Generating a schedule for a sports league is an extremely demanding task. This paper presents a m... more Generating a schedule for a sports league is an extremely demanding task. This paper presents a method to schedule the Finnish national ice hockey league for players aged under 20. The league plays a rare triple round robin tournament. To obtain a schedule, we sequentially solve four distinct combinatorial problems. The generated schedule is superior to the manual schedule used for the 2009-2010 season. We were able to find a feasible solution with only minor violations in one soft constraint.
Generating a schedule for a professional sports league is an extremely demanding task. Good sched... more Generating a schedule for a professional sports league is an extremely demanding task. Good schedules have many benefits for the league, such as higher incomes, lower costs and more interesting and fairer seasons. This paper presents the format played in the Finnish major ice hockey league in the 2013-2014 season. The format is very complicated requiring computational intelligence to generate an acceptable schedule. We have used the PEAST algorithm to schedule the league since the 2008-2009 season. We report our computational results especially for the 2013-2014 season.
Good rosters have many benefits for an organization, such as lower costs, more effective utilizat... more Good rosters have many benefits for an organization, such as lower costs, more effective utilization of resources and fairer workloads. This paper introduces the unlimited shift generation problem. The problem is to construct a set of shifts such that the staff demand at each timeslot is covered by a suitable number of employees. A set of real-world instances derived from the actual problems solved for various companies is presented, along with our results. This research has contributed to better systems for our industry partners.
This paper considers the Red-Blue Transportation Problem (Red-Blue TP), a generalization of the t... more This paper considers the Red-Blue Transportation Problem (Red-Blue TP), a generalization of the transportation problem where supply nodes are partitioned into two sets and so-called exclusionary constraints are imposed. We encountered a special case of this problem in a hospital context, where patients need to be assigned to rooms. We establish the problem's complexity, and we compare two integer programming formulations. Furthermore, a maximization variant of Red-Blue TP is presented, for which we propose a constant-factor approximation algorithm. We conclude with a computational study on the performance of the integer programming formulations and the approximation algorithms, by varying the problem size, the partitioning of the supply nodes, and the density of the problem.
This paper presents a method to schedule a triple round robin tournament, which involves minitour... more This paper presents a method to schedule a triple round robin tournament, which involves minitournaments, each hosted by one team. A key issue is that at the end of the season the number of home games should be balanced over the teams, despite the fact that in minitournament matches only the host team plays at home. This format is played in the Finnish national ice hockey league for players under the age of 20 years, where the problem is further complicated by many other constraints, for example, preassigned matches resulting from away tours that should limit the distances travelled by the teams. To obtain a schedule for this league, we sequentially solve four distinct combinatorial problems. This method allows us to construct a schedule for the 2009-2010 season, which is superior to the official schedule: it has no hard constraint violations, and outperforms the official schedule on three of five soft constraints.
ABSTRACT This paper presents an application of optimization modeling to the winning of a popular ... more ABSTRACT This paper presents an application of optimization modeling to the winning of a popular cycling game. The application includes real-life data of contempory cyclists. It also has the potential to motivate students with a competitive but fun "race" for a solution. Because the developed optimization model contains features of knapsack problems, multiperiod inventory problems, and logical constraint modeling, it is perfectly suitable for a concluding case study in an undergraduate operations research/management science course. The application was originally developed for an MBA operations research course focusing on spreadsheet modeling skills, but it can also be used in courses that focus on algebraic modeling of optimization problems.
We consider the so-called Transportation Problem with Exclu- sionary Side Constraints (TPESC), wh... more We consider the so-called Transportation Problem with Exclu- sionary Side Constraints (TPESC), which is a generalization of the ordinary transportation problem. We conflrm that the TPESC is NP-hard, and we analyze the complexity of difierent special cases. For instance, we show that in case of a bounded number of suppliers, a pseudo-polynomial time al- gorithm exists, whereas the case of
Generating a schedule for a sports league is an extremely demanding task. This paper presents a m... more Generating a schedule for a sports league is an extremely demanding task. This paper presents a method to schedule the Finnish national ice hockey league for players aged under 20. The league plays a rare triple round robin tournament. To obtain a schedule, we sequentially solve four distinct combinatorial problems. The generated schedule is superior to the manual schedule used for the 2009-2010 season. We were able to find a feasible solution with only minor violations in one soft constraint.
Generating a schedule for a professional sports league is an extremely demanding task. Good sched... more Generating a schedule for a professional sports league is an extremely demanding task. Good schedules have many benefits for the league, such as higher incomes, lower costs and more interesting and fairer seasons. This paper presents the format played in the Finnish major ice hockey league in the 2013-2014 season. The format is very complicated requiring computational intelligence to generate an acceptable schedule. We have used the PEAST algorithm to schedule the league since the 2008-2009 season. We report our computational results especially for the 2013-2014 season.
Good rosters have many benefits for an organization, such as lower costs, more effective utilizat... more Good rosters have many benefits for an organization, such as lower costs, more effective utilization of resources and fairer workloads. This paper introduces the unlimited shift generation problem. The problem is to construct a set of shifts such that the staff demand at each timeslot is covered by a suitable number of employees. A set of real-world instances derived from the actual problems solved for various companies is presented, along with our results. This research has contributed to better systems for our industry partners.
This paper considers the Red-Blue Transportation Problem (Red-Blue TP), a generalization of the t... more This paper considers the Red-Blue Transportation Problem (Red-Blue TP), a generalization of the transportation problem where supply nodes are partitioned into two sets and so-called exclusionary constraints are imposed. We encountered a special case of this problem in a hospital context, where patients need to be assigned to rooms. We establish the problem's complexity, and we compare two integer programming formulations. Furthermore, a maximization variant of Red-Blue TP is presented, for which we propose a constant-factor approximation algorithm. We conclude with a computational study on the performance of the integer programming formulations and the approximation algorithms, by varying the problem size, the partitioning of the supply nodes, and the density of the problem.
This paper presents a method to schedule a triple round robin tournament, which involves minitour... more This paper presents a method to schedule a triple round robin tournament, which involves minitournaments, each hosted by one team. A key issue is that at the end of the season the number of home games should be balanced over the teams, despite the fact that in minitournament matches only the host team plays at home. This format is played in the Finnish national ice hockey league for players under the age of 20 years, where the problem is further complicated by many other constraints, for example, preassigned matches resulting from away tours that should limit the distances travelled by the teams. To obtain a schedule for this league, we sequentially solve four distinct combinatorial problems. This method allows us to construct a schedule for the 2009-2010 season, which is superior to the official schedule: it has no hard constraint violations, and outperforms the official schedule on three of five soft constraints.
ABSTRACT This paper presents an application of optimization modeling to the winning of a popular ... more ABSTRACT This paper presents an application of optimization modeling to the winning of a popular cycling game. The application includes real-life data of contempory cyclists. It also has the potential to motivate students with a competitive but fun "race" for a solution. Because the developed optimization model contains features of knapsack problems, multiperiod inventory problems, and logical constraint modeling, it is perfectly suitable for a concluding case study in an undergraduate operations research/management science course. The application was originally developed for an MBA operations research course focusing on spreadsheet modeling skills, but it can also be used in courses that focus on algebraic modeling of optimization problems.
We consider the so-called Transportation Problem with Exclu- sionary Side Constraints (TPESC), wh... more We consider the so-called Transportation Problem with Exclu- sionary Side Constraints (TPESC), which is a generalization of the ordinary transportation problem. We conflrm that the TPESC is NP-hard, and we analyze the complexity of difierent special cases. For instance, we show that in case of a bounded number of suppliers, a pseudo-polynomial time al- gorithm exists, whereas the case of
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