Computational study for workforce scheduling and routing problems

We present a computational study on 112 instances of the Workforce Scheduling and Routing Problem (WSRP). This problem has applications in many service provider industries where employees visit customers to perform activities. Given their similarity, we adapt a mathematical programming model from the literature on vehicle routing problem with time windows (VRPTW) to conduct this computational study on the WSRP. We generate a set of WSRP instances from a well-known VRPTW data set. This work has three objectives. First, to investigate feasibility and optimality on a range of medium size WSRP instances with different distribution of visiting locations and including teaming and connected activities constraints. Second, to compare the generated WSRP instances to their counterpart VRPTW instances with respect to their difficulty. Third, to determine the computation time required by a mathematical programming solver to find feasible solutions for the generated WSRP instances. It is observed that although the solver can achieve feasible solutions for some instances, the current solver capabilities are still limited. Another observation is the WSRP instances present an increased degree of difficulty because of the additional constraints. The key contribution of this paper is to present some test instances and corresponding benchmark study for the WSRP

A greedy heuristic for workforce scheduling and routing with time-dependent activities constraints

We present a greedy heuristic (GHI) designed to tackle five time-dependent activities constraints (synchronisation, overlap, minimum difference, maximum difference and minimum-maximum difference) on workforce scheduling and routing problems. These types of constraints are important because they allow the modelling of situations in which activities relate to each other time-wise, e.g. synchronising two technicians to complete a job. These constraints often make the scheduling and routing of employees more difficult. GHI is tested on set of benchmark instances from different workforce scheduling and routing problems (WSRPs). We compare the results obtained by GHI against the results from a mathematical programming solver. The comparison seeks to determine which solution method achieves more best solutions across all instances. Two parameters of GHI are discussed, the sorting of employees and the sorting of visits. We conclude that using the solver is adequate for instances with less than 100 visits but for larger instances GHI obtains better results in less time

Mixed integer programming with decomposition to solve a workforce scheduling and routing problem

We propose an approach based on mixed integer programming (MIP) with decomposition to solve a workforce scheduling and routing problem, in which a set of workers should be assigned to tasks that are distributed across different geographical locations. This problem arises from a number of home care planning scenarios in the UK, faced by our industrial partner. We present a mixed integer programming model that incorporates important real-world features of the problem such as defined geographical regions and flexibility in the workers? availability. Given the size of the real-world instances, we propose to decompose the problem based on geographical areas. We show that the quality of the overall solution is affected by the ordering in which the sub-problems are tackled. Hence, we investigate different ordering strategies to solve the sub-problems and show that such decomposition approach is a very promising technique to produce high-quality solutions in practical computational times using an exact optimization method

Computational study for workforce scheduling and routing problems

We present a computational study on 112 instances of the Workforce Scheduling and Routing Problem (WSRP). This problem has applications in many service provider industries where employees visit customers to perform activities. Given their similarity, we adapt a mathematical programming model from the literature on vehicle routing problem with time windows (VRPTW) to conduct this computational study on the WSRP. We generate a set of WSRP instances from a well-known VRPTW data set. This work has three objectives. First, to investigate feasibility and optimality on a range of medium size WSRP instances with different distribution of visiting locations and including teaming and connected activities constraints. Second, to compare the generated WSRP instances to their counterpart VRPTW instances with respect to their difficulty. Third, to determine the computation time required by a mathematical programming solver to find feasible solutions for the generated WSRP instances. It is observed that although the solver can achieve feasible solutions for some instances, the current solver capabilities are still limited. Another observation is the WSRP instances present an increased degree of difficulty because of the additional constraints. The key contribution of this paper is to present some test instances and corresponding benchmark study for the WSRP

Alphabetization in a Second Language at Wayuu Indigenous Schools in the State of Zulia: Curriculum, Educational Policies and Teaching Practice

El objetivo de la investigación fue analizar las políticas de alfabetización en castellano empleadas por las docentes de Educación Preescolar de la Parroquia Idelfonso Vásquez del Municipio Maracaibo, Estado Zulia. La investigación fue descriptiva-explicativa. Las técnicas de recolección fueron la entrevista y el análisis documental, siendo un cuestionario el instrumento utilizado. Dadas las características de la recogida de datos se optó por un análisis de la información cuali-cuantitativo. Se encontró que la alfabetización es predominantemente en castellano, con base en metodologías tradicionales. Los resultados indican que existe en los niños interés por la lengua escrita en castellano, pero presentan algunas dificultades de comunicación cuando la docente de aula desconoce la lengua materna. Se concluye que hace falta la ejecución efectiva de políticas de alfabetización cónsonas con el marco legal de la educación intercultural bilingüe y con los principios de una didáctica de la segunda lenguaThe aim of this research was to analyze Spanish literacy policies employed by pre-school teachers in the Idelfonso Vásquez Parish in Maracaibo, State of Zulia. The research was descriptive and explanatory; data collection techniques were the interview and documentary analysis. A questionnaire was used as the instrument. Information was analyzed from a quali-quantitative perspective. Analyses revealed that literacy takes place predominantly in Spanish, based on traditional methodologies. Results showed that children are interested in the written language in Spanish but have some communication difficulties when the classroom teacher does not know their mother tongue. The main conclusion is that there is a need for implementing effective literacy policies that comply both with the legal framework for intercultural bilingual education and with the principles of second language teaching

Diagnostico del estado actual de consevación de Puya raimondii en Arequipa – Perù.

The diagnosis of the current state of conservation of Puya raimondii Hams in Arequipa, Perú. – The authors show the results of a survey carried out in Perù, Arequipe region, and Bolivia, on the geographical distribution of Puya raimondii Harms. After describing the systematic and nomenclature of the Andinian species, the study of the biological, ecological and conservation status of this endemic plant species has been performed, as well. They have also described the density population and the risk of genetic erosion caused of both natural and anthropic pressure. Finally they evaluated the use of this plant species as animal feeding, popular medicine traditional local use

TICs e a sua utilização na disciplina de educação física no ensino primário

Resumen: Introducción: En los últimos años se ha visto cómo se ha pasado de una enseñanza más tradicional al empleo de las tecnologías en prácticamente todos los ámbitos. El área de Educación Física es una de las disciplinas que menos ha evolucionado. Objetivos: Reflejar el área de educación física y la Cultura Digital en Andalucía, cómo han evolucionado las clases de E.F. de primaria en la legislación a nivel nacional y los recursos de los que disponen los centros escolares a nivel autonómico (Andalucía). Métodos: Se ha utilizado como herramienta para recoger información la encuesta. Resultados y discusión: Se ha comparado los datos obtenidos de las encuestas realizadas a 14 profesores. Conclusiones: Pese a que se suele tener la idea de que los profesores más jóvenes usan más la tecnología, los resultados muestran lo contrario.Abstract: Introduction Recent years have seen a shift from more traditional education to the use of technology in virtually all areas. The area of Physical Education is one of the disciplines that has evolved the least. Aim: To reflect the area of physical education and digital culture in Andalusia, how primary education classes have evolved in legislation at a national level and the resources available to schools at an autonomous level (Andalusia). Methods: The survey has been used as a tool to collect information Results & discussion: The data obtained from surveys of 14 teachers have been compared. Conclusions: Although it is often thought that younger teachers use technology more, the results show the opposite.Resumo: Introdução: Nos últimos anos assistiu-se a uma mudança da educação mais tradicional para a utilização da tecnologia em praticamente todas as áreas. A área da Educação Física é uma das disciplinas que menos evoluiu. Objectivos: Para reflectir a área da educação física e da cultura digital na Andaluzia, a forma como as aulas de educação física na escola primária evoluíram na legislação a nível nacional e os recursos disponíveis para as escolas a nível regional (Andaluzia). Métodos: O inquérito tem sido utilizado como instrumento de recolha de informação Resultados e discussão: Foram comparados os dados obtidos a partir de inquéritos realizados junto de 14 professores. Conclusões: Embora se pense frequentemente que os professores mais jovens utilizam mais a tecnologia, os resultados mostram o oposto

Mixed integer programming with decomposition for workforce scheduling and routing with time-dependent activities constraints

We present a mixed integer programming decomposition approach to tackle workforce scheduling and routing problems (WSRP) that involve time-dependent activities constraints. The proposed method is called repeated decomposition with conflict repair (RDCR) and it consists of repeatedly applying a phase of problem decomposition and sub-problem solving, followed by a phase dedicated to conflict repair. Five types of time dependent activities constraints are considered: overlapping, synchronisation, minimum difference, maximum difference, and minimum-maximum difference. Experiments are conducted to compare the proposed method to a tailored greedy heuristic. Results show that the proposed RDCR is an effective approach to harness the power of mixed integer programming solvers to tackle the difficult and highly constrained WSRP in practical computational time

An investigation of heuristic decomposition to tackle workforce scheduling and routing with time-dependent activities constraints

This paper presents an investigation into the application of heuristic decomposition and mixed-integer programming to tackle workforce scheduling and routing problems (WSRP) that involve time dependent activities constraints. These constraints refer to time-wise dependencies between activities. The decomposition method investigated here is called repeated decomposition with conflict repair (RDCR) and it consists of repeatedly applying a phase of problem decomposition and sub-problem solving, followed by a phase dedicated to conflict repair. In order to deal with the time-dependent activities constraints, the problem decomposition puts all activities associated to the same location and their dependent activities in the same sub-problem. This is to guarantee the satisfaction of time-dependent activities constraints as each sub-problem is solved exactly with an exact solver. Once the assignments are made, the time windows of dependent activities are fixed even if those activities are subject to the repair phase. The paper presents an experimental study to assess the performance of the decomposition method when compared to a tailored greedy heuristic. Results show that the proposed RDCR is an effective approach to harness the power of mixed integer programming solvers to tackle the difficult and highly constrained WSRP in practical computational time. Also, an analysis is conducted in order to understand how the performance of the different solution methods (the decomposition, the tailored heuristic and the MIP solver) is affected by the size of the problem instances and other features of the problem. The paper concludes by making some recommendations on the type of method that could be more suitable for different problem sizes