Contributed Session Wed.3.H 2013

Wednesday, 15:15 - 16:45 h, Room: H 2013

Cluster 11: Integer & mixed-integer programming [...]

Scheduling III


Chair: Rüdiger Stephan



Wednesday, 15:15 - 15:40 h, Room: H 2013, Talk 1

Nelson Hein
Mathematical model of hierarchical production planning

Coauthors: Adriana Kroenke, Volmir Eugênio Wilhelm


The use of hierarchical model is mostly related to some of the advantages it may provides this type of planning, like a lower requirement for higher level of detailed information, a more simplified formulation of the global model and the gradual introduction of the random effects. Furthermore, beside the advantage of reducing the computational resources, this approach allows a better establishment of parallelism between his formulation and the hierarchy of decisions in the organization. Hierarchical models have been widely used to represent the processes of planning operations in companies. So far, the practical implementation of these models has been made under a, somewhat, formal approach. In this case, a hierarchical model is presented, which takes into consideration a great deal of the complexity that is commonly brought up in production environments. A methodology based on goal programming (applied to different disaggregation procedures to make room for the hierarchical planning) is utilized to solve this matter. This study aims at presenting a proposed methodology, the results obtained when applying it in a practical case, and the conclusions that derive from it.



Wednesday, 15:45 - 16:10 h, Room: H 2013, Talk 2

Diego Fernando Recalde
Scheduling the Ecuadorian professional football league by integer programming

Coauthors: Ramiro Torres, Polo Vaca


A sports schedule fixes the dates and venues of games between teams in a sports league. Constructing a sports schedule is a highly restrictive problem. The schedule must meet constraints due to regulations of a particular sports league Federation and it must guarantee the participation of all teams on equal terms. Moreover, economic benefits of teams, and other agents involved in this activity are expected.
Until 2011, the Ecuadorian Football Federation (FEF) has developed schedules for their professional football championship manually. In early 2011, the authors presented to the FEF authorities several evidences that the use of mathematical programming to elaborate feasible sports schedules could easily exceed the benefits obtained by the empirical method. Under the last premises, this work presents an Integer
Programming formulation for scheduling the professional football league in Ecuador, which is solved to optimality, and also a three phase decomposition approach for its solution. The schedules obtained fulfilled the expectations of the FEF and one of them was adopted as the official schedule for the 2012 edition of the Ecuadorian Professional Football Championship.



Wednesday, 16:15 - 16:40 h, Room: H 2013, Talk 3

Rüdiger Stephan
Smaller compact formulation for lot-sizing with constant batches


We consider a variant of the classical lot-sizing problem in which the capacity in each period is an integer multiple of some basic batch size. Pochet and Wolsey (MathOR 18, 1993) presented an O(n2 min{n,C}) algorithm to solve this problem and a linear program with O(n3) variables and inequalities, where n is the number of periods and C the batch size. We provide a linear program of size O(n2 min{n,C}), that is, in case that C < n, our formulation is smaller.


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