Ellipsoidal methods for adaptive choice-based conjoint analysis

© 2019 INFORMS.Questionnaires for adaptive choice-based conjoint analysis aim at minimizing some measure of the uncertainty associated with estimates of preference parameters (e.g., partworths). Bayesian approaches to conjoint analysis quantify this uncertainty with a multivariate distribution that is updated after the respondent answers. Unfortunately, this update often requires multidimensional integration, which effectively reduces the adaptive selection of questions to impractical enumeration. An alternative approach is the polyhedral method for adaptive conjoint analysis, which quantifies the uncertainty through a (convex) polyhedron. The approach has a simple geometric interpretation and allows for quick credibility-region updates and effective optimization-based heuristics for adaptive question selection. However, its performance deteriorates with high response-error rates. Available adaptations to this method do not preserve all of the geometric simplicity and interpretabilit

A dynamic clustering approach to data-driven assortment personalization

© 2017 INFORMS.We consider an online retailer facing heterogeneous customers with initially unknown product preferences. Customers are characterized by a diverse set of demographic and transactional attributes. The retailer can personalize the customers' assortment offerings based on available profile information to maximize cumulative revenue. To that end, the retailer must estimate customer preferences by observing transaction data. This, however, may require a considerable amount of data and time given the broad range of customer profiles and large number of products available. At the same time, the retailer can aggregate (pool) purchasing information among customers with similar product preferences to expedite the learning process. We propose a dynamic clustering policy that estimates customer preferences by adaptively adjusting customer segments (clusters of customers with similar preferences) as more transaction information becomes available. We test the proposed approach with

Scheduling the South American Qualifiers to the 2018 FIFA World Cup by integer programming

Every four years, the 10 national teams members of the South American Football Confederation (CONMEBOL) compete for one of the South American slots in the final phase of the FIFA World Cup. The qualifying competition consists of a double round robin tournament. The matches are scheduled in 9 closely spaced pairs known as double rounds. Every team plays twice in each double round. The tournament is spread over 2 years, so the double rounds are months apart. After using the same mirrored schedule for about twenty years, and persistent complaints from its members, CONMEBOL decided to change the schedule for the 2018 World Cup. Supported by one of CONMEBOL's members, we used integer programmming to construct schedules that overcome the main drawbacks of the previous approach. After exploring many design criteria, we proposed a candidate schedule based on a French scheme. The main feature of the proposed schedule is that every team plays once at home and once away on each double round, a departure from traditional symmetric (mirrored) schemes. This proposal was unanimously approved by CONMEBOL members and is currently being used in the qualifier tournament for the 2018 FIFA World Cup in Russia.Fil: Duran, Guillermo Alfredo. Universidad de Chile; Chile. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Guajardo, Mario. NHH Norwegian School of Economics; NoruegaFil: Sauré, Denis. Universidad de Chile; Chil

Learning in Combinatorial Optimization: What and How to Explore

We study dynamic decision making under uncertainty when, at each period, a decision maker implements a solution to a combinatorial optimization problem. The objective coefficient vectors of said problem, which are unobserved before implementation, vary from period to period. These vectors, however, are known to be random draws from an initially unknown distribution with known range. By implementing different solutions, the decision maker extracts information about the underlying distribution but at the same time experiences the cost associated with said solutions. We show that resolving the implied exploration versus exploitation tradeoff efficiently is related to solving a lower-bound problem (LBP), which simultaneously answers the questions of what to explore and how to do so. We establish a fundamental limit on the asymptotic performance of any admissible policy that is proportional to the optimal objective value of the LBP problem. We show that such a lower bound might be asymptotically attained by policies that adaptively reconstruct and solve the LBP at an exponentially decreasing frequency. Because the LBP is likely intractable in practice, we propose policies that instead reconstruct and solve a proxy for the LBP, which we call the optimality cover problem (OCP). We provide strong evidence of the practical tractability of the OCP, which implies that the proposed policies can be implemented in real time. We test the performance of the proposed policies through extensive numerical experiments, and we show that they significantly outperform relevant benchmarks in the long-term and are competitive in the short-term.National Science Foundation (NSF) NSF - Directorate for Engineering (ENG) 1233441 Complex Engineering Systems Institute CONICYT: PIA FB081

An analytics approach to the FIFA ranking procedure and the World Cup final draw

This paper analyzes the procedure used by FIFA up until 2018 to rank national football teams and define by random draw the groups for the initial phase of the World Cup finals. A predictive model is calibrated to form a reference ranking to evaluate the performance of a series of simple changes to that procedure. These proposed modifications are guided by a qualitative and statistical analysis of the FIFA ranking. We then analyze the use of this ranking to determine the groups for the World Cup finals. After enumerating a series of deficiencies in the group assignments for the 2014 World Cup, a mixed integer linear programming model is developed and used to balance the difficulty levels of the groups.Fil: Cea, Sebastián. Universidad de Chile; ChileFil: Duran, Guillermo Alfredo. Universidad de Chile; Chile. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; ArgentinaFil: Guajardo, Mario. Nhh Norwegian School Of Economics, Noruega; NoruegaFil: Sauré, Denis. Universidad de Chile; ChileFil: Siebert, Joaquín. Universidad de Chile; ChileFil: Zamorano, Gonzalo. Universidad de Chile; Chil

Scheduling the Chilean Soccer League by Integer Programming

Since 2005, Chile’s professional soccer league has used a game-scheduling system based on an integer linear programming model. The Chilean league managers have considered several criteria for the last tournaments’ scheduling, involving operational, economic and sporting factors, thus generating a highly constrained problem, in practice unsolvable by their last methodology. This led to the adoption of a model with real conditions, some of them totally new in the use of sports scheduling techniques in soccer leagues. The schedules so obtained have meant greater benefits for the teams, given by lower costs and higher incomes, fairer seasons and tournaments that are more attractive to sports fans. Such success has completely fulfilled the expectations of the Asociación Nacional de Fútbol Profesional (ANFP), the organizing body for Chilean professional soccer

Scheduling the Main Professional Football League of Argentina

In this paper, we describe our work in scheduling Argentina’s First Division professional football league, the Superliga. Following existing work in sports scheduling, we develop an integer programming model for the Superliga season schedule and then, solve it using a decomposition approach. Unlike previous work, this scheme is based on the creation and assignment of cluster patterns, which take advantage of the model’s geographically driven handling of sporting fairness. We also model the assignment of matches to specific dates and time slots while simultaneously considering various conditions relating to or imposed by game broadcasters, the government, and international tournament calendars. Our work was implemented to schedule the Superliga’s 2018–2019 and 2019–2020 seasons, achieving clear improvements on a number of criteria over the previous approach.Fil: Duran, Guillermo Alfredo. Universidad de Chile; Chile. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Calculo. - Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Calculo; ArgentinaFil: Guajardo, Mario. Norwegian School Of Economics; NoruegaFil: Gutiérrez, Facundo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Cálculo; ArgentinaFil: Marenco, Javier Leonardo. Universidad Nacional de General Sarmiento. Instituto de Ciencias. Área de Matemática; ArgentinaFil: Sauré, Denis. Universidad de Chile; ChileFil: Zamorano, Gonzalo. Universidad de Chile; Chil

An analytics approach to the FIFA ranking procedure and the World Cup final draw

his paper analyzes the procedure used by FIFA up until 2018 to rank national football teams and define by random draw the groups for the initial phase of the World Cup finals. A predictive model is calibrated to form a reference ranking to evaluate the performance of a series of simple changes to that procedure. These proposed modifications are guided by a qualitative and statistical analysis of the FIFA ranking. We then analyze the use of this ranking to determine the groups for the World Cup finals. After enumerating a series of deficiencies in the group assignments for the 2014 World Cup, a mixed integer linear programming model is developed and used to balance the difficulty levels of the groups