Xiaolan Xie

Deadlock analysis of Petri nets using siphons and mathematical programming

This paper exploits the potential of siphons for the analysis of Petri nets, It generalizes the well-known Commoner condition and is based on the notion of potential deadlocks which are siphons that eventually become empty. A linear programming based sufficient condition under which a siphon is not a potential deadlock is obtained. Based on the new sufficient condition, a mathematical programming approach and a mixed-integer programming approach are proposed for checking general Petri nets and structurally bounded Petri nets respectively without explicitly generating siphons. Stronger results are obtained for asymmetric choice nets and augmented marked graphs. In particular, we show that an asymmetric choice net is live iff it is potential-deadlock-free and an augmented marked graph is live and reversible iff it is potential-deadlock-free.

Design of a live and maximally permissive Petri net controller using the theory of regions

This paper addresses the forbidden state problem of Petri nets (PN) with liveness requirement and uncontrollable transitions. The proposed approach computes a maximally permissive PN controller, whenever such a controller exists. The first step, based on a Ramadge-Wonham-like reasoning (1989), determines the legal and live maximal behavior the controlled PN should have. In the second step, the theory of regions is used to design control places to add to the original model to realize the desired behavior. Furthermore, necessary and sufficient conditions for the existence of control places realizing the maximum permissive control are given. A parameterized manufacturing application of significant state space is used to show the efficiency of the proposed approach.

Deadlock prevention policy based on Petri nets and siphons

This paper presents a deadlock prevention method for a class of flexible manufacturing systems where deadlocks are caused by unmarked siphons in their Petri net models. This method is an iterative approach consisting of two main stages. At each iteration, a fast deadlock detection technique developed by mixed integer programming is used to find an unmarked maximal siphon. An algorithm is formalized that can efficiently obtain an unmarked minimal siphon from the maximal siphon. The first stage, called siphons control, of the proposed method is to add, for each unmarked minimal siphons, a control place to the original net with its output arcs to the sink transitions of the minimal siphon. The objective is to prevent a minimal siphon from being unmarked. The second stage, called augmented siphons control, is to add a control place to the modified net with its output arcs to the source transitions of the resultant net if the resource places are removed. The second stage is required since adding control places in the first stage may create new unmarked siphons. In addition, the second stage assures that there are no new unmarked siphons generated. The relation of the proposed method and the liveness and reversibility of the controlled net have been obtained. Finally, manufacturing examples are presented to illustrate the method and to allow comparison with earlier methods.

A stochastic model for operating room planning with elective and emergency demand for surgery

This paper describes a stochastic model for Operating Room (OR) planning with two types of demand for surgery: elective surgery and emergency surgery. Elective cases can be planned ahead and have a patient-related cost depending on the surgery date. Emergency cases arrive randomly and have to be performed on the day of arrival. The planning problem consists in assigning elective cases to different periods over a planning horizon in order to minimize the sum of elective patient related costs and overtime costs of operating rooms. A new stochastic mathematical programming model is first proposed. We then propose a Monte Carlo optimization method combining Monte Carlo simulation and Mixed Integer Programming. The solution of this method is proved to converge to a real optimum as the computation budget increases. Numerical results show that important gains can be realized by using a stochastic OR planning model.

A siphon-based deadlock prevention policy for flexible manufacturing systems

A siphon-based algorithm for deadlock prevention of a type of Petri nets called S3PMR, which is a subclass of S3PGR2, is presented in this correspondence. The proposed method is an iterative approach by adding two kinds of control places called ordinary control (OC) places and weighted control (WC) places to the original model to prevent siphons from being unmarked. An OC place with ordinary arcs, which optimally prevent a siphon from becoming unmarked, is employed whenever it is possible, and otherwise, the WC places that adopt a conservative policy of controlling the release of parts into the system are used. Furthermore, this algorithm is not only for the subclass Petri nets but also for S3PR, ES 3PR, S2LSPR, and S3PGR2 nets. The authors prove the liveness and reversibility of the controlled net, and hence establish the correctness of the deadlock prevention policy. Finally, numerical experiments indicate that the proposed policy appears to be more permissive than closely related approaches in the literature

A Simulation Optimization Methodology for Supplier Selection Problem

Strategic sourcing plays a critical role in supply chain planning. Supplier selection is one of the decisions that determine the long-term viability of a company. In this paper, a new simulation optimization methodology is presented to make decisions on supplier selection. The methodology is composed of three basic modules: A genetic algorithm (GA) optimizer, a discrete-event simulator and a supply chain modelling framework. The GA optimizer continuously search different supplier portfolio and related operation parameters. Corresponding simulation models are automatically created through an object-oriented process. After simulation runs, the fitness value of candidate supplier portfolio is derived from the estimations of key performance indicators (KPI). The fitness is returned to the GA to be utilized in searching the next prominent direction. By using the proposed methodology, the supply chain planner is able to optimize the supplier portfolio with taking uncertainties into consideration. Finally, a real-life case study is presented to illustrate the applicability of the proposed methodology. Experimental results are presented and analysed.

Optimisation of invariant criteria for event graphs

The problem of obtaining a cycle time that is smaller than a given value in a strongly connected event graph, while minimizing an invariant linear criterion, is addressed. This linear criterion is based on a p-invariant of the strongly connected event graph under consideration. Some properties of the optimal solution are proved, and a heuristic algorithm and an exact algorithm which make it possible to reach a solution to the problem are given. Applications of the results to the evaluation of job shops and Kanban systems are proposed. >

Joint optimization of preventive maintenance and inventory control in a production line using simulation

This paper proposes an integrated method for preventive maintenance and inventory control of a production line, composed of n machines (n ≥ 1) without intermediate buffers. The machines are subject to failures and an age-dependent preventive maintenance policy is used. Approximate analytical results are proposed for the one machine case. Simulation software is used to model and simulate the behaviour of the production line of n machines under various maintenance and inventory control strategies. A methodology combining the simulation and genetic algorithms is proposed jointly to optimize maintenance and inventory control policies. Results are compared with the analytical solutions.

ERCN-merged nets and their analysis using siphons

This paper generalizes the modular approach proposed by Jeng and DiCesare (1995) for modeling manufacturing systems with shared resources. First, the-dynamic behavior of each resource is modeled separately using extended resource control nets (ERCNs). An important feature of ERCNs is their capability to express explicitly assembly operations and parallel processes, which is not possible with resource control nets. Interactions among the resources are then modeled through merging of common transitions and common transition subnets. This paper provides conditions, expressed in terms of siphons, under which reversibility and liveness of the integrated model are obtained. Relations between siphons, circular structure and circular-wait are formally established.

Supply management in assembly systems

We consider the case when n components are needed to assemble a given product. Components are provided by suppliers, and the period between the order time and the time a component is available (i.e., the lead time) is a random variable with a known distribution. The due date for the assembled product is also known. The costs to be taken into account are the inventory costs of the components and the backlogging cost of the assembled product. We propose an iterative algorithm which leads to the optimal order instants of the components.