Abstract--This paper considers a problem for scheduling jobs on two identical parallel machines, the aim was to minimize two criteria in particular, makespan and total flow time. In order to solve this problem, two approaches were considered. A mechanism was proposed as an approach to solve this type of problem with a setting of a 2-player non-cooperative game, under the framework of a 2x2 non-sum zero matrix; each player looking after one of the criteria suggested in the scheduling problem. On the other hand, a Genetic Algorithm, known as Strength Pareto Evolutionary Algorithm (SPEA), was applied to the problem. The comparison between both approaches suggests a complementarity among rational agents approach models and machine enforced solution approaches. The resulting Pareto Front set of points were plotted and curves were compared, showing promising results for game theoretic applications to scheduling under multiple objectives.Keywords-identical parallel machines, makespan, total flow time, non-cooperative game, SPEA, Pareto Front.Resumen--Este articulo contempla el problema de programación de la producción en una configuracion de maquinas en paralelo con el objetivo de minimizar dos criterios en particular: el lapso y el tiempo total de flujo. En este problema en particular, el incremento de uno de estos objetivos resulta en la reduccion del otro, por lo que se propone su solucion bajo enfoques metaheuristicos. Dos tipos de algoritmos fueron considerados: uno basado en la teoria de juegos y el otro en los algoritmos genéticos. Para el primero se diseña un mecanismo de juego no cooperativo entre dos jugadores, en donde cada jugador busca optimizar cada criterio de programación de las máquinas. Para el segundo enfoque se implementa el algortimo genético SPEA, en donde se seleccionan aquellas soluciones dominantes en ambos objetivos. Resultados de ambos enfoques resultan en un Frente de Pareto, las cuales representan las soluciones dominantes para ambos objetivos. Estos resultados demuestran que ambos enfoques son complementarios: SPEA arroja resultados que cubren todo el frente de Pareto, mientras que el algoritmo de Juegos No Cooperativo indica la programación mas conveniente para cada agente en particular.
The success of any project lies in a great manner on keeping costs in the estimated values, as well as meeting customer required due date. Therefore, there is a current need of developing an information system that facilitates the creation and managing of projects and their processes, including costing schemes, as well as monitoring an optimizing project's makespan. In order to address this situation a user-friendly information system (IS) was developed. This IS includes an optimization module that reduces the project's execution time, thus, minimizing costs and ultimately providing the manager with the right tools for the correct development of the project. Therefore, a better planning of activities in a reduced time is accomplished. In this way, the project manager is equipped with a decision support system (DSS) that allows a better decision making and, thanks to this performance optimization, a cost-effective solution can be delivered to the company. The optimization module is the main innovative component in this IS, considering that addresses the problem as a multiobjective one, considering at the same time makespan and cost. This module is based on global bacteria optimization (GBO). This becomes the most relevant improvement when compared to other ISs in the market.
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