Guillermo Durán

We apply mathematical and computational techniques to the development of an approach for optimizing the waste collection system of the Argentine city of Berazategui, 26 km south of Buenos Aires. Taking full account of the city’s particular characteristics, our objective is to not only improve the system’s efficiency but also ensure equitable workloads for waste collection truck crews, including both drivers and collectors. The optimization problem is partitioned into three stages. In the first stage, a heuristic constructs structurally simple collection zones that are balanced in terms of collectors’ walking distances. In the second stage, a mixed-integer linear programming model designs a collection truck route for each zone and minimizes its length. In the third and final stage, each truck is assigned to two zones in such a way as to equalize to the extent possible the length of drivers’ working day. Because working-day length is influenced by multiple factors, we formulate this objective as a biobjective optimization problem and solve it by integer linear programming coupled with an iterative algorithm. The city implemented the approach in early 2020, resulting in a markedly more equitable workload distribution and significant fuel savings and maintenance expense for the city. History: This paper was refereed. Funding: This work was partly financed by the Universidad de Buenos Aires Ciencia y Técnica [Grant 20020170100495BA] (Argentina) and Proyectos de Investigación Plurianuales - Consejo Nacional de Investigaciones Científicas y Técnicas [Grant 11220200100084CO (Argentina)]. G. A. Durán is also funded by the Instituto Sistemas Complejos de Ingeniería in Chile [Grants Iniciativa Científica Milenio - Fondo de Innovación para la Competitividad P05-004-F and Comisión Nacional de Investigación Científica y Tecnológica FB0816].

The year 2020 saw the world turned upside down by the coronavirus pandemic. Countless human activities were suspended or cancelled as the virus spread across the globe. In this paper, we show how the regular season matches of Ecuador's professional football league were rescheduled due to the disruption caused by the pandemic. As with many others, this league had to reschedule its remaining games to fit within in a much shorter period of time than originally planned. To address this problem, we developed two mathematical models that designed new match calendars. The first one, a round assignment model, rescheduled the various rounds in the season still to be played while the second one, a day assignment model, took the solutions of the first model as input to assign the matches within each round to specific days. The implementation of our models secured a well-balanced number of days off before each match across all of the teams. Also, it enabled the league to conclude a full season without cancelling any matches or changing the schedule format, unlike what occurred in many other leagues, and won the approval of all stakeholders including league officials, players, team coaches, the TV broadcaster and fans.

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.

The first division clubs in Argentinean professional football maintain teams in each of six youth leagues, classed by age as major divisions (Under-20, Under-18, Under-17) and minor divisions (Under-16, Under-15, Under-14). Regular season play in these leagues typically follows a single round-robin format; the minor divisions play the same schedule as the majors but with the home-away status of the matches reversed. This setup can give rise to very significant differences in travel distances between the major and minor division teams of a given club, which is a frustrating situation for club officials, coaches, and players alike but almost impossible to avoid with manual season scheduling techniques. Nor are these methods able to take into account any number of other criteria that go into the design of a satisfactory match calendar. This paper reports on models developed using mathematical programming to simultaneously schedule multiple leagues while also meeting a series of other desirable conditions. The central criterion is a better balance in the travel distances of the various teams, pursued through the application of two alternative solution approaches: one based on regional team clusters and the other on explicit analysis of actual distances between the teams’ home venues. The solutions generated by these approaches have been used by the organizers of the Argentinean youth leagues to draw up their season schedules since 2018, which has resulted in a series of benefits for all stakeholders.