Supply chain modelling and managing,using timed coloured Petri nets: a case study

This paper aims at developing a new methodology for designing and managing a supply chain (SC) and, at the same time, for evaluating the performance of every stakeholder involved in a production chain. The methodology proposed has been applied to a footwear supply chain and is based on coloured Petri nets (CPNs). The supply chain analysed in this paper is a complex production system consisting of a network of manufacturers and service suppliers related to logistics systems that provide transportation and storage. The model developed uses coloured, timed Petri nets to represent a supply chain and it is such that resources are the Petri Net (PN) places, the tokens are jobs, orders and/or products, while the colours represent job attributes. These colours are used to encode different data types and values that are attached to tokens. A “coloured token” represents a specific production order or a certain amount of a particular material supplied. Thus, it can be processed in different ways and it can be easily localised within the CPN model. The use of coloured Petri nets allows companies to create a compact representation of states, actions and events of the modelled system. The particular structure of this network allows the designers the easy realisation of a simulator using an “object-oriented”, dedicated programming, which is a useful tool for developing what-if analyses.     

Nested coloured timed Petri nets for production configuration of product families

Production configuration is as an effective technique to deal with product variety while maintaining production stability and efficiency. It involves a diverse set of process elements (e.g., machines, operations), a high variety of component parts and assemblies and many constraints arising from product and process variety. Production configuration entails the selection and subsequent arrangement of process elements into complete production processes and the final evaluation of configured multiple alternatives. To better understand production configuration and its implementation, we study the underlying logic for configuring production processes using a dynamic modelling and visualisation approach. This is accomplished by developing a new formalism of nested coloured timed Petri nets (PNs). In view of the inherent modelling difficulties, in the formalism three types of nets–process nets, assembly nets and manufacturing nets–together with a nested net system are defined. Using an industrial example of vibration motors, we show how the proposed formalism can be applied to specify production processes at different levels of abstraction to achieve production configuration.     

Petri-net based applications for supply chain management: an overview

Supply networks are discrete event dynamic systems consisting of suppliers, manufacturers, distributors, and customers. It is a difficult and challenging task to model such a complex system. Recently, characterised as being capable of model parallelism and synchronisation, Petri nets (PNs) have attracted great attention for modelling and studying a supply network. Since each type of Petri net has its unique properties to model specific applications, this paper reviews and classifies Petri net applications for supply chain management (SCM). According to the decision problems facing SCM, we have the Petri net applications classified into three areas: competitive strategy, firm focused tactics, and operational efficiency. Categorising the Petri net applications will provide a guideline to industry practitioners and research academics to choose the appropriate Petri net for the problem. In addition, the paper attempts to offer future directions in applying the Petri net to SCM including: (1) modelling with uncertainty elements; (2) addressing the scalability issue of Petri nets; (3) integrating Petri nets with other tools; and (4) extending Petri nets to emerging applications.     

Review of supply chain configuration and design decision-making for new product

The nature of competitive markets continuously pushes manufacturers to develop new products to meet the increasingly diversified customer demands. Manufacturers thus have to handle the complexities generated during the total life cycles of various product types, from product design to procurement, production, marketing and recycling. Though some management practices in mass customisation help to improve the performance of manufacturing systems, there are still some fundamental problems not covered. Joint decision-making of product and supply chain design, for example, is one of them. The existing industrial practice tends to treat these two problems separately. Decoupling these two problems decrease the design complexity but may lead to suboptimal decision outcome. To enhance understanding of the interconnected decisions for supply chain management and product design, this review collects related literature on this topic and focuses on the analysis of existing papers from an operation research perspective.     

Transient inter-production scheduling based on Petri nets and constraint programming

In this article, we focus on the transient inter-production scheduling problem between two cyclic productions in the framework of flexible manufacturing systems. This problem is first formulated as a reachability problem in timed Petri nets (TPN), then solved using a methodology based on constraint programming. Our work is based on the controlled executions proposed by Chretienne to model the sequence of transition firing dates. Our methodology is based on a preliminary resolution of the state equation between initial and final states in the underlying non-TPN. Then, we choose a duration T _max corresponding to the maximal duration time of the scheduling. For each solution S of the state equation, we build a controlled execution from the sequence of firings in S. After the propagation of firing date constraints and reachability constraints in the TPN, we use constraint programming to enumerate the set of feasible controlled executions.     

基于有色Petri网的产品协同开发过程建模方法研究

产品协同开发过程具有层次性、分布性、离散性和动态性等特点,采用合理方法构建其有效的过程模型成为协同开发过程管理与优化的基础性条件.将有色Petri网(CPN)技术引入产品协同开发过程建模中,针对性地提出了产品协同开发过程CPN模型的描述性定义;并从协同开发特点出发,为支持基本过程逻辑的描述由工作流原语定义了基本网模型结构;为了描述复杂协同关系,结合模块化方法及库所变迁性质给出了扩展网模型结构的构建方法.该方法实现了将协同开发过程关系从基本到复杂都能映射到相应CPN网上,并通过实例进一步说明了该方法的有效性.     

A heuristic-based approach to integrate the product line selection decision to the supply chain configuration

Product platform development (PPD) as an approach to mass customisation (MC) helps an organisation to reduce costs as well as ensure timely deliveries. Varieties are offered to different market segments by combining and incorporating different modules at different levels. Modules at different levels are essentially features that a customer segment is looking for. It is apparent that overall optimisation would require simultaneous consideration of not only PPD but also other supply chain constraints. In this paper, an attempt has been made to develop a mixed integer linear programming (MILP) model for sourcing, production planning, and PPD decisions. Based on analyses of the model, a heuristic solution procedure has been suggested. The heuristic developed in this paper attempts to decompose the problem and then assimilate the outputs from the simpler parts to obtain the final solution. Finally, a simple example to illustrate the solution procedure is presented.     

Evaluation of the logistic model of the reconfigurable manufacturing system based on generalised stochastic Petri nets

To reveal the influence on system performance by the logistic model of reconfigurable manufacturing system (RMS), the generalised stochastic Petri nets (GSPN) modular modelling approach is presented in this paper. It is based upon the characteristics of a bottleneck service. According to this approach, the bottleneck service in the production process is found first. By corresponding different resources in the service to different modules of the GSPN, the module is reconfigured. The analysis of the model using the Markov chain is hereby presented, as is the average utilisation factor of RMS. Following this, the production capacity of different products and the average productivity of reconfigurable manufacturing cells (RMCs) are discussed.     

Scheduling of flexible manufacturing systems based on Petri nets and hybrid heuristic search

This paper proposes and evaluates a hybrid search strategy and its application to flexible manufacturing system (FMS) scheduling in a Petri net framework. Petri nets can concisely model multiple lot sizes for each job, the strict precedence constraint, multiple kinds of resources, and concurrent activities. To cope with the complexities for FMS scheduling, this paper presents a hybrid heuristic search strategy, which combines the heuristic A* strategy with the DF strategy based on the execution of the Petri nets. The search scheme can invoke quicker termination conditions, and the quality of the search result is controllable. To demonstrate this, the scheduling results are derived and evaluated through a simple FMS with multiple lot sizes for each job. The algorithm is also applied to a set of randomly generated more complex FMSs with such characteristics as limited buffer sizes, multiple resources, and alternative routings.     

基于随机Petri网的铜带拉弯矫直机可用度分析

为了合理确定铜带拉弯矫直机的校验周期,提高其生产效率,确保其矫直精度,根据某铜板带公司拉弯矫直机9个月的维修数据,对拉弯矫直机的失效模式进行随机Petri网建模,将系统失效模式转换成相应的随机Petri网;基于马尔科夫过程对随机Petri网进行瞬态概率求解,并得到该拉弯矫直机失效模式的稳态概率;利用或门对应的随机Petri网模型分析,计算不同校验周期下拉弯矫直机的可用度.综合考虑设备可用度和经济效益,确定了合理的校验周期,为拉弯矫直机的长周期运行提供了依据.     

Supply chain focus dependent sensitivity of the point of product differentiation

Customer preferences for variety in the product(s) with improved customer service and lower prices are forcing the supply chains to overhaul the current practices from design to operational level. Postponement or delayed differentiation of the products is one such strategy, primarily deployed in mass customisation settings. Life cycles are shrinking not only for individual products but for product families as well. In this context, supply chain responsiveness becomes one of the crucial factors that need to be effectively managed to succeed in the present day competitive markets. Our model, that considers inventory costs and the supply chain responsiveness costs would aid a supply chain manager to make informed decisions with regard to the ideal location for the point of differentiation (POD), while striking the right balance between holding costs and the supply chain responsiveness costs. We also make use of a dimensionless parameter called the ‘coefficient of inverse responsiveness’ that not only facilitates the introduction of responsiveness related costs into the model but also improves the scalability and simplifies the analysis and interpretation of the results. Based on the strategic model developed, we offer some context-specific counter-intuitive managerial insights with respect to the sensitivity of the location of the POD in a supply chain.     

Concurrent product configuration and process planning,towards an approach combining interactivity and optimality

In mass customisation, defining concurrently the configured product and the planning of the associated production process is a key issue in the customer/supplier relationship. Nevertheless, few studies propose supporting the decision-maker during the resolution of this significant problem. After studying the decision-maker's needs and problem characterisation (modelling and scale aspects), we propose in this paper a two-step approach with the aid of some tools. The first step allows the customer or internal requirements to be captured interactively with a constraint-based approach. However, this step does not lead to one single solution, e.g. there are many uninstantiated remaining decision variables. In this paper, we suggest adding an original optimisation step to complete this task. Thus, the contribution of the study is twofold: first, methodologically to define a new two-step approach that meets industrial needs; and second, to provide adapted tools especially for the optimisation step. The optimisation step, using a multi-criteria constrained evolutionary algorithm, allows the user to select their own cost/cycle time compromise among a set of Pareto optimised solutions. A conventional evolutionary algorithm is adapted and modified, with the inclusion of filtering processing, in order to avoid generating invalid solutions. Experimentations are described, and a comparison is made with a branch-and-bound approach that outlines the interest in the propositions.     

支持敏捷供应链重构的模块化Petri网建模与分析

建立了敏捷供应链重构的过程框架，将敏捷供应链的重构分为结构重构和运行策略重构两个方面，结构重构主要是有关供应链节点的选择与评价过程，策略重构是在供应链结构形式以后，对其各节点的库存，物流、供货等策略的控制，在结构重构中采用模块化的Petri网建模方法进行分析，并以一虚拟的供应链为例进行仿真     

A coloured Petri net-based hybrid heuristic search approach to simultaneous scheduling of machines and automated guided vehicles

To achieve a significant improvement in the overall performance of a flexible manufacturing system, the scheduling process must consider the interdependencies that exist between the machining and transport systems. However, most works have addressed the scheduling problem as two independent decision making problems, assuming sufficient capacity in the transport system. In this paper, we study the simultaneous scheduling (SS) problem of machines and automated guided vehicles using a timed coloured Petri net (TCPN) approach under two performance objectives; makespan and exit time of the last job. The modelling approach allows the evaluation of all the feasible vehicle assignments as opposed to the traditional dispatching rules and demonstrates the benefits of vehicle-controlled assignments over machine-controlled for certain production scenarios. In contrast with the hierarchical decomposition technique of existing approaches, TCPN is capable of describing the dynamics and evaluating the performance of the SS problem in a single model. Based on TCPN modelling, SS is performed using a hybrid heuristic search algorithm to find optimal or near-optimal schedules by searching through the reachability graph of the TCPN with heuristic functions. Large-sized instances are solved in relatively short computation times, which were a priori unsolvable with conventional search algorithms. The algorithm’s performance is evaluated on a benchmark of 82 test problems. Experimental results indicate that the proposed algorithm performs better than the conventional ones and compares favourably with other approaches.     

Think globally act locally approach for the synthesis of a liveness-enforcing supervisor of FMSs based on Petri nets

This paper, by using Petri nets (PNs), reports a general approach, called a think globally, act locally (TGAL) method, to compute liveness-enforcing supervisors (LES) for flexible manufacturing systems (FMSs) prone to deadlocks. A place called global sink/source place (GP) is introduced provisionally help us to decide a set of monitors such that deadlock states can be removed. The TGAL method proceeds with liveness enforcement by an iterative way in which a complete state enumeration is computed at each step. The resulting LES is generally maximally permissive or suboptimal, without solving intractable integer linear programming (ILP) problems. Given a system, a sufficient condition is developed to decide whether the TGAL method can find maximally permissive, that is, optimal supervisors. Several typical FMSs popularly studied in the literature are used as the examples to demonstrate the proposed method.     

Adaptable product configuration system based on neural network

In the rapidly diversifying and globalising market, product configuration is implemented in a dynamic environment with continuous change of configuration knowledge. The adaptability of the product configuration system, which is defined as the capability to adjust product configurator, human resources and organisational resources to fit a new environment, is becoming more and more crucial. To keep the adaptability, this research suggests an adaptable product configuration (APC) system which transforms the development of the configuration system in a dynamic environment from a straightforward process to a closed circle. In the existing research on product configuration, most issues are addressed separately by different approaches and most approaches lack a systematic view which considers the interaction among product configurator, resources and environment. The circle of APC is therefore divided into several isolated stages and involves intensive human work, consumes a lot of organisational resources and results in a long response time. To successfully implement APC, this research adopts an artificial neural network and a specific rule extraction mechanism to develop a product configuration system. The neural network is able to automatically acquire configuration knowledge from historical transaction data and then directly apply it without further knowledge programming. Rule extraction mechanism has the capability to interpret the behaviour of the trained neural network and make it comprehensible and adjustable. Finally, knowledge acquisition, representation and application in product configuration are incorporated into the same connectionist methodology. And consequently, the APC circle is accelerated and the adaptability of the product configuration system is improved. A case study of computer configuration is presented.     

Scheduling manufacturing systems with blocking: a Petri net approach

This paper introduces a Petri net-based approach for scheduling manufacturing systems with blocking. The modelling of the job routings and the resource and blocking constraints is carried out with the Petri net formalism due to their capability of representing dynamic, concurrent discrete-event dynamic systems. In addition Petri nets can detect deadlocks typically found in systems with blocking constraints. The scheduling task is performed with an algorithm that combines the classical A* search with an aggressive node-pruning strategy. Tests were conducted on a variety of manufacturing systems that included classical job shop, flexible job shop and flexible manufacturing scheduling problems. The optimisation criterion was makespan. The experiments show that the algorithm performed well in all types of problems both in terms of solution quality and computing times.     

A framework for designing supply chain disruptions management considering productive systems and carrier viewpoints

With the advent of the global and digital world, the number of geographically dispersed firms throughout the world has increased and the problem of Supply Chain (SC) disruption appeared as a main concern to many industries. In such context, designing disruptions management strategies for a robust SC has become a critical worldwide issue that is still under-explored. Since its design phase, this class of robust and global SC must integrate technologies and agents of production. However, the existing works only consider the Productive Systems (PSs) and the carrier viewpoint must also be considered since goods should be produced and distributed at the right quantity, at the right place and at the right time. In this complex task of designing disruptions management, a formal method must be used to integrate technologies ensuring the compliance of certain requirements, such as: developing collaborative and autonomous models, allowing reuse templates, considering analysis/simulation abilities and facilitating the interaction among engineering practitioners. Therefore, this paper presents a framework to model, analyse, control and monitor the robust and global SC, designing and integrating models with Petri Net, agent-based model techniques for disruptions management and considering both PSs and carrier viewpoints. A case study is investigated and the findings demonstrated the proposed solution supports decisions making for solving problems of design, analysis and control.