Karim Labadi

Modeling and performance evaluation of supply chains using batch deterministic and stochastic Petri nets

Batch deterministic and stochastic Petri nets are introduced as a tool for modeling and performance evaluation of supply chains. The new model is developed by enhancing deterministic and stochastic Petri nets (DSPNs) with batch places and batch tokens. By incorporating stochastic Petri nets (SPNs) with the batch features, inhibitor arcs, and marking-dependent weights, operational policies of supply chains such as inventory policies can be easily described in the model. Methods for structural and performance analysis of the model are developed by extending existing ones for DSPNs. As applications, an inventory system and an industrial supply chain are modeled and their performances are evaluated analytically and by simulation, respectively, using this BSPN model. The applications demonstrate that our model and associated methods can solve some important supply chain modeling and analysis issues. Note to Practitioners-This paper was motivated by the problem of performance analysis and optimization of supply chains but it also applies to other discrete event systems where materials are processed in finite discrete quantities (batches) and operations are performed in a batch way because of batch inputs and/or in order to take advantages of the economies of scale. Existing Petri net modeling and analysis tools for such systems ignore their batch features, making their modeling complicated. This paper suggests a new model called batch deterministic and stochastic Petri nets (BDSPNs) by enhancing deterministic and stochastic Petri nets with batch places and batch tokens. Methods for structural and performance analysis of the model are developed. We then show how an inventory system and a real-life supply chain can be modeled and their performances can be evaluated analytically and by simulation respectively based on the model. The model and associated analysis methods therefore provide a promising tool for modeling and performance evaluation of supply chains.

Stochastic Petri Net Modeling, Simulation and Analysis of Public Bicycle Sharing Systems

Public Bicycle-Sharing Systems (PBSS) have been appearing in more and more cities around the world in the last few years. Although their apparent success as an alternative form of public transportation mode, there are major challenges confronting the operators while few scientific works are available to support such complex dynamical systems to influence their economic viability and operational efficiency. One of the most crucial factors for the success of a PBS system is its ability to ensure that bicycles are available for pick up and vacant berths available for bicycle drop off at every station. In this paper, we develop an original discrete event approach for modelling and performance evaluation of public bicycle-sharing systems by using Petri nets with time, inhibitor arcs and variable arc weights.

Modeling and Performance Evaluation of Inventory Systems Using Batch Deterministic and Stochastic Petri Nets

This paper presents our work on modeling and performance analysis of inventory systems using batch deterministic and stochastic Petri nets (BDSPNs). It addresses issues frequently raised by industrial companies, but did not receive enough attention by the Petri nets (PNs) community in spite of its important role in the study of discrete event systems. The BDSPN is a new class of PNs capable of describing the synchronization of discrete and batch token flows in discrete batch processes. Such processes appear in inventory systems or more general supply chains where materials are purchased in finite discrete quantities (batches of different sizes), and many operations such as inventory replenishment and customer order fulfillment are usually performed in a batch way because of the batch nature of customer orders and/or in order to take advantages of the economies of scale. In this paper, the BDSPN model is formally introduced, and its conflict resolutions of transitions and batch firing indexes are addressed. The model is then applied to the modeling and performance evaluation of various inventory systems. Analytic performance evaluation techniques are developed for the model with illustrative applications to the inventory systems. Our study shows that the model is powerful for both modeling and performance evaluation of the systems.

Modeling, Analysis, and Optimization of Logistics Systems Petri Net Based Approaches

Driven by fierce global competition, effective supply chain logistics management has become one major concern of many enterprises. This has created needs for modelling, performance analysis and optimization tools that can help the enterprises to optimize their logistics networks and operations. In this paper, after demonstrating the advantages of Petri nets as modelling and analysis tools of logistics systems, an overview of the recent development on Petri net based approaches for modeling, performance analysis, and optimization of supply chains is given and future research opportunities in this area are explored

Performance evaluation of nonlinear weighted T-system

This article deals with the analysis of discrete event systems which can be modelled by timed event graphs with multipliers (TEGMs). These graphs are an extension of weighted T-systems studied in the Petri net literature. These models do not admit a linear representation in (min, +) algebra. This nonlinearity is due to the presence of weights on arcs. To mitigate this problem of nonlinearity and to apply some basic results used to analyse the performances of linear systems in dioid algebra, we propose a linearisation method of mathematical model reflecting the behaviour of a TEGM in order to obtain a (min, +) linear model.

'PSA-SPN' - A Parameter Sensitivity Analysis Method Using Stochastic Petri Nets: Application to a Production Line System

The dynamic behavior of a discrete event dynamic system can be significantly affected for some uncertain changes in its decision parameters. So, parameter sensitivity analysis would be a useful way in studying the effects of these changes on the system performance. In the past, the sensitivity analysis approaches are frequently based on simulation models. In recent years, formal methods based on stochastic process including Markov process are proposed in the literature. In this paper, we are interested in the parameter sensitivity analysis of discrete event dynamic systems by using stochastic Petri nets models as a tool for modelling and performance evaluation. A sensitivity analysis approach based on stochastic Petri nets, called PSA‐SPN method, will be proposed with an application to a production line system.

Batch deterministic and stochastic Petri nets approach for modeling and performance analysis of inventory systems: application to (s, S) inventory system

This paper is dedicated to modeling and performances analysis of inventory systems using BDSPN, a stochastic Petri net model capable of describing essential characteristics of logistical systems (batch behaviors, randomness, operational policies, synchronization of various flows). In this paper, an analytic method based on the Markov regenerative theory introduced by Choi for a particular class of stochastic Petri nets is presented and applied to our model. An inventory system with (batch) stochastic demand; constant replenishment lead time and continuous review (s, S) policy is modeled and its performances are evaluated using the analytic method

Interval analysis to optimise a production line of pharmaceuticals

In this paper, we focus on optimisation through simulation of a production line and packaging of pharmaceuticals. Precisely, we propose to couple our simulation model with an optimisation algorithm to determine the optimal number of pallets to insert in the conveyors to maximise the production rate. The idea of the proposed optimisation algorithm is original. It is based on an iterative division of the interval of possible solutions.

Performance Evaluation of Timed Petri Nets in Dioid Algebra

The theory of Discrete Event Dynamic Systems focuses on the analysis and conduct systems. This class essentially contains man-made systems that consist of a finite number of resources (processors or memories, communication channels, machines) shared by several users (jobs, packets, manufactured objects) which all contribute to the achievement of some common goal (a parallel computation, the end-to-end transmission of a set of packets, the assembly of a product in an automated manufacturing line).

Parameter Perturbation Analysis through Stochastic Petri Nets: Application to an Inventory System

Sensitivity analysis is used to determine how “sensitive” a performance measure of a model is with respect to a change in the value of the parameters of the model. Parameter sensitivity analysis of a model is usually performed as a series of tests in which the model analyst sets different values for the parameters of the model to see how a change in the parameters causes a change in the dynamic behavior of the model. Broadly speaking, this analysis is to see what happens when the value of some crucial parameters of a model changes. If a small change in the value of a parameter leads to a big change in the performance of the model, the parameter needs a closer look. It is a useful tool for performance evaluation of a model as well as its model building. Hence, sensitivity analysis can help the modeler to understand the dynamics of a system. Sensitivity analysis is often used to estimate the sensitivity of a performance measure of a system with respect to its decision variables (parameters) by evaluating the gradient (derivatives) of the performance measure at each given value of the parameters. With the gradient, the system performance measure can be optimized by using a gradient method. Moreover, sensitivity analysis can be used to identify key parameters of a system by discovering the parameters whose small change in value leads to a big change in the behavior of the system. In model building, sensitivity analysis can be used to validate a model with unkown parameters by studying the uncertainties of the model associated with the parameters. In the past, sensitivity analysis was usually based on simulation. One of the major research fields in this area is perturbation analysis (PA). The approach firstly applied to an engineering problem was proposed by Ho, Eyler and Chien in 1979. With great efforts made by many researchers in more than one decade, fundamental results for PA have been obtained. Currently, formal sensitivity analysis approaches based on stochastic processes were proposed in the literature. Particularly, efficient algorithms were developed to compute the performance derivates of Markov processes with respect to infinitesimal changes of their parameters (infinitesimal generators) (Cao et al., 1998, 1997). Besides the fundamental works in developing its theory and algorithms, perturbation analysis has also