Solving surgical cases assignment problem by a branch-and-price approach

In this paper, we study a surgical cases assignment problem (SCAP) of assigning a set of surgical cases to several multifunctional operating rooms with an objective of minimizing total operating cost. Firstly, we formulate this problem as an integer problem and then reformulate the integer program by using Dantzig-Wolf decomposition as a set partitioning problem. Based on this set partitioning formulation, a so-called branch-and-price exact solution algorithm, combining Branch-and-Bound procedure with column generation (CG) method, is designed for the proposed problem where each node is the linear relaxation problem of a set partitioning problem. This linear relaxation problem is solved by a CG approach in which each column represents a plan for one operating room and is generated by solving a sub-problem (SP) of single operating room planning problem. The computational results indicate that the decomposition approach is promising and capable of solving large problems.

Multicriteria approach to rank scheduling strategies

This paper deals with multicriteria decision-making applied to discrete-continuous scheduling problems. The need for reusability and modularity leads us to build a "generic" optimization and simulation framework, while the need to quickly generate good compromises between conflicting objectives requires the implementation of multicriteria scheduling models. This paper describes the practical possibilities of two hybrid models within this framework, the first one uses a lexicographical sort and the second one a multicriteria method to rank scheduling strategies. The two hybrids are applied to a real-life highly constrained industrial problem.

Wine-Gauging at Damme [The evidence of a late medieval manuscript]

Abstract. During the late Middle Ages, Damme, the outport of Bruges, was an important staple town, i.a. for wines. The measurement of the volume of the barrels for tax and excise purposes was farmed out to the Hospital of St. John. Although the practice of measuring wine barrels was performed throughout the Middle Ages, few medieval documents about how this was done are known. The history of Damme shows that gauging was performed in the Low Countries as well as in France during this period, thereby undermining the assertion that the gauging rod is a Southern German invention. It will be shown that the manuscript which is presented here is one of the oldest in which the construction of the gauging rod is explained. The way in which this was done is very peculiar. Also on the back of the manuscript are some monastic ciphers; in this notation every number is written as a single cipher.Résumé. Jauger les tonneaux de vin dans le port de Damme. Le témoignage d'un manuscrit de la fin de l'époque médiévale. À la fin du Moyen Âge, Damme, Г avant-port de Bruges, était une importante ville d'étape, en particulier pour le commerce des vins. La mesure du volume des tonneaux était effectuée à des fins fiscales et était affermée à l'Hôpital Saint John. Quoique le jaugeage du vin fût courant tout au long du Moyen Âge, il subsiste peu de documents qui permettent de savoir de quelle manière il était pratiqué. L'histoire de Damme montre que cette technique était malgré tout employée aux Pays-Bas aussi bien qu'en France pendant toute cette période, détruisant par là l'assertion selon laquelle les instruments de jauge étaient une invention de l'Allemagne du Sud. On montrera que le manuscrit ici présenté est l'un des plus anciens dans lesquels la méthode de jauge soit explicitée et que la méthode utilisée était très particulière. En outre, au verso du manuscrit, se trouvent des nombres de type monastique qui correspondent à un système de notation original dans lequel chaque chiffre est figuré par un signe spécifique.Meskens Ad, Bonte Germain, Groot Jacques de, Jonghe Mieke de, King David A. Wine-Gauging at Damme [The evidence of a late medieval manuscript]. In: Histoire & Mesure, 1999 volume 14 - n°1-2. Varia. pp. 51-77