# Balanced partitioning for school canteen meat supply

1 G-SCOP_ROSP - Recherche Opérationnelle pour les Systèmes de Production
G-SCOP - Laboratoire des sciences pour la conception, l'optimisation et la production
Abstract : In France, schools are grouped in order to set up public calls for tender to purchase things. In this study, we are interested in the design of these calls for the supply of four categories of meats: poultry, lamb, beef and pork. It consists in proposing, for each category of meat, a partitioning of the set of schools. In the context of short and local supply chain, the objective of this partitioning is to allow a maximum number of suppliers, in particular the local ones, to respond to the calls. A public call for tender is set up for each part of the partition, and if a supplier wins a tender he has to deliver all the schools included in the part. Data are a set of schools with their location and demand, a set of suppliers with their location, scope of action and minimal profitability ratio, and a selling price of the meat. A meat supplier respond to a call for tender if (1) all the schools are inside his scope of action, and (2) the delivery of the schools within one route achieve a minimal profitability ratio. For every subset of schools, an average profitability ratio can be computed, based on the ones of the suppliers who can respond. The problem has an original constraint: the profitability ratios of the parts of the solution need to be balanced. Otherwise, suppliers may choose to respond only to the tenders with high profitability ratios. The optimization problem studied is NP-hard as a generalisation of Set Partitioning. A formulation of the problem as an Integer Linear Program is proposed. The balancing of the profitability ratios is integrated as a constraint or in the objective function with a penalty cost. As the number of potential subsets is too important, two solving methods are considered. The first one is a local search algorithm. The second one is based on the shortlisting of the subsets and can be improved using a column generation approach. Some results on real case instances are presented in order to compare the two methods.
Document type :
Conference papers

https://hal.archives-ouvertes.fr/hal-00833955
Contributor : Maxime Ogier <>
Submitted on : Thursday, June 13, 2013 - 5:21:21 PM
Last modification on : Monday, December 7, 2020 - 12:26:04 PM

### Identifiers

• HAL Id : hal-00833955, version 1

### Citation

Maxime Ogier, Van-Dat Cung, Nicolas Catusse, Julien Boissière. Balanced partitioning for school canteen meat supply. 26th Conference of the European Chapter on Combinatorial Optimization (ECCO), May 2013, Paris, France. ⟨hal-00833955⟩

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