The optimal control of a single machine processing a certain number of jobs and modelled as a discrete-event dynamic system is considered. The sequence of jobs is fixed, whereas their timing and ...sizes represent the control variables of the system. The objective function to be optimised is a weighted sum of the inventory cost and of the quadratic deviations of job lot-sizes and completion times from those specified by the production demand. The problem is formalised as a multistage optimal control problem and solved by a procedure making use of dynamic programming techniques; in this way, a proper real time control scheme is obtained.
A model of an intermodal terminal in which freight only arrives and departs stored in containers is presented. The container terminal is thought of as divided into areas, each one associated with a ...kind of container handling operation. The complexity of the system to represent is further increased by the fact that the material transportation system inside the terminal is (at least) partially automated. For such a transportation system, made up of different kinds of (unmanned) vehicles, a Petri net model is proposed, with the objective of regulating its faulty behaviours. An example relevant to a case study is reported to show a practical application of the proposed model.
The problem of optimally defining and controlling the behaviour of a single machine processing a certain number of jobs and modelled as a discrete event dynamic system is addressed. The number of ...jobs, their sizes, and their service sequence are fixed, whereas their timing is the matter of the optimisation problem. The objective function to be optimised is a weighted sum of the inventory cost of the quadratic deviations from the due-dates of jobs and their completion times, and the quadratic deviations between the unitary processing times of jobs and those specified by the regular system functioning. An optimisation problem with quadratic cost function and nonlinear constraints is stated and formalised as a multi-stage optimal control problem. The control problem is solved by a procedure making use of dynamic programming techniques; the optimal closed-loop control laws at each stage are thus obtained.
Significant classes of transportation systems can be represented by Petri net models. In this paper, Petri nets are applied to provide a modular representation of urban traffic systems regulated by ...signalized intersections. The basic idea is to consider such systems to be composed of elementary structural components, namely, intersections and road stretches. In order to describe thoroughly the movement of vehicles in the traffic network, a microscopic representation is adopted and realized via timed Petri nets. An interesting feature of the designed model consists in the possibility of representing the offsets among different traffic light cycles as embedded in the structure of the model itself. In turn, that allows us to simply implement the coordination among traffic light timings, which facilitates the description and solution of the relevant optimization problems.
A novel hybrid model for transportation systems is proposed, in which the functioning is represented via a continuous-time model whenever no changes in the traffic flow occur, whereas the changes in ...the system behaviour are modelled through a discrete event system coupled with the continuous-time system, on which acts as a regulator. The hybrid modelling methodology proposed is based on the use of a special class of Petri nets, the hybrid stochastic Petri nets (HSPN). These nets are composed of some discrete parts, and some continuous parts. The discrete part of the HSPN 'regulates' the continuous PN, which models the functioning of the transportation system, making the continuous-time part adapt according to the variation occurred in the system behaviour. As a result, the model reacts to any change in the current system behaviour by adapting the traffic parameters to the new state.
This paper formalizes a unique decisional framework to state different problems relevant to automated manufacturing systems, such as production planning, material requirements planning, and online ...management. Since the manufacturing systems are modelled as discrete-event systems, the (timed) Petri net formalism can be adopted to represent their dynamics. Moreover, in order to make the decisional problems addressed computationally tractable, it is assumed that the manufacturing systems can be represented by means of a particular class of timed Petri nets-the timed event graphs. Two particular optimization problems are discussed in the paper: the first one is relevant to the minimization of production and inventory costs, while satisfying a pre-specified production demand; and the second one refers to an online management problem in which the deviations between the actual system behaviour and a pre-defined nominal behaviour are sought to be minimized.
The problem of providing a modular representation of urban traffic and roadways by means of Petri nets is addressed. A modular modelling methodology is presented. After defining the urban traffic ...model and identifying each one of its components, it is possible to define for each element a hybrid Petri net module (HPNM), and provide an internal representation of it at a desired level of detail. A synthesis procedure allows one to join the single modules and provide the representation of the whole urban roadway considered in terms of hybrid Petri nets. An interesting characteristic proper to the proposed methodology is the complete independence of HPNMs from their internal representations. This allows one to change the model without any effort by increasing/decreasing the specified level of detail of some HPNMs making up the HPN-model of the whole system.
Optimal lot splitting on parallel machines Di Febbraro, A.; Minciardi, R.; Sacone, S.
2001 European Control Conference (ECC),
09/2001
Conference Proceeding, Journal Article
The control of manufacturing systems consisting of a certain number of parallel machines processing a given number of jobs is addressed in this work. A decentralised scheme composed of two decisional ...levels is defined in which, at a local level, the optimal control of each single machine is considered, whereas, at a higher level, the performances of a manufacturing system consisting of several machines are optimised. The relevant optimisation problem, with a quadratic cost function and non-linear constraints, is stated and solved as a multistage control problem to which dynamic programming techniques are applied to determine the sequence of optimal control closed-loop policies.
