Stochastic optimization of staffing for multiskill call centers

Dans cette thèse, nous étudions le problème d’optimisation des effectifs dans les centres d’appels, dans lequel nous visons à minimiser les coûts d’exploitation tout en offrant aux clients une qualité de service (QoS) élevée. Nous introduisons également l'utilisation de contraintes probabilistes qui exigent que la qualité de service soit satisfaite avec une probabilité donnée. Ces contraintes sont adéquates dans le cas où la performance est mesurée sur un court intervalle de temps, car les mesures de QoS sont des variables aléatoires sur une période donnée. Les problèmes de personnel proposés sont difficiles en raison de l'absence de forme analytique pour les contraintes probabilistes et doivent être approximées par simulation. En outre, les fonctions QoS sont généralement non linéaires et non convexes. Nous considérons les problèmes d’affectation personnel dans différents contextes et étudions les modèles proposés tant du point de vue théorique que pratique. Les méthodologies développées sont générales, en ce sens qu'elles peuvent être adaptées et appliquées à d'autres problèmes de décision dans les systèmes de files d'attente. La thèse comprend trois articles traitant de différents défis en matière de modélisation et de résolution de problèmes d'optimisation d’affectation personnel dans les centres d'appels à compétences multiples. Les premier et deuxième article concernent un problème d'optimisation d'affectation de personnel en deux étapes sous l'incertitude. Alors que dans le second, nous étudions un modèle général de programmation stochastique discrète en deux étapes pour fournir une garantie théorique de la consistance de l'approximation par moyenne échantillonnale (SAA) lorsque la taille des échantillons tend vers l'infini, le troisième applique l'approche du SAA pour résoudre le problème d’optimisation d'affectation de personnel en deux étapes avec les taux d’arrivée incertain. Les deux articles indiquent la viabilité de l'approche SAA dans notre contexte, tant du point de vue théorique que pratique. Pour être plus précis, dans le premier article, nous considérons un problème stochastique discret général en deux étapes avec des contraintes en espérance. Nous formulons un problème SAA avec échantillonnage imbriqué et nous montrons que, sous certaines hypothèses satisfaites dans les exemples de centres d'appels, il est possible d'obtenir les solutions optimales du problème initial en résolvant son SAA avec des échantillons suffisamment grands. De plus, nous montrons que la probabilité que la solution optimale du problème de l’échantillon soit une solution optimale du problème initial tend vers un de manière exponentielle au fur et à mesure que nous augmentons la taille des échantillons. Ces résultats théoriques sont importants, non seulement pour les applications de centre d'appels, mais également pour d'autres problèmes de prise de décision avec des variables de décision discrètes. Le deuxième article concerne les méthodes de résolution d'un problème d'affectation en personnel en deux étapes sous incertitude du taux d'arrivée. Le problème SAA étant coûteux à résoudre lorsque le nombre de scénarios est important. En effet, pour chaque scénario, il est nécessaire d'effectuer une simulation pour estimer les contraintes de QoS. Nous développons un algorithme combinant simulation, génération de coupes, renforcement de coupes et décomposition de Benders pour résoudre le problème SAA. Nous montrons l'efficacité de l'approche, en particulier lorsque le nombre de scénarios est grand. Dans le dernier article, nous examinons les problèmes de contraintes en probabilité sur les mesures de niveau de service. Notre méthodologie proposée dans cet article est motivée par le fait que les fonctions de QoS affichent généralement des courbes en S et peuvent être bien approximées par des fonctions sigmoïdes appropriées. Sur la base de cette idée, nous avons développé une nouvelle approche combinant la régression non linéaire, la simulation et la recherche locale par région de confiance pour résoudre efficacement les problèmes de personnel à grande échelle de manière viable. L’avantage principal de cette approche est que la procédure d’optimisation peut être formulée comme une séquence de simulations et de résolutions de problèmes de programmation linéaire. Les résultats numériques basés sur des exemples réels de centres d'appels montrent l'efficacité pratique de notre approche. Les méthodologies développées dans cette thèse peuvent être appliquées dans de nombreux autres contextes, par exemple les problèmes de personnel et de planification dans d'autres systèmes basés sur des files d'attente avec d'autres types de contraintes de QoS. Celles-ci soulèvent également plusieurs axes de recherche qu'il pourrait être intéressant d'étudier. Par exemple, une approche de regroupement de scénarios pour atténuer le coût des modèles d'affectation en deux étapes, ou une version d'optimisation robuste en distribution pour mieux gérer l'incertitude des données.In this thesis, we study the staffing optimization problem in multiskill call centers, in which we aim at minimizing the operating cost while delivering a high quality of service (QoS) to customers. We also introduce the use of chance constraints which require that the QoSs are met with a given probability. These constraints are adequate in the case when the performance is measured over a short time interval as QoS measures are random variables in a given time period. The proposed staffing problems are challenging in the sense that the stochastic constraints have no-closed forms and need to be approximated by simulation. In addition, the QoS functions are typically non-linear and non-convex. We consider staffing optimization problems in different settings and study the proposed models in both theoretical and practical aspects. The methodologies developed are general, in the sense that they can be adapted and applied to other staffing/scheduling problems in queuing-based systems. The thesis consists of three articles dealing with different challenges in modeling and solving staffing optimization problems in multiskill call centers. The first and second articles concern a two-stage staffing optimization problem under uncertainty. While in the first one, we study a general two-stage discrete stochastic programming model to provide a theoretical guarantee for the consistency of the sample average approximation (SAA) when the sample sizes go to infinity, the second one applies the SAA approach to solve the two-stage staffing optimization problem under arrival rate uncertainty. Both papers indicate the viability of the SAA approach in our context, in both theoretical and practical aspects. To be more precise, in the first article, we consider a general two-stage discrete stochastic problem with expected value constraints. We formulate its SAA with nested sampling. We show that under some assumptions that hold in call center examples, one can obtain the optimal solutions of the original problem by solving its SAA with large enough sample sizes. Moreover, we show that the probability that the optimal solution of the sample problem is an optimal solution of the original problem, approaches one exponentially fast as we increase the sample sizes. These theoretical findings are important, not only for call center applications, but also for other decision-making problems with discrete decision variables. The second article concerns solution methods to solve a two-stage staffing problem under arrival rate uncertainty. It is motivated by the fact that the SAA version of the two-stage staffing problem becomes expensive to solve with a large number of scenarios, as for each scenario, one needs to use simulation to approximate the QoS constraints. We develop an algorithm that combines simulation, cut generation, cut strengthening and Benders decomposition to solve the SAA problem. We show the efficiency of the approach, especially when the number of scenarios is large. In the last article, we consider problems with chance constraints on the service level measures. Our methodology proposed in this article is motivated by the fact that the QoS functions generally display ``S-shape'' curves and might be well approximated by appropriate sigmoid functions. Based on this idea, we develop a novel approach that combines non-linear regression, simulation and trust region local search to efficiently solve large-scale staffing problems in a viable way. The main advantage of the approach is that the optimization procedure can be formulated as a sequence of steps of performing simulation and solving linear programming models. Numerical results based on real-life call center examples show the practical viability of our approach. The methodologies developed in this thesis can be applied in many other settings, e.g., staffing and scheduling problems in other queuing-based systems with other types of QoS constraints. These also raise several research directions that might be interesting to investigate. For examples, a clustering approach to mitigate the expensiveness of the two-stage staffing models, or a distributionally robust optimization version to better deal with data uncertainty

Staffing optimization with chance constraints in call centers

Les centres d’appels sont des éléments clés de presque n’importe quelle grande organisation. Le problème de gestion du travail a reçu beaucoup d’attention dans la littérature. Une formulation typique se base sur des mesures de performance sur un horizon infini, et le problème d’affectation d’agents est habituellement résolu en combinant des méthodes d’optimisation et de simulation. Dans cette thèse, nous considérons un problème d’affection d’agents pour des centres d’appels soumis a des contraintes en probabilité. Nous introduisons une formulation qui exige que les contraintes de qualité de service (QoS) soient satisfaites avec une forte probabilité, et définissons une approximation de ce problème par moyenne échantillonnale dans un cadre de compétences multiples. Nous établissons la convergence de la solution du problème approximatif vers celle du problème initial quand la taille de l’échantillon croit. Pour le cas particulier où tous les agents ont toutes les compétences (un seul groupe d’agents), nous concevons trois méthodes d’optimisation basées sur la simulation pour le problème de moyenne échantillonnale. Étant donné un niveau initial de personnel, nous augmentons le nombre d’agents pour les périodes où les contraintes sont violées, et nous diminuons le nombre d’agents pour les périodes telles que les contraintes soient toujours satisfaites après cette réduction. Des expériences numériques sont menées sur plusieurs modèles de centre d’appels à faible occupation, au cours desquelles les algorithmes donnent de bonnes solutions, i.e. la plupart des contraintes en probabilité sont satisfaites, et nous ne pouvons pas réduire le personnel dans une période donnée sont introduire de violation de contraintes. Un avantage de ces algorithmes, par rapport à d’autres méthodes, est la facilité d’implémentation.Call centers are key components of almost any large organization. The problem of labor management has received a great deal of attention in the literature. A typical formulation of the staffing problem is in terms of infinite-horizon performance measures. The method of combining simulation and optimization is used to solve this staffing problem. In this thesis, we consider a problem of staffing call centers with respect to chance constraints. We introduce chance-constrained formulations of the scheduling problem which requires that the quality of service (QoS) constraints are met with high probability. We define a sample average approximation of this problem in a multiskill setting. We prove the convergence of the optimal solution of the sample-average problem to that of the original problem when the sample size increases. For the special case where we consider the staffing problem and all agents have all skills (a single group of agents), we design three simulation-based optimization methods for the sample problem. Given a starting solution, we increase the staffings in periods where the constraints are violated, and decrease the number of agents in several periods where decrease is acceptable, as much as possible, provided that the constraints are still satisfied. For the call center models in our numerical experiment, these algorithms give good solutions, i.e., most constraints are satisfied, and we cannot decrease any agent in any period to obtain better results. One advantage of these algorithms, compared with other methods, that they are very easy to implement

Binary-Continuous Sum-of-ratios Optimization: Discretization, Approximations, and Convex Reformulations

We study a class of non-convex sum-of-ratios programs which can be used for decision-making in prominent areas such as product assortment and price optimization, facility location, and security games. Such an optimization problem involves both continuous and binary decision variables and is known to be highly non-convex and intractable to solve. We explore a discretization approach to approximate the optimization problem and show that the approximate program can be reformulated as mixed-integer linear or second-order cone programs, which can be conveniently handled by an off-the-shelf solver (e.g., CPLEX or GUROBI). We further establish (mild) conditions under which solutions to the approximate problem converge to optimal solutions as the number of discretization points increases. We also provide approximation abounds for solutions obtained from the approximated problem. We show how our approach applies to product assortment and price optimization, maximum covering facility location, and Bayesian Stackelberg security games and provide experimental results to evaluate the efficiency of our approach

On a multistage discrete stochastic optimization problem with stochastic constraints and nested sampling

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Thói quen phát triển chuyên môn của giáo viên ở các trường phổ thông Việt Nam

Nguồn lực và chất lượng giáo viên là một trong những mối quan tâm thiết yếu để phát triển giáo dục bền vững. Thông qua phân tích bộ dữ liệu “Khảo sát thói quen phát triển chuyên môn giáo viên các trường phổ thông ở Việt Nam năm 2019” với 464 quan sát về thói quen học tập của giáo viên phổ thông từ các trường công lập và tư thục trên cả nước, chúng tôi thực hiện nghiên cứu phân tích thói quen phát triển chuyên môn của giáo viên. Nghiên cứu này là một phần kết quả của dự án nghiên cứu về năng lực chuyên môn giáo viên phổ thông Việt Nam giai đoạn 2020 – 2025 của Trung tâm nghiên cứu và Phát triển Giáo dục EdLab Asia. Bằng cách phân tích dữ liệu về số giờ tham gia hoạt động phát triển chuyên môn của giáo viên ở từng loại hình trường, nghiên cứu chỉ ra sự khác biệt về thói quen học tập của giáo viên các cấp phổ thông theo từng loại hình nhà trường. Nghiên cứu cũng chỉ ra rằng hoạt động phát triển chuyên môn giáo viên của trường tư thục tốt hơn trường công lập. Kết quả của nghiên cứu là gợi ý cho các nhà hoạch định chính sách, các nhà quản lý giáo dục tại các cơ sở giáo dục phổ thông, không kể công-tư tham chiếu và điều chỉnh các kế hoạch, chương trình phát triển chuyên môn giáo viên

Dataset of Vietnamese students’ intention in respect of study abroad before and during COVID-19 pandemic

The Covid-19 Pandemic had completely disrupted the worldwide educational system. Many schools chose the online delivery mode for students in case learning losses incurred during social distance decree. However, as to these students who are currently in the study abroad planning stages, reached an intention crossroads, whether standing for certain unchanging decisions in study abroad destinations or changing swiftly due to the unexpected policies in quarantine. This case opened to interpretation, which was based on our e-survey since 3 May to 13 May 2020 with 397 responses covering a range of Vietnamese students. In this dataset, we focused on (i) Students’ Demographics; (ii) The previous intention of students to study abroad before and during the Covid-19 ravaged and (iii) Their intention afterwards

Straightforward Procedure for Laboratory Production of DNA Ladder

DNA ladder is commonly used to determine the size of DNA fragments by electrophoresis in routine molecular biology laboratories. In this study, we report a new procedure to prepare a DNA ladder that consists of 10 fragments from 100 to 1000 bp. This protocol is a combination of routinely employed methods: cloning, PCR, and partial digestion with restriction enzymes. DNA fragments of 100 bp with unique restriction site at both ends were self-ligated to create a tandem repeat. Once being cloned, the tandem repeat was rapidly amplified by PCR and partially digested by restriction enzymes to produce a ladder containing multimers of the repeated DNA fragments. Our procedure for production of DNA ladder could be simple, time saving, and inexpensive in comparison with current ones widely used in most laboratories

Evaluation of EBNA-1 (epstein-barr virus nuclear antigen-1) gene prevalence in nasopharyngeal carcinoma in Vietnamese patients

This study examined the presence of Epstein-Barr virus (EBV) in nasopharyngeal carcinoma (NPC) based on the detection of EBNA-1 (Epstein-Barr virus nuclear antigen-1) by Polymerase Chain Reaction (PCR), in Vietnamese population. Firstly, we systematically analyzed the mean of percentage weighted of the presence of EBNA-1 in previous relevant studies. Experimentally, 31 nasopharyngeal cancer biopsies and 20 healthy samples were enrolled in current to evaluate the frequency of candidate genes. As the results, the frequency of EBNA-1 was 77.42%, whereas, none of any cases of healthy samples were found to positive to target gene. The p value < 0.05 (p = 0.0001) showed that it was significant correlation between the presence of this candidate gene and nasopharyngeal cancer. Moreover, a high odds ratio (OR) and relative risk (RR) of candidate gene, (OR = 68.16, RR = 2.41) were calculated. Therefore, the detection of EBNA-1, which performed by PCR, could serve as a good supplement to early diagnosis and prognosis of NPC in Vietnamese population

A Multicentre Molecular Analysis of Hepatitis B and Blood-Borne Virus Coinfections in Viet Nam

Hepatitis B (HBV) infection is endemic in Viet Nam, with up to 8.4 million individuals estimated to be chronically infected. We describe results of a large, multicentre seroepidemiological and molecular study of the prevalence of HBV infection and blood-borne viral coinfections in Viet Nam. Individuals with varying risk factors for infection (n = 8654) were recruited from five centres; Ha Noi, Hai Phong, Da Nang, Khanh Hoa and Can Tho. A mean prevalence rate of 10.7% was observed and levels of HBsAg were significantly higher in injecting drug users (IDUs) (17.4%, n = 174/1000) and dialysis patients (14.3%, n = 82/575) than in lower-risk groups (9.4%; p<0.001). Coinfection with HIV was seen in 28% of HBV-infected IDUs (n = 49/174) and 15.2% of commercial sex workers (CSWs; n = 15/99). HCV infection was present in 89.8% of the HBV-HIV coinfected IDUs (n = 44/49) and 40% of HBV-HIV coinfected CSWs (n = 16/40). Anti-HDV was detected in 10.7% (n = 34/318) of HBsAg positive individuals. Phylogenetic analysis of HBV S gene (n = 187) showed a predominance of genotype B4 (82.6%); genotypes C1 (14.6%), B2 (2.7%) and C5 (0.5%) were also identified. The precore mutation G1896A was identified in 35% of all specimens, and was more frequently observed in genotype B (41%) than genotype C (3%; p<0.0001). In the immunodominant ‘a’ region of the surface gene, point mutations were identified in 31% (n = 58/187) of sequences, and 2.2% (n = 4/187) and 5.3% (n = 10/187) specimens contained the major vaccine escape mutations G145A/R and P120L/Q/S/T, respectively. 368 HBsAg positive individuals were genotyped for the IL28B SNP rs12979860 and no significant association between the IL28B SNP and clearance of HBsAg, HBV viral load or HBeAg was observed. This study confirms the high prevalence of HBV infection in Viet Nam and also highlights the significant levels of blood-borne virus coinfections, which have important implications for hepatitis-related morbidity and development of effective management strategies

Prevalence and correlates of zinc deficiency in pregnant Vietnamese women in Ho Chi Minh City

Background: Although Vietnam is a region with a plant-based diet that has a high zinc deficiency, epidemiological data showing how this affects pregnant women are limited. This study explores the prevalence of zinc deficiency and possible correlates in pregnant Vietnamese women in Ho Chi Minh City. Methods: This was a crosssectional study conducted at a general hospital in Ho Chi Minh City, Vietnam. All pregnant women who came to their first antenatal care visit from November 2011 to June 2012 were recruited. Those taking a vitamin and/or mineral supplement were excluded. Serum zinc concentrations, determined by a standard colorimetric method, of 10.7 mol/L-17.5 mol/L (70.0 g/dL-114 g/dL) were classified as normal and under 10.7 mol/L (70.0 g/dL) as zinc deficient. Results: In total, 254 pregnant women were invited and 107 (42%) participated. The mean age of participants was 29 years, and mean gestational age was 10 weeks. Median zinc concentration in serum was 13.6 mol/L, and the prevalence of zinc deficiency was 29% (95% CI=21%-39%). The daily intake of a milk product supplement was the only significant correlate of zinc deficiency of the items investigated (adjusted OR=0.40, p=0.049). Discussion: This is the first study reporting that more than 25% of pregnant Vietnamese women in Ho Chi Minh City are zinc deficient. Further academic and clinical input is needed to confirm the scale of this neglected issue and to investigate the potential of milk product supplementation in this population