Single-machine common due date total earliness/tardiness scheduling with machine unavailability

Research on non-regular performance measures is at best scarce in the deterministic machine scheduling literature with machine unavailability constraints. Moreover, almost all existing works in this area assume either that processing on jobs interrupted by an interval of machine unavailability may be resumed without any additional setup/processing or that all prior processing is lost. In this work, we intend to partially fill these gaps by studying the problem of scheduling a single machine as to minimize the total deviation of the job completion times from an unre-strictive common due date when one or several fixed intervals of unavailability are present in the planning horizon. We also put a serious effort into investigating models with semi-resumable jobs so that processing on a job interrupted by an interval of machine unavailability may later be resumed at the expense of some extra processing time. The conventional assumptions regarding resumability are also taken into account. Several interesting cases are identified and explored, depending on the resumability scheme and the location of the interval of machine unavailability with respect to the common due date. The focus of analysis is on structural properties and drawing the boundary between polynomially solvable and NP−complete cases. Pseudo-polynomial dynamic programming algorithms are devised for NP−complete variants in the ordinary sense

Resolución de un problema real de asignación de personal a proyectos de auditoría

[ES] En este trabajo se aplican métodos de programación de la producción para modelizar y resolver un problema real de asignación y secuenciación de proyectos de auditoría al que se hace frente en el órgano de control interno del gobierno federal brasileño. En este problema, un gestor debe determinar, a partir de un conjunto predefinido de proyectos (obligatorios y optativos), el calendario laboral anual de cada uno de los auditores de su equipo, teniendo por objetivo maximizar la suma de beneficios asociados a la realización de los proyectos de naturaleza optativa. Los proyectos poseen restricciones de release times y deadlines, mientras los auditores presentan restricciones de indisponibilidades deterministas. Se propone un modelo de programación entera mixta (MIP) para la comprensión matemática del problema y también para intentar resolverlo óptimamente, pero no se encuentran soluciones óptimas exactas en un tiempo de computación razonable para los propósitos de la investigación. Solamente para las instancias pequeñas y medianas (hasta 10 auditores y 110 proyectos) aleatoriamente generadas para el problema se consigue obtener buenas soluciones factibles. Para las instancias de tamaño más grande, el modelo matemático solo es capaz de encontrar una cota superior relativa a la relajación lineal del problema. De este modo, se desarrollan dos algoritmos heurísticos constructivos con el lenguaje de programación Julia, los cuales logran encontrar, en un tiempo computacional muy pequeño, soluciones de alta calidad para el conjunto total de instancias probadas. Se hace una modificación en el segundo heurístico con el objetivo de incrementar su rendimiento y, al final, mediante un análisis de variancia (ANOVA), se verifica si las medias de los valores de las soluciones encontradas por cada uno de los heurísticos presentan diferencias estadísticamente significativas.[EN] In this work, production scheduling methods are applied to model and solve a real problem of audit projects assignment and scheduling, which is faced in the internal control body of the Brazilian federal government. In this problem, a manager must determine, from a predefined set of projects (required and optional ones), the annual work calendar of each auditor of his team, with the objective of maximizing the sum of benefits associated with the execution of the optional projects. There are restrictions of release times and deadlines concerning the projects, while auditors have restrictions related to deterministic unavailabilities. A mixed integer linear programming model (MIP) is proposed for the mathematical understanding of the problem and still for trying to solve it optimally, but no exact optimal solutions are found in a reasonable computational time for the purposes of the investigation. Only for small and medium-sized instances (up to 10 auditors and 110 projects) randomly generated for the problem, good feasible solutions can be obtained. For larger instances, the mathematical model is only able to find a best bound related to the linear relaxation of the problem. Then, two constructive heuristic algorithms are developed with Julia programming language, which succeed to find, in a very small computational time, high quality solutions for all randomly generated instances of the problem. A modification is introduced in the second heuristic with the aim of increase its performance and, finally, through a variance analysis (ANOVA), it is verified if the means of the solutions found by each heuristic differ amongst themselves in a statistically significant way.Teodoro Lima, R. (2019). Resolución de un problema real de asignación de personal a proyectos de auditoría. http://hdl.handle.net/10251/129497TFG