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This article addresses the problem of scheduling economic lots in a multi-product single-machine environment. A mixed integer non-linear programming formulation is developed, which finds the optimal sequence and economic lots. The model takes explicit account of initial inventories, setup times, allows setups to be scheduled at arbitrary epochs in continuous time and models backorders. To solve the problem we develop a hybrid approach, combining a genetic algorithm and linear programming. The approach is tested on a set of instances taken from the literature and compared with other approaches. The experimental results validate the quality of the solutions and the effectiveness of the proposed approach. [ABSTRACT FROM AUTHOR]

This paper describes a biased random-key genetic algorithm ( BRKGA) for the minimization of the open stacks problem ( MOSP). The MOSP arises in a production system scenario, and consists of determining a sequence of cutting patterns that minimize the maximum number of open stacks during the cutting process. The proposed approach combines a BRKGA and a local search procedure for generating the sequence of cutting patterns. A novel fitness function for evaluating the quality of the solutions is also developed. Computational tests are presented using available instances taken from the literature. The high quality of the solutions obtained validate the proposed approach. [ABSTRACT FROM AUTHOR]

This paper presents a local search, based on a new neighborhood for the job-shop scheduling problem, and its application within a biased random-key genetic algorithm. Schedules are constructed by decoding the chromosome supplied by the genetic algorithm with a procedure that generates active schedules. After an initial schedule is obtained, a local search heuristic, based on an extension of the graphical method of Akers, is applied to improve the solution. The new heuristic is tested on a set of 205 standard instances taken from the job-shop scheduling literature and compared with results obtained by other approaches. The new algorithm improved the best-known solution values for 57 instances. [ABSTRACT FROM AUTHOR]