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The purpose of this paper is to implement a dynamic model as a base for evaluating the resilience of a traffic network, capable of describing its evolution shortly after the occurrence of a disruptive event. First of all, a User-Equilibrium traffic assignment problem is solved in order to obtain an estimation of the system state before the disruption. Starting from the critical event, a Progressive Assignment procedure is performed in order to obtain reasonable traffic assignments on the network, taking into account the users' tolerance to increases in travel times as well as the inherent inertia of the system.

The purpose of this paper is to present an assignment model as a basis for evaluating the performance of a traffic network, capable of describing its evolution immediately after the occurrence of a disruptive event. First of all, a User-Equilibrium traffic assignment problem is solved in order to obtain an estimation of the system state before the disruption. Starting from the critical event, a Progressive Assignment procedure is performed in order to obtain reasonable traffic assignments on the network, taking into account the users’ tolerance to increases in travel times as well as the inherent inertia of the system. Therefore a metric for the description of the network performance is proposed as well as implementation of the model on a test network.

This paper proposes an optimization approach for sizing port rail networks and planning railway shunting operations by adopting a discrete-time model of the overall system. First, a mixed-integer linear mathematical programming problem is defined in order to optimize shunting operations to be performed on the considered network by satisfying certain arrivals and departures of import and export flows. Moreover, the proposed procedure can be used to evaluate the capacity of a port rail network, in terms of maximum number of trains that can be managed over a certain time horizon, and to carry out what-if analyses aimed at testing different scenarios. The effectiveness of the proposed approach is shown by applying the optimization problem to a real case study referred to the port rail network of La Spezia Container Terminal located in Northern Italy. A computational analysis realized by varying the dimension and complexity of the problem instances is also reported in this paper to discuss the computational performance of the proposed model.

Summarization: This work addresses the problem of controlling freeway traffic systems with coordinated ramp metering, by taking into account not only the reduction of travel times for the drivers but also the improvement of safety conditions. Specifically, a coordinated ramp metering control strategy is sought by defining and solving an optimal control problem in which the objective function to be minimized is a weighted sum of the total time spent and the expected number of crashes. The resulting problem is a finite-horizon nonlinear optimal control problem with constrained control variables. It is solved by applying the feasible direction algorithm, in the specific version adopting the derivative backpropagation method RPROP. The simulation results show the effectiveness of the proposed method both in reducing the total time spent by the drivers and in increasing safety conditions. Παρουσιάστηκε στο: 5th IEEE International Conference on Models and Technologies for Intelligent Transportation Systems

Summarization: The definition of a new control scheme for freeway traffic systems is the objective of the present paper. The main innovative aspect of this work stands in the fact that, besides considering the reduction of traffic congestion, also safety-related aspects are explicitly taken into account in the formulation of the control problem. More specifically, two different performance indexes including a relation between the number of accidents and the traffic density in a freeway stretch are defined. The solution of the control problem is sought by applying a derivative-free procedure in which two phases are sequentially adopted: A global search carried out through a specific version of the Simulated Annealing algorithm, and a local search performed by an algorithm chosen within an open-source library for nonlinear optimization. Some numerical results are reported in the paper to compare the two control functions and to verify the effectiveness of the proposed approach. Παρουσιάστηκε στο: 19th IEEE International Conference on Intelligent Transportation Systems

A class of production systems are considered in this paper with the aim of determining closed-loop strategies providing the production effort as functions of the system state. The key feature of the considered class of systems is that the demand and the way it is satisfied are asynchronous sequences of part requests and instantaneous withdrawals, respectively, generated by discrete-event processes, whereas the production process has continuous-time dynamics. The optimization problem, whose objective is to minimize inventory and lateness costs, is restated as an optimal control problem by exploiting some structural properties of the optimal solution. Then, optimal closed-loop strategies are found with dynamic programming techniques.

The objective of this work is to study optimal Vendor-Managed Inventory policies in distributions systems in which demand and delivery processes are characterized by a discrete-event dynamics. In Vendor-Managed Inventory policies, the supplier organizes the deliveries to the customer in order to satisfy its demand by minimizing transportation costs and holding costs of the customer. In the considered case, a simple network composed of one supplier and one customer is studied, in which the supplier can use a limited number of capacitated vehicles; the objective is to plan the delivery policy over a finite horizon. The optimization problem resulting from the considered system characterized by discrete-event processes is then rewritten in a discrete-time form. For this problem different solution methods are proposed in the paper, based on the statement of mathematical programming problems and the definition of appropriate algorithms. These methods are then compared through some experimental results.

The optimal control of a single machine processing a certain number of jobs and modeled as a discrete-event dynamic system is considered. The number of jobs and their sequence are fixed, whereas their timing and sizes represent the control variables of the system. The objective function to be optimized is a weighted sum of the quadratic earliness and tardiness of each job, and of the quadratic deviations of job lot sizes and actual machine service speeds from those specified by the production demand and by the regular machine speeds. An optimization problem with quadratic cost function and nonlinear constraints is stated and formalized as a multistage optimal control problem. Necessary conditions to be satisfied by an optimal control sequence are derived. A simpler model is also considered in which the machine speeds are fixed; in this case, the control problem is solved by a procedure making use of dynamic programming techniques. The optimal control laws at each stage are thus obtained.

This paper deals with mixed logical dynamical systems controlled via model predictive schemes. For this class of systems a centralized MPC approach is firstly introduced, in which the finite horizon optimal control problem is a mixed-integer quadratic programming problem aiming at minimizing the deviations of the system variables from their equilibrium points. Since the application in real time of these MPC schemes is sometimes limited because of the high computational load necessary to solve the finite horizon optimal control problem, a distributed MPC scheme is proposed, characterized by two different and alternative algorithms. An important application is then introduced to assess the proposed approaches, i.e. ramp metering freeway traffic control. Referring to this applicative case, the two distributed control algorithms are compared, via simulation, with the centralized MPC scheme and with a completely decentralized one.

This paper deals with a distribution system with one origin and one destination in which the shipments are realized with a limited fleet of capacitated vehicles. An optimization problem is defined to find the optimal shipment policies in order to satisfy the external demand, by minimizing holding costs of the customer and transportation costs. Note to Practitioners - A distribution system with one origin and one destination characterized by a Vendor-Managed Inventory policy is considered. In such a system the supplier plans the deliveries to the customer in order to minimize the customer's inventory and the transportation costs. Besides the definition of some solution methods based on mathematical programming techniques, an algorithmic approach for solving the considered optimization problem is also derived in this paper. Even though this approach is suboptimal, it provides very effective solutions and its major strength stands in the possibility of easily implementing it without the use of mathematical programming solvers.

A model of a cyclic manufacturing system representable as a deterministic timed event graph is considered in this paper. It is possible to apply analytical techniques for performance evaluation of such systems. On this basis, a two-level optimization problem is considered. The higher level refers to the maximization of the system productivity with respect to the assignment of operations to machines, the lot sizes, and the service sequences at the various machines, assuming that unlimited work-in-progress and buffers of finite dimension are available. The lower level deals with the minimization of an aggregate cost taking into account the work-in-progress and the buffer dimensions.

The paper is aimed at the definition of an efficient control framework for freeway systems. To this end, a Model Predictive Control scheme based on the cell transmission model is adopted in which the considered control action refers to ramp metering. Two major aspects characterize the paper. First, the prediction model is formulated as a mixed logical dynamical system (i.e. it is described by linear dynamic equations and linear inequalities in which both real and integer variables are involved) in order to obtain a finite-horizon optimal control problem with the structure of a mixed-integer quadratic programming problem. In such a problem the objective function quadratically penalizes the deviation of the state variables from a specific equilibrium point. Secondly, an event-triggered scheme is used to further reduce the computational load of the control scheme making it more adequate for real applications. Numerical results based on data coming from a real case study relevant to Grenoble South Ring are also presented and discussed.

This paper proposes a heuristic decomposition approach for scheduling truck trips with the goal of satisfying the demand of a container single carrier while minimizing its costs. The approach foresees three phases: a pre-processing step, in which the demand is decomposed in two parts and a set of rules for combining trips are defined, and two optimization phases. The first mixed linear integer optimization model allows to combine trips two by two in order to decrease the number of empty or partially empty trips, while the second optimization problem enables assigning trucks to trips with the goal of minimizing travel costs. The efficiency of the proposed methodology is analyzed using a real simple case over a local network and the results are presented.

A two-level framework is proposed in this paper for a class of complex systems in order to optimize, at a tactical planning level, the activities over a medium-term horizon, and to control, at an operational level, the system resource functioning over a short-term horizon or in real time. At the tactical planning level, an aggregate model of the system is defined and an optimization problem is stated and solved; the optimal solution of such a problem provides a reference plan to be tracked. At the operational level, both optimal control strategies are employed to face perturbations that may affect the system, and a detailed discrete-event or hybrid model is defined to verify some properties and performance indexes of the system. The application of the proposed framework to a logistic intermodal node is illustrated.

Objective of this paper is to define an efficient control framework for freeway systems based on ramp metering. First of all, a Model Predictive Control (MPC) scheme is proposed in which the well known nonlinear cell transmission model (CTM) is used for the prediction. The model is then reformulated as a mixed logical dynamical (MLD) system, i.e. it is described by linear dynamic equations and linear inequalities in which both continuous and binary variables are present. In this way, the finite-horizon optimal control problem in the MPC scheme is transformed into a mixed integer quadratic programming problem whose objective function quadratically penalizes the deviation of the state variables from a specific equilibrium point. It is shown that the resulting control law stabilizes the system. Moreover, in order to make it more suitable for a real-time use, the foregoing control strategy is redesigned into an event-triggered control scheme. The idea is to update the control law only when the considered error exceeds a pre-specified threshold. Simulation results demonstrate how the use of the triggering rule allows to preserve the good performance of the proposed control scheme, while reducing the overall computational load.

The main objective of this work is to model and optimize the rail cycle in seaport terminals. The model proposed in the paper represents the transfer of import containers from their storage in the yard until their exit from the terminal by train. At this purpose, the standing of containers and their movements inside the terminal are modelled by a set of queues, whose dynamic evolution is described by discrete-time equations, where the state variables represent the queue lengths and the control variables take into account the utilization of terminal resources (handling systems as well as tracks) and the timing of train movements from the terminal towards their destinations. On the basis of this model, an optimization problem is defined that consists in minimizing the transfer delays of containers in the terminal while satisfying specific real constraints. This model has been tested on real data regarding an Italian container terminal, as reported in the paper.

This paper deals with an inventory-production system in which raw parts are transformed into processed parts, in order to satisfy a time-varying positive demand over a given time horizon. The production resource is capacitated whereas the inventory is unbounded; the external demand is known and is expressed as a piecewise constant function changing at asynchronous time instants. The objective is to find the optimal service speed pattern, assumed to be a piecewise constant function, which minimizes setup, production, and holding costs; hence, the decisions concern both the values of the service speed and the (asynchronous) time instants at which it changes. The optimization problem defined for this class of systems has a parametric structure and includes both nonlinear and combinatorial aspects. In the paper, some structural properties of any optimal solution are firstly proven, and then a solution procedure that allows finding an optimal solution in polynomial times is provided.

In this paper we deal with the operational planning of transportation operations in an intermodal network. The objective is to satisfy a given transportation demand by using road vehicles and trains, in order to minimize the total transportation cost and meeting a set of operational constraints. We propose a linear integer programming model and an Ant Colony Optimization metaheuristic approach in a pure and a hybrid version. We present and compare the results obtained testing all the approaches on a benchmark set made of randomly generated problem instances. The tests show the appreciable behavior of the IP model, that however requires a considerable amount of time, and the ability of the hybrid ACO to generate high quality solutions for all the benchmark instances with a quite reduced computational effort.

In this paper we present two mathematical formulations and a heuristic approach for the train load planning problem of import containers at a seaport container terminal. The problem consists of determining how to assign a set of containers of different length and weight to the wagons of a train in order to satisfy capacity constraints of both the wagons and the train, while minimizing the rehandling operations in the stocking area where containers are waiting for being loaded on trains and maximizing the train utilization. Some computational results will be reported in the paper in which the heuristic approach is compared with the solution of the mathematical programming formulation.

In this paper we propose a planning procedure for serving freight transportation requests in a railway network with fast transfer equipment at terminals. We consider a transportation system where different customers make their requests (orders) for moving boxes, i.e., either containers or swap bodies, between different origins and destinations, with specific requirements on delivery times. The decisions to be taken concern the route (and the corresponding sequence of trains) that each box follows in the network and the assignment of boxes to train wagons, taking into account that boxes can change more than one train and that train timetables are fixed. The planning procedure includes a pre-analysis step to determine all the possible sequences of trains for serving each order, followed by the solution of a 0–1 linear programming problem to find the optimal assignment of each box to a train sequence and to a specific wagon for each train in the sequence. This latter is a generalized assignment problem which is NP-hard. Hence, in order to find good solutions in acceptable computation times, two MIP heuristic approaches are proposed and tested through an experimental analysis considering realistic problem instances.

The paper deals with the optimal control of production processes characterized by the possibility of performing operations (relevant to the processing of a set of jobs) with variable execution times. A production process relevant to a single machine is addressed first. An optimization problem with a quite general cost function is considered, and some properties of optimal solutions are derived. Then, a particular version of the problem is analyzed, in which the cost function is the weighted sum of the quadratic earliness and tardiness of jobs and of quadratic deviations between pre-defined nominal unitary processing times and the actual ones. The decision variables of the problem are the possible idle times inserted before job executions and the processing times of jobs. This single machine problem is stated as an optimal control problem and a closed-loop solution is derived. Then, a second production process is considered, in which multiple machines serve jobs in parallel, again with variable processing times and with different processing costs. With reference to this second production scheme, a significant decision problem refers to the splitting of jobs over the different machines. Then, on the basis of a sensitivity analysis of the single machine problem solution, some conditions to verify the optimality of a pre-defined splitting are derived. An on-line splitting scheme using such conditions is finally presented.

A specific class of production systems is considered in this paper with the aim of minimizing inventory and production costs, over a finite horizon. In such a class of systems, all processes (arrival and departure of parts, production, demand to be satisfied) are modelled as piece-wise constant functions that change their values at asynchronous time instants. The decision variables are the constant rate at which raw parts enter the system and the service rate at the various time instants. In the paper, both the case of completely known demand and that of incomplete demand is taken into account. In both cases, a solution algorithm is provided in order to determine the optimal (or sub-optimal, in case of incomplete demand) solution of the optimization problem.

A production node within a network of interconnected production centers (as in supply chains) is considered in this paper, with the aim of optimizing inventory levels and production effort. The proposed Hybrid Inventory-Production model consists of two inventories (the input one for raw parts and the output one for processed parts) and a production resource which transforms parts and moves them from the input to the output inventory, at a certain rate. The production node interacts with other nodes in the network by the arrival process (raw parts entering the node) and the departure process (processed parts leaving the node). In HIP systems, arrival and departure processes, as well as the production process, are supposed to be piece-wise constant functions that change their values at asynchronous time instants. Based on this model and considering different cost terms, a mixed-integer nonlinear optimization problem has been defined. Then, some assumptions have been considered and the optimization problem has been simplified until obtaining a linear statement.

In this paper, supply chain nodes are considered, with the aim of optimizing the production of parts belonging to different classes (the case of two classes is here taken into account). The production node is modelled by a discrete-event model, being the system state, consisting of the continuous level of input and output inventories, affected by the asynchronous processes relevant to part arrivals and product departures. Moreover, also the resource capacity of the node is represented by a continuous variable (to be shared among the two classes). In the paper, two optimization problems are proposed: the former is only stated due to its intrinsic complexity, whereas the latter (a simplified version of the former) is stated and solved. In the latter problem, an optimization is performed each time an event occurs, in order to determine which the next event is, when the next event will occur, how many raw parts/products will arrive/depart, and which portions of production capacity are assigned to the two classes.

The main objective of this paper consists in modelling, optimizing, and controlling container transfer operations inside intermodal terminals. More specifically, maritime container terminals are here considered, involving three kinds of transportation modes, i.e., maritime, rail, and road transport. Generally speaking, an intermodal port terminal can be seen as a system of container flows with two interfaces, towards the hinterland and towards the sea, respectively. Moreover, inside a terminal, unloading operations of inbound containers, container storage, and loading operations of outbound containers are carried out. A simple model for maritime container terminals is proposed in this paper. In the model, a system of queues represents the standing of containers and their movements inside the terminal. The dynamic evolutions of these queues are described by discrete-time equations, where the state variables represent the queue lengths and the control variables take into account the utilization of terminal resources such as load/unload handling rates. On the basis of the proposed model, an optimization problem is defined that consists in minimizing the transfer delays of containers in the terminal. The problem is stated as an optimal control problem whose solution is sought by adopting a receding-horizon strategy.

A multiple model based nonlinear control scheme for nonlinear discrete-time systems is considered. A set of optimal receding-horizon feedback control functions is defined, based on a description of the nonlinear plant by means of interpolation of a set of local models, using a family of nonlinear validity functions. To obtain the control law to be applied to the plant, interpolation of the local control actions is done, using the same validity function family. This choice allows to carry out the stability analysis of the equilibrium of the multiple model control scheme.

This paper shows that it is possible to formalize and to put in a proper form an optimization problem consisting in the optimization of the work-in-progress (WIP) in a manufacturing system, while ensuring a minimum value for the throughput of each product. The decision variables involved in this problem are the lot sizes for the various products and components and the system initial state, as regards the number of tokens in each place of the net. In spite of the limited modelling capability of timed event graphs, the considered structure of manufacturing systems is by no means trivial. Actually, the fact that the set of decision variables includes the lot sizes makes the production flows in the system optimized in practice. The main novelty of this paper with respect to previous works concerns the possibility of dealing with situations in which no machine acts as a bottleneck one. The optimization problem arising is thus more difficult than the two-level optimization problem.

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 decentralized scheme is defined in which at a local level, the optimal control of each single machine is considered, whereas, at a higher level, the optimal splitting of jobs on parallel machines is taken into account. At the local level, an optimization problem with quadratic cost function and nonlinear constraints is stated as a multistage control problem and solved by means of dynamic programming techniques.

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.

The optimal control of a production facility consisting of a single machine processing a certain number of jobs with a fixed service sequence is considered. The objective of the problem is that of determining the optimal timing and lot-sizing of the considered jobs. Necessary conditions for optimality are derived which allow the determination of an optimal solution for the control problem.

Timed Event Graphs can be applied successfully to the modelling, the analysis and the optimization of manufacturing systems. The choice of using such a particular class of Petri Nets allows to apply a set of related algebraic results to determine some performance measures as functions of a set of decision parameters. On this basis, performance optimization problems can be posed and solved as mathematical programming problems. In this paper, the problem consisting in the maximization of the weighted system throughput, while keeping the steady-state flow time of each product limited by an a-priori upper bound, is considered. This problem turns out to be a linear fractional programming one, which can be solved by means of standard techniques and software tools.

Some problems related to modelling and controlling an intermodal urban transportation system are addressed in this paper. The transportation network is modelled as an oriented graph in which nodes represent single-mode or intermodal stations. For the system considered, a discrete event model integrating different transportation services is proposed. Some disturbances are included to model the stochastic nature of the system. Based on such a model, a special-purpose traffic simulator has been designed. It produces the data necessary to solve the optimization problem which has the objective of guaranteeing the regularity of the transportation services, i.e., the fulfilment of the timetable. Due to the presence of a statistically unknown noise, such an optimization problem results in a particular tracking problem, which cannot be solved by applying the dynamic programming. Thus, a heuristic solution is proposed, reporting also some experimental results about its performance.

A model of manufacturing systems is considered in which several classes of products are repeatedly manufactured, according to the requirements specified by customer orders. The problem considered is the development of control strategies capable of reacting to deviations of the system behaviour from a nominal behaviour defined solving a suitable problem at the scheduling level. The degrees of freedom allowed for the control problem are: the execution times of some elementary operations, the lot-sizes, and the variables expressing the timing of the production process. It is shown that, under suitable hypotheses about the nominal behaviour, the system can be represented by means of a particular class of timed Petri nets. Moreover, the structure of the control problem is that of a continuous variable problem with quadratic cost and linear (or sometimes quadratic) constraints.

The class of Petri nets denoted as timed event graphs can be used to represent a wide class of manufacturing systems. This fact allows one to apply analytical techniques for performance evaluation of such Petri nets. This, in turn, permits to state mathematical programming problems whose objective is the optimization of manufacturing system performances. In this paper, the optimization of the system throughput is considered, with respect to the definition of the lot sizes in a cyclic manufacturing process. As a secondary optimization objective, the minimization of the work-in-progress, while keeping the system working at its maximum productivity, is considered. >

In this paper, the proposed Hybrid Inventory-Production model represents a manufacturing center with two inventories (the input one for raw parts and the output one for processed parts) and a production resource which moves parts from the input to the output inventory, at a certain rate. In the considered modelling framework, time-driven and event-driven dynamics coexist, yielding to a hybrid system. An optimization problem is defined where decisions concern the production process (piece-wise constant function changing its value at asynchronous time instants) and the arrival process. Then, an optimal control problem is stated in order to find the closed-loop solutions as functions of the system state. In particular, a multi-stage optimal control problem is defined and it is solved by applying dynamic programming techniques.

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.

A hybrid model for the representation of a generic production center of a supply chain is presented and discussed in this paper. The model is characterized by two inventory levels (defined as continuous variables) and by arrival and departure processes of raw materials and final products modelled as finite and discrete-time sequences which are realized in asynchronous time instants. An optimization problem relevant to the minimization of the inventory cost for raw materials and of order costs is introduced and solved. The decision variables of the problem are relevant to the arrival process (as they correspond to the number of orders, the time instants in which raw materials enter the node and the ordered quantities). Some important properties of the optimal solution are proved in the paper and a solution procedure is provided.

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.

The objective of the paper is to show that relatively complex manufacturing systems can be modeled as time event graphs and that significant optimization problems can be stated and solved using this representation. Particular attention is focused on the multi-objective optimization of the system throughput, and of a function weighting the work-in-progress along with the buffer space in finite buffers, with respect to: 1) the lot-sizes of the components flowing through the system; 2) the service sequences at the various machines; and 3) the work-in-progress and the (finite) buffer sizes. A two-step optimization procedure has been set up, in which the first step corresponds to the maximization of the system throughput, under the assumption of unlimited work-in-progress and buffer sizes. As a second step, the minimization of the remaining objective is carried out taking into account the constraint of achieving the optimum throughput provided by the solution of the higher level problem. Both the above problems are intrinsically combinatorial. In particular, for the higher level problem, a branch-and-bound approach is proposed, where at each node a relaxed problem having a linear fractional structure is solved. Despite the limited modeling capability of timed event graphs, it is possible, through the determination of the lot-sizes, to optimize the material flow in the system. Of course, the application of dynamic material flow policies is prevented in this framework. However, the optimization of the lot-sizes turns out to be equivalent to that of static routing coefficients. Further research activity is being devoted to the extension of the proposed approach to open (that is, non-cyclic) manufacturing systems and to the optimization of different performance objectives (for instance, the product flow times). In this case, analytic tools based on max-plus algebra are to be used, in order to obtain the expressions of the quantities of interest as functions of the decision variables.

A class of manufacturing systems that can be modelled by use of timed event graphs is considered in this paper. The interest for considering such a subclass of timed Petri nets is due to the possibility of applying a set of mathematical results, mainly based on the use of max-plus algebra, for performance analysis. Basing on these results, some significant performance indexes can be computed as functions of a certain set of decision parameters. Then, the system throughput optimization problem can be stated as a linear fractional programming problem. >