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<p>Many types of services are provided using some equipment or machines, e.g. transportation systems using vehicles. Designs of these systems require capacity decisions, e.g., the number of vehicles. In my dissertation, I use many-server and conventional heavy-traffic limit theory to derive asymptotically optimal capacity decisions, giving the desired level of delay and availability performance with minimum investment. The results provide near-optimal solutions and insights to otherwise analytically intractable problems.</p> <p>The dissertation will comprise two essays. In the first essay, &ldquoAsymptotic Analysis of Delay-based Performance Metrics and Optimal Capacity Decisions for the Machine Repair Problem with Spares,&rdquo I study the M/M/R machine repair problem with spares. This system can be represented by a closed queuing network. Applications include fleet vehicles' repair and backup capacity, warranty services' staffing and spare items investment decisions. For these types of systems, customer satisfaction is essential; thus, the delays until replacements of broken units are even more important than delays until the repair initiations of the units. Moreover, the service contract may include conditions on not only the fill rate but also the probability of acceptable delay (delay being less than a specified threshold value).</p> <p>I address these concerns by expressing delays in terms of the broken-machines process; scaling this process by the number of required operating machines (or the number of customers in the system); and using many-server limit theorems (limits taken as the number of customers goes to infinity) to obtain the limiting expected delay and probability of acceptable delay for both delay until replacement and repair initiation. These results lead to an approximate optimization problem to decide on the repair and backup-capacity investment giving the minimum expected cost rate, subject to a constraint on the acceptable delay probability. Using the characteristics of the scaled broken-machines process, we obtain insights about the relationship between quality of service and capacity decisions. Inspired by the call-center literature, we categorize capacity level choice as efficiency-driven, quality-driven, or quality- and efficiency-driven. Hence, our study extends the conventional call center staffing problem to joint staffing and backup provisioning. Moreover, to our knowledge, the machine-repair problem literature has focused mainly on mean and fill rate measures of performance for steady-state cost analysis. This approach provides complex, nonlinear expressions not possible to solve analytically. The contribution of this essay to the machine-repair literature is the construction of delay-distribution approximations and a near-optimal analytical solution. Among the interesting results, we find that for capacity levels leading to very high utilization of both spares and repair capacity, the limiting distribution of delay until replacement depends on one type of resource only, the repair capacity investment.</p> <p>In the second essay, &ldquoDiffusion Approximations and Near-Optimal Design of a Make-to-Stock Queue with Perishable Goods and Impatient Customers,&rdquo I study a make-to-stock system with perishable inventory and impatient customers as a two-sided queue with abandonment from both sides. This model describes many consumer goods, where not only spoilage but also theft and damage can occur. We will refer to positive jobs as individual products on the shelf and negative jobs as backlogged customers. In this sense, an arriving negative job provides the service to a waiting positive job, and vice versa. Jobs that must wait in queue before potential matching are subject to abandonment. Under certain assumptions on the magnitude of the abandonment rates and the scaled difference between the two arrival rates (products and customers), we suggest approximations to the system dynamics such as average inventory, backorders, and fill rate via conventional heavy traffic limit theory.</p> <p>We find that the approximate limiting queue length distribution is a normalized weighted average of two truncated normal distributions and then extend our results to analyze make-to-stock queues with/without perishability and limiting inventory space by inducing thresholds on the production (positive) side of the queue. Finally, we develop conjectures for the queue-length distribution for a non-Markovian system with general arrival streams. We take production rate as the decision variable and suggest near-optimal solutions.</p> / Dissertation

Submitted by Izabel Franco (izabel-franco@ufscar.br) on 2016-10-26T17:09:15Z No. of bitstreams: 1 TeseSCF.pdf: 10747360 bytes, checksum: 8a9b640ece219d76af8f66468c70af0a (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-11-08T18:25:43Z (GMT) No. of bitstreams: 1 TeseSCF.pdf: 10747360 bytes, checksum: 8a9b640ece219d76af8f66468c70af0a (MD5) / Approved for entry into archive by Marina Freitas (marinapf@ufscar.br) on 2016-11-08T18:25:51Z (GMT) No. of bitstreams: 1 TeseSCF.pdf: 10747360 bytes, checksum: 8a9b640ece219d76af8f66468c70af0a (MD5) / Made available in DSpace on 2016-11-08T18:25:59Z (GMT). No. of bitstreams: 1 TeseSCF.pdf: 10747360 bytes, checksum: 8a9b640ece219d76af8f66468c70af0a (MD5) Previous issue date: 2016-06-22 / Não recebi financiamento / This work deals with the analysis of queueing systems for Call Centers regarding the possibility of the customer abandon the system before being served, due to his/her impatience. The Call Centers are service organizations that predominantly serve customers by phone calls and are considered a particular kind of Contact Centers that serve their costumers through phone, fax, e-mail, chat, mobile devices and other communication channels. From a business point of view, the main concern on the management of the Call Center is the offer quality service with minimum cost. The perception of the quality of services offered is expressed, by customer, for example, through the abandonment of queue, which is considered one of the most important operational measures to evaluate the performance of a Call Center. This work aims to present and apply analytical queueing models with abandonment, represented by generic probability distributions (particularly mixed distributions), as an effective analysis approach to represent the problem of congestion in Call Center systems and support decisions of dimensioning and operations on these systems. Two studies were conducted with Call Center extracted data of a company located in the countryside of São Paulo State, Brazil and another located overseas, in Israel. The parameters (e.g, arrival rate, service rate, abandonment rate) and some measures of performance (e.g, average waiting time, waiting probability, abandonment probability and traffic intensity) were established based on these data. These sampling measures were equated with the same measures achieved by the analytical queueing models M/M/c+G, M/Gc/1+G and M/G/c+G considered in this research, using the parameters obtained empirically and mixed, Exponential, Fatigue Life, Normal and Lognormal distributions to represent the abandonment (patience) of users. It was observed that in some cases, depending on the considered performance measure, the queueing models with mixed distributions for the abandonment have better results (minor deviations, compared to the real data) than their corresponding with nonmixed distributions. It was observed, also, that independently of the analyzed performance measures, the Call Centers may be represented by a analytical queueing model with a mixed distribution for abandonment times, which behaves better than the others. There were no evidences that the mixed distributions to represent the abandonment times were the best in all analyzed performance measures, but they were always competitive. It was used, also, an experimental model of discrete simulation that properly represents the Call Center in order to check the results of the analytical models and explore alternative scenarios. The same scenarios were considered with the theoretical model and the performance measures achieved by the simulation and by the theoretical models were compared, showing the potential of the use of the approaches based on analytical models with abandonment for the Call Centers analysis. / Este trabalho trata da análise de sistemas de filas para Call Center considerando a possibilidade do cliente abandonar o sistema antes de ser servido, devido a sua impaciência. Os Call Centers são organizações de serviço que predominantemente servem os clientes via chamada telefônica e são considerados um tipo particular dos Centros de Contato, que atendem seus clientes por meio de telefone, fax, e-mail, chat, dispositivos móveis e outros canais de comunicação. Do ponto de vista dos negócios, a principal preocupação na gestão de um Call Center é oferecer serviço de qualidade com mínimo custo. A percepção da qualidade dos serviços oferecidos é manifestada, pelo cliente, por exemplo, por meio do abandono da fila de espera, que é considerado uma das medidas operacionais mais importantes para avaliar o desempenho de um Call Center. O objetivo deste trabalho é apresentar e aplicar modelos analíticos de filas com abandono, representado por distribuições genéricas (particularmente distribuições mistas), como uma abordagem de análise efetiva para representar o problema de congestão em sistemas de Call Centers e apoiar decisões de dimensionamento e operação nesses sistemas. Dois estudos foram conduzidos com dados extraídos do Call Center de uma empresa localizada no interior do Estado de São Paulo e de outro localizado no exterior, em Israel. Os parâmetros (por exemplo, taxa de chegada, taxa de serviço e taxa de abandono) e algumas medidas de desempenho (por exemplo, tempo médio de espera, probabilidade de esperar, probabilidade de abandonar e intensidade de tráfego) são determinadas com esses dados. Essas medidas amostrais são comparadas com as mesmas medidas obtidas por meio dos modelos analíticos de fila M/M/c+G, M/Gc/1+G e M/G/c+G considerados nesse estudo, que utilizam os parâmetros obtidos empiricamente e as distribuições mistas, Exponencial, Fatigue Life, Normal e Lognormal para representar o abandono (paciência) dos usuários. Observou-se como resultado, que em alguns casos, dependendo da medida de desempenho considerada, os modelos de fila com distribuição mista para o abandono têm apresentado resultados melhores (desvios menores em relação aos dados reais) que os seus correspondentes com distribuições não mistas. Observou-se, também, que independentemente das medidas de desempenho analisadas, os Call Centers podem ser representados por um modelo analítico de fila com uma distribuição mista para os tempos de abandono, que se comporta melhor do que os outros. Não houve evidências que as distribuições mistas para representar os tempos de abandono foram as melhores em todas as medidas de desempenho analisadas, mas foram sempre competitivas. Utilizou-se, também, um modelo experimental de simulação discreta, que representa apropriadamente o Call Center, para verificar os resultados dos modelos analíticos e explorar cenários alternativos. Os mesmos cenários foram considerados com o modelo teórico e as medidas de desempenho obtidas pela simulação e pelo modelo teórico foram comparadas, mostrando o potencial do uso de abordagens baseadas em modelos analíticos com abandono para análise de Call Centers.