Column generation for a multitrip vehicle routing problem with time windows, driver work hours, and heterogeneous fleet

This study addresses a vehicle routing problem with time windows, accessibility restrictions on customers, and a fleet that is heterogeneous with regard to capacity and average speed. A vehicle can performmultiple routes per day, all starting and ending at a single depot, and it is assigned to a single driverwhose totalwork hours are limited.Acolumn generation algorithmis proposed.The column generation pricing subproblem requires a specific elementary shortest path problem with resource constraints algorithm to address the possibility for each vehicle performingmultiple routes per day and to address the need to set the workday’s start time within the planning horizon. A constructive heuristic and a metaheuristic based on tabu search are also developed to find good solutions.

The Spanish mathematician Norberto Cuesta recovered from oblivion

This paper1 outlines the activity as a mathematician, historian, and compromised person of the Spanish mathematician Norberto Cuesta Dutari (1907-1989) and its relationship with the social and political situation in Spain under General Franco’s regime between 1939 and 1977 and the first years of the democratic restoration. It is shown that he was able to achieve a good mathematical production, though he never was close to the establishment and therefore could not profit from a number of opportunities for personal and institutional promotion. This article is the result of an elaboration of information directly gathered from its main protagonist, a number of secondary sources, and the primary sources: his papers and books, from which a hopefully complete list can be found in Appendix I

Following the steps of spanish mathematical analysis: from Cauchy to Weierstrass between 1880 and 1914

[EN] Rigorous Mathematical Analysis in the Cauchy style was not accepted in a straightforward manner by the European mathematical community of the central years of the 19th Century. In average, only around forty years after the 1821 Cours d'Analyse did Cauchy's treatment become a standard in the more mathematically advanced countries, as a paradigm that remained in use until the arithmetisation of Analysis by Weierstrass replaced it before the end of the century. ln this paper the authors show how rigorous Mathematical Analysis à la Cauchy was adopted in Spain quite late -around 1880- and how in sorne more forty years, the Weierstrassian formulation became the usual presentation in Spanish texts