توزیع بهینه زمان واقعی زمان بندی شبکه های تولید انعطاف پذیر الگو گرفته به عنوان سیستم های دینامیکی هیبرید

The paper considers a class of flexible manufacturing networks. We employ hybrid dynamical systems to model such networks. The main and new achievement of the paper is that we propose a distributed implementable in real time scheduling rule such that the corresponding closed-loop system is stable and optimal. In stable systems the processes converge to periodic ones. The paper gives computing relations for the determination of the parameters of the periodic processes. These are very much suitable for planning purposes. On this basis—and this, we consider, is also a new, significant result—optimal arrival (demand) rates determination method is proposed. Quality characteristics are outlined. Field of application of hybrid dynamical approach for FMS scheduling is analyzed. The results open perspectives for MRP level task planning. Example and simulation results are presented.

Hybrid dynamical systems (HDS) have attracted considerable attention in recent years (see e.g. [1], [2] and [3] and references therein). In general, HDS are those that combine continuous and discrete behavior and involve, thereby, both continuous and discrete state variables. In many cases, such systems operate as follows. While the discrete state remains constant, the continuous one obeys a definite dynamical law. Transition to another discrete state implies a change of this law. In its turn, the discrete state evolves as soon as a certain event occurs with both the evolution and the event depending on the continuous state. The class of HDS introduced in the paper consists of complex switched server queueing networks. This class of HDS was introduced in [4] and [5] to model flexible manufacturing systems (see also [2], [6], [7], [8], [9] and [10]). A flexible manufacturing system considered in this paper produces several part-types on a network of machines. Raw parts are inputs to the network. Parts arrive at a machine and are awaiting in buffers. Each unit of a given part-type requires a predetermined processing time at each of several machines, in a given order. A set-up time is required whenever a machine switches from processing one part-type to another.

The new results outlined in this paper, namely, the proposed feedback control policy guarantee the system stability for most general cases. In stable systems, the processes converge to periodic ones as the time goes to infinity. In practice, the processes may be considered periodic for planning purposes, most frequently, after a quite short time. Even more, it is possible to construct such initial conditions which provide zero transient time. That is, in this case, the processes are periodic just from the start. Then, as it is outlined in this paper, it is possible to determine optimum arrival rates which result in the minimum of the upper limit value of the over-time coefficient which is the relation of upper limit value of production time to the net manufacturing time on the generalized bottleneck machine group. In such a way it becomes possible to determine such system parameters which provide a given, suitably small time excess comparing with the global minimum of overall completion time. Amazing feature of the given approach is that the planning procedure leads to the determination of a single parameter. This is the arrival rate coefficient k. Its optimal value is the function of the set-up relation coefficient which value is the relation of the estimation of the (highest value of the) sum of the set-up times and the net manufacturing time on the generalized bottleneck machine-group. The more flexible the systems are, the less the value of this coefficient is. Small set-up relation coefficients make the use of hybrid dynamical approach very effective. Excellent system performances may be obtained in a very simple way. The proposed method makes possible to determine the application range of hybrid dynamical control.