Section: New Results
Performance evaluation and systems sizing
Participants : Didier Anciaux, Lyes Benyoucef, Sofiane Dellagi, Sophie Hennequin, Thibaud Monteiro, Nidhal Rezg, Nathalie Sauer, Alexandre Sava.
This part concerns the performance evaluation of critical problems. Setting up a new production system of goods or services, or modifying either the physical structure or the operation of an existing system, requires the system's performance to be evaluated and optimized.
Industrial systems and services systems
The first general subject concerns the scheduling of flexible systems (production or services) without storage capacity and with a specific blocking constraint encountered in many industrial processes. In classical blocking situations, a machine remains blocked by a job until this job starts the operation on the next machine in the routing. For the particular type of blocking constraints considered in our work, the machine remains blocked by a job until its operation on the downstream machine is finished (RCb constraint). Another new type of blocking constraint has been proposed and defined [63] . Heuristics and genetic algorithms for solving these Flow-shop problems are developed and different initial populations are tested to find the best adapted [40] [41] . A mixed-integer linear programming model and a lower bound. has been proposed to the hybrid Flow-Shop case [47] .The metaheuristic called electromagnetism-like optimization heuristic (EM) developed to minimize the makespan of Flow-shop has been adapted to the hybrid Flow-Shop case [48] . To solve the Job-Shop scheduling problem, possible conflicts situations are characterized and a heuristic method which avoids conflicting situations has been proposed [63] .
The impact of delays such as transportation, production or lead-times, is also studied in another aspect of our research program. The basic idea of this study is to develop Perturbation Analysis (PA) for performance evaluation and optimization of failure-prone manufacturing systems. Indeed, in the domain of discrete event systems, it was discovered in the early 1980s that event-driven dynamics give rise to state trajectories (sample paths) from which one can very efficiently and nonintrusively extract sensitivities of various performance metrics with respect to at least certain types of design or control parameters. This has led to the development of a theory for perturbation analysis in discrete event systems. Using PA, one obtains unbiased gradient estimates of performance metrics that can be incorporated into standard gradient-based algorithms for performance evaluation and optimization purposes.
Systems with delays hardly have begun to be investigated, and the few existing results indicate that the problem may become challenging, and the PA derivatives are more complicated than those that would be obtained for the system without delay. In our work we consider two models: discrete and continuous flow models, with inclusion of delivery times for more realistic performance evaluation and optimization of failure-prone manufacturing systems. While in most traditional continuous flow models the flow rates involved are treated as fixed parameters, a continuous flow model has the extra feature of treating flow rates as stochastic processes. Furthermore, continuous models have been shown to be very useful in simulating various kinds of high volume manufacturing systems and in this case are a good approximation of discrete settings. However, when the study should consider each part independently, discrete flow models are more appropriate. Unfortunately, PA estimates could become in this case biased (hence unreliable for control purposes) when significant discontinuities in sample functions appear.
One salient feature of our work is the explicit modeling of delays without destroying the nature of pure continuous and discrete flow models. Thus, the main innovation of our research is to consider these both models with delays and to define PA estimates for performance evaluation and optimization. In a first step, discrete flow model for a simple manufacturing system composed by a failure-prone machine, a buffer and a customer is considered. The demand is stochastic and the delivery time between the buffer and the customer is supposed to be constant. The control policy applied to the machine is a hedging point policy which has been proved to be optimal for a system without delivery times and which ensures that the material does not exceed a given number of parts. A simulation based on perturbation analysis is then proposed for performance evaluation [38] and optimization. The goal of the optimization is to evaluate the optimal buffer level (hedging point) to minimize the total cost function which is the sum of inventory cost, backlog cost, transportation cost [39] , [64] . The PA estimates are shown to be unbiased and comparison with discrete event system simulation proves that our results are very interesting and performing. This problem is then extended to a system with stochastic delivery times with similar results [37] . In a second step of our work, the study of both continuous and discrete flow models with constant delivery times is pursued. By theoretical and numerical results it is shown that these models have the same behavior and for each model unbiased gradient estimates are obtained [65] .
Another research domain we considered deals with the optimization of production - distribution systems. We considered a multi-stage production-distribution system made up of production plants separated by warehouses. Customer orders arrive randomly to the finished goods warehouse according to a compound Poisson process. The quantity of each order is a random non negative integer variable and the quantities of different orders are iid random variables. First of all we developed an analytical approach to solve the optimization problem for a production-distribution system with two levels [21] . However, as the size of the system increased, building an accurate analytical model became very difficult. Consequently, we proposed a simulation based optimization method to optimize the system when both the performance function and some constraints are evaluated by stochastic discrete event simulation [22] . We showed that, under some mild assumptions, the algorithm converge to a local optimum with probability 1.
Reconfigurable manufacturing systems (RMS) have been acknowledged as a promising means of providing manufacturing companies with the required production capacities and capabilities. This is accomplished through reconfiguring the system elements over the time for a diverse set of individualized products often required in small quantities and with short delivery lead time. In [30] , we focused on the various enhanced features of the RMS when compared to the existing manufacturing systems and identified the need for the changeover. The various requirements of this kind of manufacturing structure are identified. Further the problems and the research gaps with the implementation are listed and possible steps to be taken for the successful implementation of RMS in practice are presented.
Moreover, to map the manufacturing system capabilities and other characteristics, RMS necessitate the developpment of a suitable index. As a new result, we developed an index to measure the reconfigurability of RMSs keeping in mind their various core characteristics such as modularity, scalability, convertibility and diagnosability. These characteristics are mapped together using Multi-Attribute Utility Theory (MAUT). We can easily use this index to find the reconfigurability of a system possessing different characteristics [17] .
Case of supply chains
This subject concerns supply chains. We begin by the more classic logistic systems, and then move on to enterprise networks which are characterized by an extensive use of information technology.
Integrated supply chains are complex systems and their modeling, analysis and optimization requires carefully defined approaches/methodologies. Also, the complexities may vary greatly from industry to industry and from enterprise to enterprise. In contrast to traditional integrated supply chains, integrated long supply chains are more complex, with many parallel physical, information and financial flows occurring in order to ensure that products and/or services are delivered in the right quantities, with the requested quality to the right place in a cost effective manner at the right time. There is no generally accepted method by researchers and practitioners for designing, operating and evaluating agile integrated long supply chains. Therefore, our research work has attempted to investigate technologies, systems and paradigms for the effective management of long integrated agile supply chains. More specifically, a vision of the future technical issues and an insight into the future scientific and industrial advances required to meet future market and public demands are addressed. Two developed approaches for modeling and evaluating agility in integrated long supply chains respectively Fuzzy Intelligent based approach and Fuzzy association rules mining based approach are developed [36] .
Supplier selection with order splitting represents one of the most important functions to be performed by the purchasing department that determines the long-term viability of dynamic supply chains. As a second result, a novel approach for automatic knowledge acquisition, which clubs supplier selection process with order splitting for dynamic supply chains based on the attained knowledge from the variations in the market is developed. Moreover, the suggested approach imitates the knowledge acquisition and manipulation in a manner similar to the human schedulers who have gathered considerable knowledge and expertise in a given domain. As per this concept, those decision criteria for supplier selection are considered first, which are qualitatively meaningful like performance, service quality, innovation, risk etc. and thereafter their application is quantitatively evaluated. State variables are derived from the decision criteria to match the factors (flexibility, responsiveness, agility, position etc) associated with local competitive situation of the candidate supplier. Therefore, logically it can be inferred that the developed approach can generate decision making knowledge as a result, the developed combination of rules for supplier selection can easily be interpreted, adopted and at the same time if necessary, modified by supply chain decision makers [49] , [50] .
Moreover, another research direction addresses the integrated facility location and supplier selection for design of a stochastic distribution network with unreliable suppliers. The network is composed of a set of suppliers serving a set of retailers through a set of Distribution Centers (DCs) to locate. Each retailer faces a random demand of a single commodity, the supply lead-time from each supplier to each DC is random, and no supply lead-time between DCs and retailers are considered. Firstly, we considered the facility location/supplier selection problem where all the suppliers are reliable. The problem concerns the selection of suppliers, the location of DCs, the allocation of suppliers to DCs, and retailers to DCs, where the goal is to minimize inventory and safety stock costs at the DCs, ordering costs and transportation costs across the network, and fixed DCs location costs. Secondly, we proposed a two-period decision model in which selected suppliers are available in the first period and can fail in the second period. The facility location/supplier reliability problem is formulated as a non-linear stochastic programming problem. A Monte Carlo optimization approach combining the sample average approximation (SAA) scheme and a Lagrangian relaxation based approach is proposed [9] .
The globalization of economy and the exchanges give birth to multi-site companies who own their own production centers and distributions centers, which distribute on great geographical areas. Since always, the distribution of products with various modes of transportation is not taken into account in the management of supply chain. On the contrary, it is the external service provider of the supply chain who always manages it, but it does not support the measurement of the performance to control the cost. The discounted growth of the goods carriage per mode in European Union would encourage the decision makers to take measures to limit their use of it and especially to limit their environmental impacts. Actually, in an era with more environmental conscience on a global level (Kyoto, Goteborg, Copenhagen, etc.), the companies and service providers could no longer reject indefinitely on the community of environmental costs and will be, in all probability, subjected to heavy environmental tax in next years. The integration of the environmental and societal cost of transportation [43] , [59] , [58] in the supply chain is rarely quoted in the literature. This activity justifies the integration of the constraint in the model by the current state of environmental situation, the evolution of the legislation opposition to the problems generated by pollution (EURO 5 for European Union, for example), and the public pressure which is increasingly attentive with the environmental problems and the actions for reducing the pollution. We have also adapted multi-criteria methods AHP or ELECTRE to our model [29] , [42] , [57] .
Another research area for our team concerns the traceability phenomenon implementation within the production organization, particularly in the field of raw materials management in the food industry. The objective is to minimize the raw material's dispersion in the manufactured products. We seek to solve the problem of raw materials allocation into finished products, in order to minimize its dispersion and moreover, the products recall if needed. Dispersion optimization is made using a genetic algorithm [62] . The dispersion criteria are afterwards used to determine production's criticality in terms of sanitary risk, from which it is possible to optimize the processes of picking and dispatching. The final objective is to reduce the number of recalls in case of a crisis. This is achieved by using the decision-making aid, operational research and artificial intelligence tools [46] and [25] .
