Abstract:We consider the problem of scheduling jobs on two parallel identical machines where an optimal schedule is defined as one that gives the smallest total flowtime (the sum of the completion time of all jobs) among the set of schedules with optimal makespan (the completion time of the latest job). Utilizing an existing optimization algorithm for the minimization of makespan, we propose an algorithm to determine optimal schedules for this problem. We empirically show that the proposed algorithm can quickly find op… Show more
“…Constraints (6) and (7) ensure that a sheet is only processed when its predecessor is finished. Constraint (8) calculates the makespan for the batch of sheets. Constraint (9) ensures that every workpiece is included on a sheet and hence produced.…”
Section: Appendixmentioning
confidence: 99%
“…Solution approaches for standard problems related to the problem considered in this article have already been suggested. Gupta and Ho [8] consider the parallel machines problem for finding an optimal schedule with the smallest total flow time among the schedules with optimal makespan. Bagga and Bhambani [9] propose a simple procedure for obtaining the sequence that minimises total flow time subject to minimum makespan in the flowshop problem.…”
Sheet-metal parts typically follow a unidirectional flow in the sheet-metal shop. In the first cutting stage, a large sheet is cut to different unfolded parts with a laser cutting machine. To avoid waste material different parts are combined on a sheet. Next, the 2D parts are transformed to 3D products with air bending. In this bending stage, timeconsuming set-ups between production layouts are reduced as much as possible. Separate optimisation of cutting and air bending causes the optimisation benefits to counteract one another. Integrated models have been proposed for both singleand multiple-machine classes, but calculation times are too high and avoidable changeovers still occur.In this paper, by applying variable neighbourhood search with a number of different starting solutions, local optima of good quality are determined for minimising the makespan and the total flow time for both the single-machine and the multi-machine classes. Because the two performance measures are important for a good production plan, bicriteria optimisation by means of a simultaneous and a hierarchical approach, is also considered. Compared to the mathematical programming models for the combined cutting and bending operations, both quality and required computation time are improved for several real-life instances.
“…Constraints (6) and (7) ensure that a sheet is only processed when its predecessor is finished. Constraint (8) calculates the makespan for the batch of sheets. Constraint (9) ensures that every workpiece is included on a sheet and hence produced.…”
Section: Appendixmentioning
confidence: 99%
“…Solution approaches for standard problems related to the problem considered in this article have already been suggested. Gupta and Ho [8] consider the parallel machines problem for finding an optimal schedule with the smallest total flow time among the schedules with optimal makespan. Bagga and Bhambani [9] propose a simple procedure for obtaining the sequence that minimises total flow time subject to minimum makespan in the flowshop problem.…”
Sheet-metal parts typically follow a unidirectional flow in the sheet-metal shop. In the first cutting stage, a large sheet is cut to different unfolded parts with a laser cutting machine. To avoid waste material different parts are combined on a sheet. Next, the 2D parts are transformed to 3D products with air bending. In this bending stage, timeconsuming set-ups between production layouts are reduced as much as possible. Separate optimisation of cutting and air bending causes the optimisation benefits to counteract one another. Integrated models have been proposed for both singleand multiple-machine classes, but calculation times are too high and avoidable changeovers still occur.In this paper, by applying variable neighbourhood search with a number of different starting solutions, local optima of good quality are determined for minimising the makespan and the total flow time for both the single-machine and the multi-machine classes. Because the two performance measures are important for a good production plan, bicriteria optimisation by means of a simultaneous and a hierarchical approach, is also considered. Compared to the mathematical programming models for the combined cutting and bending operations, both quality and required computation time are improved for several real-life instances.
“…Currently, the use of hyperheuristics in the processes of production scheduling and programming in Job Shop environments has not been widely spread [4]. However, there are some hyperheuristics based on methodologies such as heuristics [5], algorithms [6][7][8][9][10], genetic algorithms [11][12][13][14], intelligent particles [15][16][17][18][19], ant colonies [20], immune systems [21], and others [22][23][24][25][26][27][28].…”
RESUMENEl objetivo del presente trabajo es disminuir el tiempo de proceso (Makespan) e incrementar el tiempo de trabajo de las máquinas, diminuyendo el tiempo de ocio en ambientes de job shop, a través del diseño de una hiperheurística basada en colonia de hormigas y algoritmos genéticos. Este trabajo se desarrolla en dos etapas: en la primera se realiza la definición e identificación de una hiperheurística para la secuenciación de procesos en ambientes job shop. En la segunda etapa es mostrada la efectividad del sistema en la programación de la producción. En el proyecto de investigación se seleccionó una empresa del sector metalmecánico, donde por medio de una combinación de colonia de hormigas y algoritmos genéticos se programa la ruta óptima para un pedido, logrando la optimización o suboptimización de su respectivo tiempo total de proceso en un porcentaje superior al 95%.Palabras clave: Taller de trabajos, programación, heurísticas, simulación, función evaluación, tiempo total de proceso, tiempo ocioso.
ABSTRACTThe objective of the present work is to diminish the total process time (Makespan)
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