scaled number of arrivals exceeds $NA$. Relying on elementary techniques, we derive the exact asymptotics of $P_N(A)$: For $a 3$ we identify (in closed-form) a function $\tilde{P}_N(A)$ such that $P_N(A) / P_N(A)$ tends to $1$ as $N \to \infty$. For $a \in [\frac{1}{3},\frac{1}{2})$ and $a\in [2, 3)$ we find a partial solution in terms of an asymptotic lower bound. For the special case that the $X_i$s are gamma distributed, we establish the exact asymptotics across all $a> 0$. In addition, we set up an asymptotically efficient importance sampling procedure that produces reliable estimates at low computational cost. The second part of the paper considers an infinite-server queue assumed to be fed by such a mixed Poisson arrival process. Applying a scaling similar to the one in the definition of $P_N(A)$, we focus on the asymptotics of the probability that the number of clients in the system exceeds $NA$. The resulting approximations can be useful in the context of staffing. Our numerical experiments show that, astoundingly, the required staffing level can actually decrease when service times are more variable

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

Routing and Staffing when Servers are Strategic

Traditionally, research focusing on the design of routing and staffing policies for service systems has modeled servers as having fixed (possibly heterogeneous) service rates. However, service systems are generally staffed by people. Furthermore, people respond to workload incentives; that is, how hard a person works can depend both on how much work there is, and how the work is divided between the people responsible for it. In a service system, the routing and staffing policies control such workload incentives; and so the rate servers work will be impacted by the system's routing and staffing policies. This observation has consequences when modeling service system performance, and our objective is to investigate those consequences. We do this in the context of the M/M/N queue, which is the canonical model for large service systems. First, we present a model for "strategic" servers that choose their service rate in order to maximize a trade-off between an "effort cost", which captures the idea that servers exert more effort when working at a faster rate, and a "value of idleness", which assumes that servers value having idle time. Next, we characterize the symmetric Nash equilibrium service rate under any routing policy that routes based on the server idle time. We find that the system must operate in a quality-driven regime, in which servers have idle time, in order for an equilibrium to exist, which implies that the staffing must have a first-order term that strictly exceeds that of the common square-root staffing policy. Then, within the class of policies that admit an equilibrium, we (asymptotically) solve the problem of minimizing the total cost, when there are linear staffing costs and linear waiting costs. Finally, we end by exploring the question of whether routing policies that are based on the service rate, instead of the server idle time, can improve system performance.Comment: First submitted for journal publication in 2014; accepted for publication in Operations Research in 2016. Presented in select conferences throughout 201

Using SIMCTS framework to model determinants of customer satisfaction: a case in an ISP

In this paper we describe a call center simulation case study that uses real data obtained from an Internet Service Provider (ISP). The case study is conducted using SIMCTS (Simulation Modelling and Analysis of Customer Satisfaction Patterns for Telecommunication Service Providers) framework [25]. The applicability of this framework to model ISP business scenario is discussed in detail. The simulation case study reveal that the dimensions of service quality have huge impact on customer satisfaction and also provide valuable insight in to gap analysis of customer perception and expectation. Various key satisfaction variables in relation to call center are modelled using SIMAN simulation language and ARENA simulation software. The simulation case study investigates service quality dimension, technical (or) functional service quality and their role in evaluation of overall satisfaction judgment. The simulation model collects transient performance measures which can be used to make competitive marketing decisions

Parameter Tolerance in Capacity Planning Models

In capacity planning for a service operation, analytical models based on queueing theory allow the user to quickly estimate the capacity required and to easily experiment with different system designs or configurations, for a given set of input parameters. An input parameter of the model could be inaccurate or may not be known beyond a good guess. In order to determine if the analysis results (and hence the system design) are robust to parameter estimation errors, sensitivity analysis can be performed. We study an alternative approach that involves specifying a tolerance range of a system performance measure and calculating a feasible region of the uncertain parameters for which the performance measure will be within the tolerance range. We illustrate this approach using basic exponential queueing models as well as a model of an order fulfillment operation in a distribution center

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).