Modelos y métricas para la versión robusta del Car Sequencing Problem con Flotas de vehículos especiales

Joaquín Bautista-Valhondo

Resumen


Partiendo del Car Sequencing Problem (CSP), introducimos el concepto de demanda parcial incierta, incorporando Flotas de vehículos especiales en un plan de demanda. Tras establecer las hipótesis de trabajo con Flotas, proponemos un modelo de programación lineal entera mixta (r-CSP) para satisfacer el máximo número de restric-ciones del CSP. Posteriormente, definimos multi-secuencia de producción y algunas métricas para evaluar su robustez. El r-CSP considera diversos escenarios de demanda y funciones para medir el requerimiento excesivo de opciones en programas de produc-ción. Dichas funciones son válidas como objetivo en problemas de optimización y como métricas de robustez de multi-secuencias de producción.

Palabras clave: Líneas de montaje, Secuenciación, Car Sequencing Problem, Flotas de vehículos, Optimización Robusta, Mix de Producción, Demanda incierta.


Models and metrics for the Robust version of the Car Sequencing Problem with Fleets of special vehicles

Abstract: In this paper we present a new problem of sequencing in assembly lines of mixed models under the name Car Sequencing Problem with Fleets of special vehicles and the acronym r-CSP (robust-CSP). After introducing the concept uncertain partial demand in Fleets of special vehicles with its peculiarities and to pose the hypotheses of the problem, we have formulated a model of optimization based In mixed integer linear programming (MILP), whose operation results in a multi-sequence manufacturing. With our proposal, the original CSP becomes a particular case of r-CSP, when there is a single product demand plan. The definition of multi-sequence allows to incorporate the concept robustness in the problems of sequencing mixed models with uncertain partial demand. For the specific case of r-CSP, we propose 7 metrics to evaluate the non-robustness and robustness of a solution; these metrics can also be used as objective functions giving rise to several mono and multi-objective variants of the optimization problem. The dimensions of the proposed optimization models are of the order of 23000 binary variables and 38000 explicit constraints of a linear nature, when considering instances of industrial size: 20 types of regular vehicles, 5 types of vehicle fleets, 10 types of optional components and 10 different demand plans, each containing 135 vehicles in one shift. Although this dimension of problem is approachable to obtain solutions through MILP, it is convenient and advisable to also resort to the use of metaheuristics to solve r-CSP. Obviously the proposals included in this work can be incorporated into other problems of sequencing mixed models in production lines, or in other scheduling problems, when the right circumstances occur.

Keywords: Assembly Lines, Sequencing, Car Sequencing Problem, Vehicle Fleets, Robust Optimization, Production Mix, Uncertain Demand.

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