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 Probl. Upr., 2010, Issue 3, Pages 17–25 (Mi pu28)

Mathematical problems of control theory

Solution of the generalized johnson problem with constraints on the schedule and time of the machine. Part 1. Exact solution methods

Yu. A. Zak

European Centre for Mechatronics Reutershagweg

Abstract: The problem of finding an optimal permutation which determines the sequence of a set of tasks in a fixed and equal for all tasks sequence of execution of certain works on different machines, is generalized to the case when the restrictions on the start and end time both for execution of individual tasks, and the time of equipment work are set. The properties of admissible and optimal sequence of tasks are studied. The formulas for calculating the lower limit of the total length of the schedule are presented. Exact and approximate methods for solving the problem are developed.

Keywords: flow-shop problem, optimal schedule, the sequence of assignments, restrictions on the start and end time.

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Document Type: Article
UDC: 519.8

Citation: Yu. A. Zak, “Solution of the generalized johnson problem with constraints on the schedule and time of the machine. Part 1. Exact solution methods”, Probl. Upr., 2010, no. 3, 17–25

Citation in format AMSBIB
\Bibitem{Zak10} \by Yu.~A.~Zak \paper Solution of the generalized johnson problem with constraints on the schedule and time of the machine. Part~1. Exact solution methods \jour Probl. Upr. \yr 2010 \issue 3 \pages 17--25 \mathnet{http://mi.mathnet.ru/pu28} 

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This publication is cited in the following articles:
1. Yu. A. Zak, “Reshenie obobschennoi zadachi Dzhonsona s ogranicheniyami na sroki vypolneniya zadanii i vremena raboty mashin. Ch. 2. Priblizhennye metody resheniya”, Probl. upravl., 4 (2010), 12–19
2. Yu. A. Zak, “Postroenie raspisanii vypolneniya zadanii dlya parallelno rabotayuschikh sistem mashin i potochnykh linii”, Probl. upravl., 6 (2013), 62–70
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