21 November 1995 Direct generation of event-timing equations for generalized flow shop systems
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Abstract
Flow shop production lines are very common in manufacturing systems such as car assemblies, manufacturing of electronic circuits, etc. In this paper, a systematic procedure is given for generating event-timing equations directly from the machine interconnections for a generalized flow shop system. The events considered here correspond to completion times of machine operations. It is assumed that the scheduling policy is cyclic (periodic). For a given flow shop system, the open connection dynamics of the machines are derived first. Then interconnection matrices characterizing the routing of parts in the system are obtained from the given system configuration. The open connection dynamics of the machines and the interconnection matrices are then combined together to obtain the overall system dynamics given by an equation of the form X(k+1) equals A(k)X(k) B(k)V(k+1) defined over the max-plus algebra. Here the state X(k) is the vector of completion times and V(k+1) is an external input vector consisting of the arrival times of parts. It is shown that if the machines are numbered in an appropriate way and the states are selected according to certain rules, the matrix A(k) will be in a special (canonical) form. The model obtained here is useful or the analysis of system behavior and for carrying out simulations. In particular, the canonical form of A(k) enables one to study system bottlenecks and the minimal cycle time during steady-state operation. The approach presented in this paper is believed to be more straightforward compared to existing max-plus algebra formulations of flow shop systems. In particular, three advantages of the proposed approach are: (1) it yields timing equations directly from the system configuration and hence there is no need to first derive a Petri net or a digraph equivalent of the system; (2) a change in the system configuration only affects the interconnection matrices and hence does not require rederiving the entire set of equations; (3) the system model is easily put into code using existing software packages such as MATLAB.
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Ali Doustmohammadi, Ali Doustmohammadi, Edward W. Kamen, Edward W. Kamen, } "Direct generation of event-timing equations for generalized flow shop systems", Proc. SPIE 2596, Modeling, Simulation, and Control Technologies for Manufacturing, (21 November 1995); doi: 10.1117/12.227228; https://doi.org/10.1117/12.227228
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