Saad Louaqad
email: louaqad@gmail.com

Oulaid Kamach
email: kamach@ensat.ac.ma

Scheduling of blocking and no wait job shop problems in robotic cells

This paper focuses on the study of job-shop problems with transportation, blocking and no-wait (BNWT JSSP). This problem is an extension of the job shop problem. We take into account transport operations of jobs between different machines using a limited number of robots. We also have blocking and no wait constraints. It means that after a completion of an operation, a job waits on its machine, thus blocking it, until the next machine and a robot are available. In the other hand, the job starts its processing on the machine immediately and without any interruption after the robot has accomplished the transportation operation, thus no wait constraints. The aim of our problem is to find a feasible order of machine operations and transport operations. Additionally to the problem description, we will present a method based on graph theory which illustrates blocking situations. As the main contribution, we will formalize this problem with an integer linear programming models and propose an heuristic based on priority rules.

I. INTRODUCTION

The JSSPs are well-known combinatorial optimization problems, which consist of a finite number of jobs and machines. Each job consists of a set of operations that has to be processed in a given order, on a set of known machines, and where each operation has a known processing time. No machine can process more than one operation at the same time. The objectives usually considered in JSSPs are the minimization of makespan.

Considerable research has been devoted to this problem in the literature. An overview of history and main techniques used along with their reported results on the available benchmarking problems for JSP can be found in [START_REF] Jain | Deterministic job-shop scheduling: Past present and future[END_REF].

Several problems in practice cannot be modeled as (classical) Job Shop, due to additional features like storage space and transportation constraints. The classical model supposes that storage space has an infinite capacity and transport operations from one machine to another take almost no time. In many practical cases, the number of buffers is limited and transports need to be considered for various reasons. Buffers may be expensive or inadequate for technological or process reasons. Transports may take a considerable amount of time, or only a limited number of mobile devices are available to execute transports operations.

The jobs shop problems with transportation, blocking and no wait constraints are met for example in factories with robotic cells. A robotic cell is a flow-shop or job-shop scheduling problem in which the jobs must be transported from machine to machine. Transports are performed by one or more robots. We have to assign the transport operations to the robots and to schedule both the machine and robot operations. Usually there is no buffer or buffers with only limited capacity to store the jobs outside the machines or the robots. This means that our scheduling must deal with blocking and no wait constraints.

Job shop models with blocking constraints (BJS) have been discussed by several authors. [START_REF] Hall | A survey of machine scheduling problems with blocking and no-wait in process[END_REF] give a survey on machine scheduling problems with blocking and no-wait constraints. [START_REF] Candar | Machine scheduling problems with blocking and no-wait in process[END_REF] describes several applications of machine scheduling with blocking and no-wait in process and reviews the computational complexity of a variety of related problems. [START_REF] Mascis | Machine scheduling via alternative graphs[END_REF] and [START_REF] Mascis | Job-shop scheduling with blocking and nowait constraints[END_REF] study several types of job shop problems including the ideal (classical) job shop, the Blocking Job Shop (with and without "swaps") and the no-wait job shop, and formulate these problems by means of alternative graphs; [START_REF] Mati | Geometric approach and taboo search for scheduling flexible manufacturing systems[END_REF] investigate scheduling of flexible manufacturing systems, study a multiresource job shop problem with blocking constraints. [START_REF] Brizuela | No-wait and blocking job-shops: Challenging problems for GA's[END_REF] develop a genetic algorithm for solving no-wait and Blocking Job Shop problems. [START_REF] Klinkert | Optimization in design and control of automated highdensity warehouses[END_REF] and [START_REF] Groflin | Local search in job shop scheduling with synchronization and blocking constraints[END_REF] introduce a generalized disjunctive graph framework for modeling various types of scheduling problems and develop a local search approach for the generalized Blocking Job Shop problem with application in automated warehouses. [START_REF] Brucker | Cyclic job shop scheduling problems with blocking[END_REF] propose a tabu search algorithm to solve the BJS problem for cyclical scheduling. [START_REF] Aitzai | A branch and bound and parallel genetic algorithm for the job shop scheduling problem with blocking[END_REF] proposes a combination of a branch and bound algorithm with alternative graphs and develops two methods based on genetic algorithms to solve the BJS problem.

Most of the above authors emphasize that scheduling problems with blocking constraints (BJS) appear more difficult to solve than the classical job shop (JS). To illustrate the differences, two structural properties of the BJS shall be mentioned here, both being related to feasibility issues. First, in contrast to JS, a feasible partial schedule cannot always be extended to a feasible complete schedule. In fact, [START_REF] Mascis | Machine scheduling via alternative graphs[END_REF] and [START_REF] Mascis | Job-shop scheduling with blocking and nowait constraints[END_REF] established that deciding whether this is possible is NP complete (this was also shown independently by [START_REF] Klinkert | Optimization in design and control of automated highdensity warehouses[END_REF]). As a consequence, any heuristic that incrementally builds up a solution (e.g. based on priority rules) risks the chance of running into infeasibility. Second, it is not straightforward to construct feasible neighbor solutions in a local search approach as moves based on simple swaps of adjacent operations typically yield infeasible schedules (while in the JS case, it is well known that swapping critical adjacent operations leads to feasible neighbors).

Applications related to the BJS problem have been reported in the processing and logistics industries, such as scheduling for the manufacturing of concrete blocks by [START_REF] Grabowski | Sequencing of jobs in some production system[END_REF] , steelmaking by [START_REF] Pacciarelli | Production scheduling in a steelmakingcontinuous casting plant[END_REF] , chemical batch production by [START_REF] Romero | Scheduling intermediate storage multipurpose batch plants using the S-graph[END_REF] , container handling at a port by [START_REF] Chen | A tabu search algorithm for the integrated scheduling problem of container handling systems in a maritime terminal[END_REF] and railway networks by [START_REF] Dariano | A branch and bound algorithm for scheduling trains in a railway network[END_REF].

Several researchers have devoted to study job shop scheduling problems with transportation constraints in various systems. However, the progress is limited as this kind of problem is difficult to solve even for simplified and small size cases.

[17] integrated transport constraints in the scheduling problem with one robot. [START_REF] Blazewicz | Scheduling tasks and vehicles in a flexible manufacturing system[END_REF] proposed a dynamic programming approach to construct optimal machine and vehicle schedules. [START_REF] Bilge | A time window approach to simultaneous scheduling of machines and material handling system in an FMS[END_REF] developed a mixed integer programming (MIP) formulation raising this constraint on the vehicles. [START_REF] Ulusoy | A genetic algorithm approach to the simultaneous scheduling of machines and automated guided vehicles[END_REF] and [START_REF] Alvarenga | A genetic and set partitioning two-phase approach for the vehicle routing problem with time windows[END_REF] elaborated a genetic algorithm. [START_REF] Soylu | A self-organizing neural network approach for the single AGV routing problem[END_REF] and [START_REF] Hurink | A tabu search algorithm for scheduling a single robot in a job shop environment[END_REF] proposed, respectively, neural networks and tabu search approaches. [START_REF] Abdelmaguid | A hybrid GA/heuristic approach to the simultaneous scheduling of machines and automated guided vehicles[END_REF] described a hybrid method composed of a genetic algorithm for the scheduling of machines and a heuristic for the scheduling of vehicles. [START_REF] Lacomme | A disjunctive graph for the job shop with several robots[END_REF] and [START_REF] Deroussi | A simple metaheuristic approach to the simultaneous scheduling of machines and automated guided vehicles[END_REF] considered a job shop problem with several robots, with fixed operation times and fixed assignment of machine for each job's operation. [START_REF] Gong | Two-machine flow shop scheduling with intermediate transportation under job physical space consideration[END_REF] studied a two machine flow shop scheduling problem with intermediate transportation with a single transporter. [START_REF] Mateo | Resolution of graphs with bounded cycle time for the cyclic hoist scheduling problem[END_REF] considered a cyclic hoist scheduling problem with a single hoist, but without assignment problem. [START_REF] Caumond | An MILP for scheduling problems in an FMS with one vehicle[END_REF] used a mixed integer linear program (MILP) to find optimal solutions for the FMS Scheduling Problem with one vehicle. [START_REF] Crama | Cyclic scheduling of identical parts in a robotic cell[END_REF] proposed a polynomial algorithm for finding the optimal cycle in a robotic cell with production of identical parts. [START_REF] Brauner | Scheduling of coupled tasks and one machine no wait robotic cells[END_REF] studied coupled task problem and one-machine robotic cell problems. It reported new algorithmic procedure for this problem with or without tolerances on the distance. [START_REF] Corra | Scheduling and routing of automated guided vehicles: a hybrid approach[END_REF] applied a decomposition method where the master problem (scheduling) is modeled with constraint programming and the subproblem (conflict free routing) with mixed integer programming.

To the best of our Knowledge there is no research that addressed the problem of job shop scheduling that take into account transfer time between machine performed by a limited number of robot and the non existence of buffers between machines that lead to blocking and no wait constraints.

Two common approaches to tackle the scheduling problems are the utilization of mathematical programming and heuristic approaches [START_REF] Stafford | Comparative evaluation of MILP flow shop models[END_REF]. By Mathematical programming methods we formulates the scheduling problems as a mixed integer linear programming (MILP) problem and then tries to solve the formulated problem by a general purpose mixed integer linear programming solver. This methods are usually suitable for small instances. However and due to the great advance recently obtained in capacity of computers and creation of fast optimization software, presentation of MILP models is becoming more and more interesting among the researchers.

In this paper, we propose two methods to address the BNWT JSSP. We develop first an integer Linear programming model based on the model of [START_REF] Manne | On the job shop scheduling problem[END_REF] and secondly we construct an heuristic based on priority rules.

This paper is structured as follows. In the next section, we will present definitions and notations associated to our model. After that, in Section 3, we develop our integer programming formulation for the BNWT JSSP. In Section 4, we illustrate the theoretical tools and properties needed for developing our Heuristic. After that, we present the algorithm of our proposed heuristic. Finally, Section 5 gives some interesting conclusions and future studies.

II. PROBLEM DEFINITION

We consider a job shop problem with several transport robots and no buffers. In this problem, a set of n jobs {J 1 , J 2 , ..., J n } are processed on a set of m machines {M 1 , M 2 , ..., M m } and transported by a set of k robots {r 1 , r 2 , ..., r k }. Transportation times are robotindependent. Every job J i require an operation order, J i = {O i1 O i2 , .., O ini }, that must be executed according to its manufacture process. Operation O ij of the job J i requires the exclusive use of M l (l ∈ {1, 2, ..., m}) for an uninterrupted duration p ij , its processing time; the preemption is not allowed; each machine can process only one job at a time; the machine which execute the operation O ij is denoted as M ij .

In addition, we consider transportation operations between two machines. Consider two successive operations of the same job O ij and O ij+1 to execute in two machines M ij and M ij+1 . T ij and t ij are respectively used to denote transport operation and transfer time of job J i from machine M ij to machine M ij+1 . Each robot can handle at most one job at one time. Loaded transfer times does not depend on the job transported, but only on the travel routes and the robot which perform the transportation operation. This times are given by C r p,l where r represents the robot and (p, l) represents the route between machine M p and M l . It is assumed that the triangle inequality is satisfied:

∀p, l ∈ {1, 2, ..., m} machine indexes.

∀r ∈ {r 1 , r 2 , ..., r k } C r p,h + C r h,l ≥ C r p,l (1)
(1) means that the direct way between two machines is at least as short as the detour through a third machine. Otherwise, the robot always takes the shorter way through the third machine. Note that a sequence of loaded transport operations indirectly induces necessary empty moves. Empty transfer time from machine M p to M l is denoted V r p,l . It is assumed that:

∀r, r ∈ {r 1 , r 2 , ..., r k } ∀p, l ∈ {1, 2, ..., m} machine indexes    V r p,p = 0 V r p,h + V r h,l ≥ V r p,l V r p,l ≤ C r p,l (2)
The first assumption means that no empty transfer time is considered if a robot waits at the same machine the next transportation operation. The second one is the triangular inequality for empty moves. The third one means that empty transfers between two machines by a robot r take less time than loaded transfers between this two machines by another robot r . (It is also valid if r = r ). In the other hand, we consider the blocking constraint because there is no machine buffer. This means that after finishing its processing on the machine, a job has to stay there until it is unloaded by the robot. During this stay, the machine is blocked and not available for processing any other job. We also consider the no wait constraint that means if the robot transporting the job J i reaches machine M ij , the operation O ij must start immediately without any interruption.

The scheduling problem objectives are: -To determine the starting time for each machine operation O ij -To assign a handling robot to each transport operation T ij and to determine its starting time -To minimize the Makespan denoted C max = max(Ci) where Ci denotes the completion time of the last operation of job J i . All data are assumed to be non-negative integers.

III. INTEGER PROGRAMMING MODEL

This section presents the ILP models to formulate BNWT JSSP. Our following is based on the model of [START_REF] Manne | On the job shop scheduling problem[END_REF]. We used their ideas to model the Blocking Job shop with no wait and transportation constraints.

To model the blocking job shop with no wait and transportation constraints, the following notations are used.

List of parameters : -p ij : the processing time of operation O ij -C r pl : on load transfer time of robot r between machine p and machine l -V r p,l : empty transfer time of robot r between machine p and machine l -H a large number List of variables: - α ij;lq : Binary variable that takes value 1 if O ij is processed before O lq and 0 otherwise. -β ij;rs : Binary variable that takes value 1 if T ij require processing on robot r s , and 0 otherwise. -δ ij;lq : Binary variable that takes value 1 if T ij is processed before T lq , and 0 otherwise. -λ ij;lq : Binary variable that takes value 1 if T ij and T lq are processed by the same robot, and 0 otherwise.

The problem is formulated as follows :

Minimize Cmax Subject to:

-Finish time of machine operations:

F or i ∈ [1, n]; j ∈ [1, m] f ij ≥ d ij + p ij (3)
-Precedence Constraints between transport operations and machine operations:

F or i ∈ [1, n]; j ∈ [1, m -1] f ij = d ij+1 d ij+1 = d ij + k s=1 β ij,rs C rs Mij Mij+1 (4)
-Precedence constraints between machine operations and transport operations:

F or i ∈ [1, n]; j ∈ [1, m -1] d ij = f ij (5)
-Disjunctive constraints between machine operations:

F or i, l ∈ [1, n]; j, q ∈ [1, m] /M ij = M lq    d ij ≥ f lq -H * α ij;lq d lq ≥ f ij -H * (1 -α ij;lq ) α ij;lq + α lq;ij = 1 (6)
-Robot assignment constraints:

F or i ∈ [1, n]; j ∈ [1, m -1], s ∈ [1, k] k s=1 β ij,rs = 1 (7)
-Disjunctive constraints between robot:

For i, l ∈ [1, n]; j, q ∈ [1, m -1]; s ∈ [1, k] (3
) Ensures that each operation is processed at least for its process duration (4) ensures that each machine operation starts immediately after the finish of the transport operation that precede it. (5) As there is no buffer in machines, transport operation starts immediately when the job leaves a machine . [START_REF] Mati | Geometric approach and taboo search for scheduling flexible manufacturing systems[END_REF] ensures that each machine process one operation at a time. [START_REF] Brizuela | No-wait and blocking job-shops: Challenging problems for GA's[END_REF] ensures that each transport operation is performed by only one Robot. [START_REF] Klinkert | Optimization in design and control of automated highdensity warehouses[END_REF] ensures that each robot process one operation at a time. no two transport operations are performed by the same robot at any time

IV. HEURISTIC A. Blocking Situation

In this section, we will look for situations that could lead to blocking states in order to avoid them during the construction of our algorithm. For this purpose, we will identify blocking situations by using a graph G s = (M, J) that we will call the graph of last scheduled operations. This graph is defined below: Consider the graph of last scheduled operations G s = (M, J). A set of vertices M represents machines; A set of arcs J represents the last scheduled operations O ij of job J i . The starting point of the last scheduled operation O ij of job J i is the machine M ij and its end point is the machine M ij+1 . Consider for example a problem with 5 machines {M 1 , M 2 , ..., M 5 } and 4 jobs {J 1 , J 2 , J 3 , J 4 }. The last scheduled operations are:

J 1 : M 1 --> M 2 ; J 2 : M 2 --> M 3 ; J 3 : M 3 --> M 1 , J 4 : M 4 --> M 5 .
The associated graph G s is modeled as follows: Following the topology of G s = (M, J), the graph contains a cycle of length p = 3 (p equals the number of jobs that forms the cycle. Under this cycle, the necessary condition of blocking (C1) is satisfied because job J 1 that is processed on the machine M 1 cannot pass to machine M 2 occupied by the job J 2 , as well as for job J 2 that is processed on machine M 2 cannot pass to machine M 3 occupied by job J 3 as well as for job J 3 that is processed on machine M 3 cannot pass to machine M 1 occupied by the job J 1 .

Blocking condition (C1) can be formulated as follows: "Systems may confront a blocking situation if the graph of the last scheduled operations G s = (M, J) contains a cycle of length p ≥ 2." Thereafter, we will check if the condition (C1) is a sufficient condition to blocking situation in BNWT JSSP.

1st Case : p = 2 Consider the graph G s with a cycle of length p = 2. When the processing of job J 1 on machine M 1 has finished, job J 1 remains blocked on machine M 1 until its transportation operation T 1 from M 1 to M 2 start. We assume that a robot r 1 is available and will be assigned to transportation operation T 1 . This operation can start and liberate the machine M 1 . No wait condition imply that the processing of job J 1 on machine M 2 must start immediately after the termination of transport operation T 1 otherwise J 1 cannot be transported by r 1 and then machine M 1 remains blocked. M 2 is blocked by J 2 and must be liberated before the termination of transport operation T 1 . Therefore, we must have a second robot to execute transport operation T 2 of J 2 before that J 1 arrives at M 2 . We assume that a robot r 1 is available. Robot r 1 will be assigned to operation T i . Before that operation T i has finished, operation T i+1 must start. For this reason, we have a second robot r 2 which will be assigned to operation T i+1 .

Assumption 1: Assume that operation T i+1 starts at the time that T i finishes: d i+1 = f i . At the time f i , r 1 arrives in front of machine M i+1 and unload job J 1 . Then it can drive empty to machine

     d ij ≥ d lq + k s=1 β lq,rs (C rs M lq M lq+1 + V rs M lq+1 ;Mij ) + (λ ij;lq -1)H -δ ij;lq H d lq ≥ d ij + k s=1 β ij,rs (C rs Mij Mij+1 + V rs Mij+1;M lq ) + (λ ij;lq -1)H + (δ ij;lq -1)H δ ij;lq + δ lq;ij = 1 (8) M i+2 . r 1 reaches M i+2 at a time equal to f i + V r1
Mi+1Mi+2 . The robot r 2 which is performing transport operation T i+1 reaches machine M i+2 at a time equal to d i+1 + C r2 Mi+1Mi+2 . According to (2) and (Assumption 1) we have:

f i + V r1 Mi+1Mi+2 ≥ d i+1 + C r2 Mi+1Mi+2
. This means that the robot r 1 reaches machine M i+2 and liberate this machine before that the robot r 2 which is executing T i+1 reaches this machine and so on until the blocking cycle is totally liberated. Proposition 2: If the graph of last scheduled operations G s contains a cycle of length p ≥ 3, the system is eternally blocked if it has a single handling robot (k = 1) and partially blocked if k ≥ 2.

B. The proposed Heuristic

In this subsection we propose a heuristic dedicated to the BNWT JSSP. During construction of the algorithm, we complete iteratively a partial schedule S. U denotes the set of non-scheduled operations. At each iteration of the heuristic, two operations are selected, namely a machine operation and a transportation operation. When a machine operation is chosen on the basis of selection rules, the transportation operation which precedes this machine operation is automatically selected and a robot is assigned according to another priority rules. The Iteration starts with the construction of the set E of eligible machine operations. An operation is eligible for partial schedule S if it is a non scheduled operation that can start without violating any constraints.

-Rule 1: Eligible operations S(M p ) that need to be processed on machine M p cannot be scheduled as long as machine M p is occupied by another job. These operations will be eliminated from the set E. -Rule 2 : Eligible operations that could lead to eternal blocking situations or even a cycle in the graph G s (M, J) with p ≥ 3 will also be eliminated from the set E.

After the determination of eligible operations, it remains to appoint the machine operation to be scheduled. For this purpose, we associate each operation O ij ⊂ E to a pair (M p , g) where M p = M ij and g is the total time of operations S(M p ) ⊂ U , g can be seen as the weight of M p on the set of non scheduled operations U .

Selection rules of machine operations: Machine operation to be scheduled is the one associated to a pair (M p , g) with the largest g (g = gmax)

-Rule 3: If we have on the set E two or more operations with the same pair (M p , gmax), we choose the operation that has the longest queue. -Rule 4: If we have on the set E two operations with the same gmax but with different machines, we schedule that terminate first. Selection rules of robots: -Rule 5: To select the robot that will perform the transportation operation, we opted to choose the robot which provides the minimal completion time of the transportation operation, which involves exploring all robots for each assignment. -Rule 6: In the case of a cycle of length p = 2, we choose the robot that has the earliest availability time. This time correspond to the empty robot arrival time at the departure machine for the loaded move.

V. CONCLUSION

In this work, we described the job shop with transportation and subject to no wait and blocking constraints. We extended an existing model from the literature and showed how an integer programming formulation can be applied to solve the problem. We illustrated the blocking situations that the system could confront and finally proposed an algorithm for the construction of a heuristic. Experimental results for the proposed algorithm are not yet provided. On future researches, we will focus on a hybrid methods based on this article proposed heuristic. Experimental results will be established to show the efficiency of our developed methods.

  d ij : the start time of machine operation O ij f ij : the completion time of machine operation O ij . (Time when operation O ij leave machine M ij d ij : the start time of transport operation T ij f ij :the completion time of transport operation T ij List of decision variables:

Fig. 1 .

 1 Fig. 1. Associated graph of last scheduled operations

Fig. 2 .

 2 Fig. 2. Graph with a cycle of length p = 2

Proposition 1 :

 1 If the graph of last scheduled operations G s = (M, J) contains a cycle of length p = 2, the system is eternally blocked if it has one handling robot (k = 1) and partially blocked if k ≥ 2. Second Case: p ≥ 3 Consider the graph G s which a cycle of length p ≥ 3

Fig. 3 .

 3 Fig. 3. graph with a cycle of length p ≥ 3

Xème Confrence Internationale : Conception et Production Intégrées, CPI 2015, 2-4 Décembre 2015, Tanger -Maroc. Xth International Conference on Integrated Design and Production, CPI 2015, December 2-4, 2015, Tangier -Morocco.


Oulfa Labbi
email: labbi.oulfa@gmail.com

Latifa Ouzizi
email: louzizi@yahoo.fr

Mohammed Douimi
email: mdouimi@yahoo.fr

Simultaneous design of a product and its supply chain integrating reverse logistic operations: An optimization model

Keywords: Supply chain design, Product redesign, Supply chain optimization, reverse logistic, Mixed integer linear programming. I

This paper deals with a recent approach that tackles the product and the supply chain design issues at the same time. On one hand, supply chain constraints must be integrated into product design phase. On the other hand, product specificities are considered while determining supply chain structure. Moreover, reverse activities are integrated to recapture value of used products and also for ecological purpose.

We study the case of an existing product's redesign. The design change affects either the components or the process of the product or both of them at once. Therefore, we prioritize the optimization of supplying, production and recycling costs. For the product redesign, bill of materials is considered. For the supply chain configuration, suppliers' selection, assembling process choice, recycling centers' location are considered as well as sub-contractors selection.

At product design phase, the design team offers several design alternatives. The aim of this work is to determine simultaneously the optimal redesign alternative accompanied with its optimal supply chain configuration integrating recycling activity. For this purpose, a mixed integer linear programming (MILP) formulation is proposed. Thus, the product redesign and the supply chain configuration chosen should optimize supply, transportation, storage and recycling of components on one hand and production, outsourcing, technologies implementation and product's recycling on the other hand. Since the product could be returned during its entire life cycle, time periods in the MILP formulation are considered to be product life cycle phases. This consideration gave a dynamic aspect to our model.

INTRODUCTION

Today, industrial organizations are working in a business environment characterized by a high competitiveness and short product life cycle. To meet different segments of customer's demands, companies must innovate and diversify their products by introducing constantly new products to the market. New product design implies, certainly, the configuration of its corresponding supply chain. A better performance is achieved only if the designed product meets customer's needs on one hand and optimizes supply chain functions on the other hand. Also, it have been pointed out that there exists a close connection between product design and supply chain performance. Novak and Eppinger [START_REF] Novak | Sourcing by design: product complexity and the supply chain[END_REF] have explored by an empirical study, the link between product architectures and vertical integration decisions of supply chains. Their analysis showed that the companies optimizing the requirements of their product architectures as well as the capacities of their supply chains will outperform the firms focusing only on supply chain structures or product characteristics.

Research studies showed that 85% of logistics costs are driven by design choices [START_REF] Laurentie | Logistic processes and methods[END_REF] and over 70% of product cost is determined by decisions during this phase of development [START_REF] H'mida | Costs estimation in design phase[END_REF].Also, most benefits of collaboration among supply chain partners lie in the design phase of the product lifecycle since the cost of design changes increases as the design phase of the product lifecycle ends and the manufacturing phase starts [START_REF] Gokhan | Development of a simultaneous design for supply chain process for the optimization of the product design and supply chain configuration problem[END_REF]. Therefore, it is important to integrate product architecture decisions and supply chain decisions during the early stages of the product development [START_REF] Nepal | Matching product architecture with supply chain design[END_REF][START_REF] Tang | A new generation of cooperative development paradigm in the tool and die making branch: strategy and technology[END_REF].

Growing awareness about raw materials shortage and environmental problems conduct enterprises to rethink their strategies to ensure the sustainability of their operations. Environmental criteria must be taken into account as well as economic feasibility. Thus, used-product collection and recovery activities are integrated to their regular supply chain. We talk then about reverse supply chain [START_REF] Ilgin | Environmentally conscious manufacturing and product recovery (ECMPRO): a review of the state of the art[END_REF][START_REF] Bienstock | Reeengineering a reverse supply chain for product returns services[END_REF]. This work integrates forward and reverse network activities to configure a close loop supply chain. Moreover, supply chain design and product design are considered simultaneously. In fact, supply chain constraints are integrated into product design phase on one hand and product specificities are also considered while determining supply chain structure. We consider that we are in the case of redesigning an existing product .The design change affects either the components or the process of the product or both of them at once. Design team, proposes several alternatives to redesign the product. The aim of this study is to select from different alternatives the best redesign accompanied with its optimal close loop supply chain. For this purpose a mixed integer linear programming model is proposed. This paper is organized as follows: In Section 2, a literature review on product and supply chain design is presented. Section 3 is dedicated to reverse logistics concept. Section 4 presents the problem. The optimization mathematical model is given in section 5. Before the conclusion, a numerical example is presented in section 6 to illustrate the application of the model proposed.

II. PRODUCT-SUPPLY CHAIN DESIGN

In the literature, the most studied problems of designing a product and its supply chain follow crossword approaches [START_REF] Baud-Lavigne | Impact de la standardisation sur la conception integrée d'une chaine logistique dans un contexte d'internationalisation[END_REF].

A first approach consists on integrating product design constraints in supply chain design by taking into account the bill of material (BOM) of the product (assembly constraints).Works following this approach assume that product's bill of material is well defined and already known ,so product design is finalized.

Cordeau et al [START_REF] Cordeau | An integrated model for logistics network design[END_REF] and Paquet et al [START_REF] Paquet | A manufacturing network design model based on processor and worker capabilities[END_REF] have proposed mixed linear programming models to design a multi-echelon supply chain and multiproduct, considering assembly constraints and detailed bills of materials.

A second cross approach consists on integrating logistic constraints in the product design. The literature suggests some methods facilitating the integration between engineering and logistics actors like Design For Logistics (DFL) [START_REF] Dowlatshahi | The role of logistics in concurrent engineering[END_REF] and Design for Supply Chain Management (DSCM) [START_REF] Lee | Managing supply chain inventory: pitfalls and opportunities[END_REF].These methods define rules to optimize logistics costs by taking into account the logistical constraints in product design. Works on DFL and DFSCM promote the use of concepts such as modular design, delayed differentiation and components standardization to lower costs related to diversity management, storage and transportation of products [START_REF] Mather | Design for Logistics (DFL) -The next challenge for designers[END_REF], [START_REF] Newlands | Logistics and Supply Chain development: part two -design of, and Design for Logistics[END_REF].In the same context, Nishigushi [START_REF] Nishiguchi | Strategic Industrial Sourcing: The Japanese Advantage[END_REF], Handfield and Nichols [START_REF] Handfield | Introduction to Supply Chain Management[END_REF] have put their interest on supplier integration at the early phases of product design. Nevertheless, these works on logistical constraints integration assume that the supply chain already exists.

A third recent approach considers the design of a product and its related supply chain simultaneously. Supply chain design must be in interaction with product design process. On one hand, supply chain constraints must be integrated into product design phase. On the other hand, product specificities should be considered while determining supply chain structure. Therefore, the supply chain must be flexible and responsive to eventual product redesigns.

Works on simultaneous design of a product and its supply chain are very recent. Baud-Lavigne et al used a mathematical model in mixed linear programming to optimize the supply chain simultaneously with products standardization [START_REF] Baud-Lavigne | Mutual impacts of product standardization and supply chain design[END_REF]. They illustrated impacts of product or component standardization on supply chain structure. El hadj khalaf et al have proposed a model to choose simultaneously modules to be produced and their suppliers, under final assembly time constraint [START_REF] El | An experimental study for the selection of modules and facilities in a mass customization context[END_REF]. El Maraghy et Mahmoudi [20] have proposed a multi-period model that simultaneously optimizes the supply chain and product nomenclature. They defined several alternative BOMs, one being selected in the optimal solution. This approach needs a complete enumeration of all product configurations. Labbi et al [START_REF] Labbi | A dynamic model for the redesign of a product and its upstream supply chain integrating PLM(Product Lifecycle Management[END_REF] have proposed a dynamic model that optimizes simultaneously the redesign of a product and its upstream supply chain considering the product lifecycle.

The simultaneous optimization of product and supply chain design is a difficult problem. Due to the complexity of the induced models, very few models address the integrated problems. They use a very large number of variables to model the problem in a comprehensive manner and are therefore difficult to solve.

III. REVERSE LOGISTICS AND CLOSE LOOP SUPPLY CHAIN

With the awareness about natural resources scarcity, companies start to adopt the green thinking by integrating the reverse logistics operations in their regular chain. The design of the green supply chain include design decisions of the supply chain integrating closed-loop reverse logistics, decisions regarding the reduction of carbon emissions, capacity utilization, energy and materials resources and regulatory factors concerns [START_REF] Mbarek | Green Closed-loop Supply Chain Network Design: A Literature Review[END_REF].Regarding the product lifecycle, the structure of a green supply chain is cyclic. Materials and information flow are exchanged in both directions between actors. This sets up a value-loop, which integrates all stages of the product lifecycle [START_REF] Paksoy | Fuzzy multiobjective optimization of a green supply chain network with risk management that includes environmental hazards[END_REF].

Research studies dealing with reverse logistics chain and closed-loop supply chain network design have known a significant increase. Neto et al [START_REF] Neto | Designing and evaluating sustainable logistics networks[END_REF] introduced a static model of linear programming in mixed integer numbers for the design of integrated closed-loop supply chain. The model allows tradeoffs assessment between cost reduction and reducing the total environmental impact of the life cycle, under the regulatory constraints. Amin and Zhang [START_REF] Amin | A multi-objective facility location model for closed-loop supply chain network under uncertain demand and return[END_REF] propose a stochastic model based on linear mixed integer programming. The model is biobjectives; it minimizes the total cost of the integrated supply chain and maximizes use level of recyclable materials and clean technologies. Chaabane et al [START_REF] Chaabane | Design of sustainable supply chains under the emission trading scheme[END_REF] propose a linear program in mixed integer numbers for the design of a green supply chain. The model is multi-period, multiproduct and bi-objectives. It is formulated based on the principles of the life cycle analysis. Amin and Zhang [START_REF] Amin | An integrated model for closed-loop supply chain configuration and supplier selection: multi-objective approach[END_REF] developed an optimization model for closed loop supply chain configuration and supplier selection, simultaneously. Lundin [START_REF] Lundin | Redesigning a closed-loop supply chain exposed to risks[END_REF] examined the effects of design changes of a closed loop supply chain network by a mathematical model. In this work, we develop an optimization model for the simultaneous design of a product and its supply chain integrating reverse logistics. We study the case of a product redesign.

IV. PROBLEM DESCRIPTION

Fig. 1 shows the structure of the close loop supply chain considered. The network consists of components' suppliers, subcontractors, a production plant, distribution centers, demand markets and recycling centers. It is supposed that the production plant is able to manufacture new products and remanufacture returned products. In the forward channel, the supply chain consists of suppliers, subcontractors, production plant, distribution centers and clients. In the reverse channel, products at the end of their life cycle are recovered from the end customers and carried to recycling centers .The returns are then carried to the direct chain to form a closed loop supply chain. It is assumed that products coming out recycling centers could be either final products or components. We are in the case of redesign of a product and we want to determine optimally the associated closed loop supply chain. At the product design phase, several design alternatives are proposed by the design team. To each design alternative corresponds a supply chain configuration. The design of the product and its supply chain that will be chosen is that which provides the best cost and incorporates as many partners of the initial supply chain.

We consider that the product P is defined by its components Ci. Fig. 2 shows the adopted definition of product's bill of materials. The redesign of this product may include the following three cases:

Redesign nomenclature consists of only components which are common with the initial product nomenclature having similar or different nomenclature's coefficients. This implies that product's design change affects the manufacturing process. The redesigned product is composed of new components that have never existed in the old nomenclature. The redesigned product combines common components and new ones.

To assemble this product according to each redesign alternative, we could either keep the same existing assembling technology (machine) or implement new technologies or have a mixture between old and new technologies.

To determine supply chain configuration, we propose a mixed integer linear programming (MILP) model. Section 5 shows in details the MILP building.

V. MATHEMATICAL MODEL

A. Mathematical model formulation 1) Problem assumptions

The considered assumptions are as follows:

The demand for components is known. Suppliers undertake the transportation of required components.

Components transportation unit cost is in the range of minimum and maximum capacity of each supplier. The producing company may call upon subcontractors to meet the product demand.

The producing company pays a fixed cost including contract and partnership costs for suppliers and subcontractors newly introduced. This is for favoring suppliers and subcontractors that already exist at the starting supply chain. Each subcontractor must respect the product's quality level required by the producing company. Each subcontractor must respect the product's quality level required by the producing company.

Only one mode of transportation is considered. Distribution centers assure the storage, the treatment and the transport of finished products. All the customers are served through distribution centers and not directly from the plants. New distribution centers could be introduced in case of the lack of capacity of the existing ones or when the new product design requires special conditions of storage that existing warehouses couldn't assure.

The production plant pays a contracting cost to distributers and recycling centers newly introduced. Recycling centers could return either component or final products to the production plant. Recycling centers assure the transport of the returns. All assembling and recycling technologies (machines) added or implanted must not exceed a maximum number in order to respect the plant capacity and the investment budget for this new product.

2) Problem sets and data

To gather the three possible redesigns cited above into a single definition of redesign components set, we propose the following definition: : Transport minimum capacity of the supplier f for the component c in period t.

: Production hourly cost for a unit of the finished product in the machine m in period t.

: fixed cost of machine m implementation in period t.

Transport unit cost of the finished product from plant to a distributor d in period t.

: Removal or jobless cost of the machine m in period t.

Recycling hourly cost for a unit of the finished product in the machine n in period t.

: Recycling hourly cost for a unit of the component c in the machine n in period t.

: fixed cost of recycling technology n implementation in period t.

: Removal or jobless cost of recycling technology n in period t.

: Fixed cost related to selection of subcontractor s in period t.

: outsourcing cost of the subcontractor s for the finished product in period t.

: Demand of the client k for the final product in period t.

: Production maximum capacity of the machine m in period t.

: Production unit time of the finished product in a machine m in period t.

: Number of copies of a machine m originally existing at the producing company.

: Maximum number allowed for the addition of a machine m in period t.

: Production maximum capacity of the subcontractor s in period t.

: Maximum quantity allowed for outsourcing the finished product in period t.

:

Recycling maximum capacity of the machine n in period t.

: contracting cost related to selection of recycling center g in period t.

: Recycling unit time of the finished product in a machine n in period t.

: Recycling unit time of the component c in a machine n in period t.

: Number of copies of a machine n originally existing at the recycling plant.

: Maximum number allowed for the addition of a machine n at the recycling plant in period t.

: Transportation cost of the recycled component from recycling center g to the production plant in period t.

: Transportation cost of the recycled finished product from recycling center g to the production plant in period t.

: Transportation cost of the returned product from client k to recycling center g in period t.

: Maximum ratio allowed for recovering component c.

: Maximum ratio allowed for recovering finished product.

: Storage unit cost of the distribution center d in period t.

: Transportation cost of the finished product from distribution center d to client k in period t.

: Fixed cost related to selection of distributor d in period t.

: Volume occupied by the finished product p.

: Volume capacity reserved to the finished product p at the distribution center d.

3) Decision variables

: Quantity of component c ordered from supplier f in period t.

: Inventory of component c at the end of period t.

: Produced quantity of the finished product in period t.

: Outsourced quantity of the finished product from the subcontractor s in period t.

: Number of copies added of a machine m in period t.

: Number of copies removed of a machine m in period t.

: Quantity of the final product transferred from the production plant to distributer d in period t.

: Quantity of the final product transferred from the distribution center d to client k in period t.

: Quantity of the final product held in distribution center d in period t.

: Quantity of the returned product t from the client k to recycling center gin period t.

: Quantity of the returned component c transferred from the recycling center g to the production plant in period t : Quantity of the returned finished product transferred from the recycling center g to the production plant in period t.

: Number of copies added of a recycling machine n at recycling center g in period t.

: Number of copies removed of a recycling machine n at recycling center g in period t.

: Binary variable for the allocation of subcontractors with = 1, if the subcontractor s supplies the plant, and = 0 otherwise. Binary variable for the allocation of components suppliers with 1, if the supplier f is selected and 0 otherwise. : Binary variable for the allocation of distribution centers d with = 1,if the distribution center d is selected , and = 0 otherwise.

: Binary variable for the allocation of recycling centers g with = 1, if the recycling center g is selected, and = 0 otherwise.

4) Objective function

For each possible redesign, the objective function is to minimize supply, transportation, recycling and storage costs of components and production, outsourcing, adding or removing production and recycling machines costs and recycling and transportation of returned products. Our objective function is as follows:

Min Min r∊ R + + + * + * + + + * ) + + + + + + + * + * (1)

5) Constraints Suppliers capacity *

(2) Purchased quantity of the component c is limited by the production capacity of its supplier f .This is valid for each component at any planning period. With this constraint, we can also check if = 0 (the supplier f is not selected for the component c) then .

Transport capacity

(3) (4) Constraints ( 3) and ( 4) show that the quantity purchased of component c is bounded by the maximum and minimum transport capacities related to the corresponding supplier f. Component demand satisfaction + ≥ ∀c,t (5) This constraint shows that the sum of amounts of a component received from all suppliers and those recovered from all recycling centers in a period and the inventory of the previous period must meet the forecasted demand for this component in this period.

Inventory constraint = + (6)
Constraint [START_REF] Tang | A new generation of cooperative development paradigm in the tool and die making branch: strategy and technology[END_REF] shows that the inventory in the end of the period (t) is a function of the quantity in stock at the end of the previous period (t-1), and purchased and recovered quantities minus the expected demand for period (t) for each component.

Finished product demand satisfaction [START_REF] Ilgin | Environmentally conscious manufacturing and product recovery (ECMPRO): a review of the state of the art[END_REF] Constraint [START_REF] Ilgin | Environmentally conscious manufacturing and product recovery (ECMPRO): a review of the state of the art[END_REF] ensures that quantities produced, recovered and outsourced of the finished product must meet its estimated demand for each period.

Subcontractors capacity (8)

Outsourced quantity of the finished product is limited by the production capacity of its subcontractor for each period.

Outsourcing limitation [START_REF] Baud-Lavigne | Impact de la standardisation sur la conception integrée d'une chaine logistique dans un contexte d'internationalisation[END_REF] The quantities outsourced of the finished product received from all subcontractors must not exceed the allowed quantity for the outsourcing in each period.

Producing capacity * ( ) (10)
Constraint [START_REF] Cordeau | An integrated model for logistics network design[END_REF] ensures that the quantities produced of finished product respect production capacities of all available machines in each period.

Machine implementation limitation -

Constraint [START_REF] Paquet | A manufacturing network design model based on processor and worker capabilities[END_REF] shows that all assembling technologies including machines that originally existed and those newly implanted must not exceed a maximum number in order to respect the plant capacity and investment budget for each machine type and each period.

Demand satisfaction for distribution centers [START_REF] Dowlatshahi | The role of logistics in concurrent engineering[END_REF] Constraint [START_REF] Dowlatshahi | The role of logistics in concurrent engineering[END_REF] shows that quantities of finished product delivered from all distributer centers should meet the demand of the client k.

Distribution center capacity constraint * (13) This constraint shows that quantities of finished product transferred from production plant to a distributor center d is limited by its capacity of storage dedicated to the product. With this constraint, we can also check if = 0 (the production plant doesn't select the distributer d) then . Flow conservation at distribution centers

+ ( 14
)
This constraint is about flow conservation at distribution centers, they must receive enough finished product from production plant in order to meet all the demands.

Recycling capacity

* ( ) (15)
Constraint [START_REF] Newlands | Logistics and Supply Chain development: part two -design of, and Design for Logistics[END_REF] ensures that the quantities recovered of components and finished products in selected recycling centers respect recycling capacities of all available machines in each period.

Machine implementation limitation [START_REF] Nishiguchi | Strategic Industrial Sourcing: The Japanese Advantage[END_REF] Constraint [START_REF] Nishiguchi | Strategic Industrial Sourcing: The Japanese Advantage[END_REF] shows that all recycling technologies including machines that originally existed and those newly implanted must not exceed a maximum number in order to respect the recycling center capacity and investment budget for each machine type and each period.

Forward and reverse channel constraint [START_REF] Handfield | Introduction to Supply Chain Management[END_REF] Constraint [START_REF] Handfield | Introduction to Supply Chain Management[END_REF] ensures that forward channel is greater than reverse one.

Returned product constraints (18) [START_REF] El | An experimental study for the selection of modules and facilities in a mass customization context[END_REF] Constraints ( 18) and [START_REF] El | An experimental study for the selection of modules and facilities in a mass customization context[END_REF] show that the maximum percentage of recycling is respected.

Non negativity and binary constraints

; ; , , ∊ {0, 1} , , , : integers.

VI. NUMERICAL EXAMPLE

To have a better insight of the model, a numerical example is presented in this part. As this model aims to optimize product and supply chain design at a strategic (long term) level, time periods are considered to be product life cycle phases. In this example we considered four periods corresponding to introduction, growth, maturity and decline phases. We consider that a producing company wants to redesign a product P. The design team proposes three alternatives P1, P2, P3 for the redesign of the initial product P. In the three redesigns, there was either a change in the components or in the process or both of them at once. Fig 3 shows the nomenclature of initial product and that of the three alternatives proposed. We suppose that the initial product is composed by three components C1, C2, and C3. Components C4 C5, C6, and C7 are new ones. The suppliers F4 and F5 are new suppliers to be introduced for new components. It's assumed that the purchasing cost, the transport cost and the defect ratio for each supplier to each component are the same in each period. To assemble the redesigned product according to each alternative, we will need either the existing machines used to assemble the initial product or new ones or both of them at once. for producing the redesigned product according to each possible redesign. We supposed that the initial product needs three machines M1, M2, and M3 to be assembled. M4 and M5 are new machines to be implanted.

We assume that there are four subcontractors (S1, S2, S3 and S4) for outsourcing the finished Products .S4 is a new subcontractor. It is also assumed that the maximum capacity of each subcontractor at each period is the same .Regarding assembling machines; we assume that the production unit cost, the production capacity, the implementation and the removal costs are the same for each period. The rest of the chain comprises three clients (K1, K2, K3), two distribution centers (D1, D2), two recycling centers (G1, G2) with two types of recycling machines(N1,N2).To achieve the design of the proposed alternatives, we will need to add a new distributor D3,a new recycling center G3 and new recycling machine N3. Tables [START_REF] Novak | Sourcing by design: product complexity and the supply chain[END_REF] to ( 14) in the appendix show data have been used for the numerical example. The mathematical model was programmed and solved using the IBM Ilog Cplex 12.2. The program was solved for each of the three alternatives. Table 15 illustrates the results obtained. Comparing the MILP objective of the three alternatives, we conclude that alternative three (P3) is the optimal one. The values of decision variables of P3 are illustrated in table 11 of the appendix.

Results show that F2, F3 and F4 are the components' suppliers that have been selected for all periods. Regarding outsourcing, S2 is the only subcontractor to be selected in introduction phase. At maturity phase, S3 and S4 were added to S2 to respond to the high product demand. In period 4, the company will not need to outsource its product since product demand decreases in decline phase. To assemble P3, the company needs to implant two new machines (type M5) at the introduction phase. To respond to the growing demand of maturity phase, one machine (type M1), one machine (type M3) and also three machines (type M5) must be added. Results show also that the producing company receives recycled components and finished products from the three recycling centers in all periods. These recycled products added to quantities produced and outsourced cover the demand of all the three clients. Regarding distribution, the three distribution centers were used for string and distributing final products.

This numerical example shows how the supply chain configuration could change when we are redesigning a product. Also, it shows the dynamic aspect of the model since the supply chain related to redesigned product evolves in each product lifecycle phase. The resolution of the model showed the great number of variables, constraints and coefficients that have been handled which reflects the heaviness of the model even if it was simulated only for a product with very few components. Therefore the resolution of the model in a real industry case will be certainly very hard.

VII. CONCLUSION

This work contributes to a recent field which is the simultaneous design of the product and its supply chain. Moreover, it integrates also reverse logistic operations in order to treat all upstream and downstream functions of the supply chain from the product design till the recycling process. Logistics constraints are integrated in the product design phase on one hand, and the product attributes are considered when deciding about supply chain partners on the other hand.

We consider that we are in the case of designing a new product starting from an existent old one and we want to determine optimally its adequate closed loop supply chain. The supply chain configuration is designed from the existing partners of the existent supply chain related to the old product and by introducing new ones necessary for the new product achievement. At product design phase, several design alternatives are proposed. Each alternative corresponds to a closed loop supply chain. The aim is to optimally choose the best suppliers, subcontractors, distribution and recycling centers. For this purpose, a mixed integer linear programming (MILP) formulation was proposed.

The MILP is solved for each design alternative. The design of the product and its supply chain that will be chosen is that which provides the best cost and incorporates as many partners of the initial supply chain.

One of the limitations of this work is that we studied only the case of designing one product and its supply chain. In our future work, we will discuss the case of designing a family of product .Also the model contains many variables and constraints which makes it difficult to solve in terms of complexity especially in the case of industry-wide problems.

Fig 1 .

 1 Fig 1. Structure of closed supply chain network adopted

Fig. 2 .

 2 Fig.2. Product nomenclature definition.

::

  set of redesign components, indexed by c, such as: = (C⁰∩ ) U ( \ C⁰) with C⁰: the set of components existing in the starting nomenclature. Similarly, : The set of redesign suppliers, indexed by f, such as: = (F⁰∩ ) U ( \ F⁰) with F⁰: the set of existing product's suppliers. : The set of machines required for the redesign (r), indexed by m, such as: = (M⁰∩ ) U ( \ M⁰) with M⁰: the set of machines used to produce the existing product. : The set of machines required for recycling the redesign (r), indexed by n, such as: = (N⁰∩ ) U ( \ N⁰) with N⁰: the set of machines necessary for recycling the existing product. : the set of product subcontractors, indexed by s, such as: = (S⁰∩ ) U ( \ S⁰) with S⁰: the set of existing product's subcontractors. : set of distribution centers corresponding to the alternative (r),indexed by d, such as : = (D⁰∩ ) U ( \ D⁰) with D⁰ the set of distribution centers employed to distribute the existing product. : set of clients corresponding to the alternative (r),indexed by k, such as : = (K⁰∩ ) U ( \ K⁰) with K⁰ the set of clients of the existing product. : set of recycling centers corresponding to the alternative (r),indexed by g, such as : = (G⁰∩ ) U ( \ G⁰) with G⁰ the set of clients of the existing product. T: the decision horizon indexed by t. R: the set of possible redesigns indexed by r. The model includes the following data: : Purchasing unit cost of supplier f for the component c in period t. : Transport unit cost of supplier f for the component c in period t. Storage unit cost of the component c. : Partnership and collaboration fixed cost of the supplier f in period t. : Demand for component c in period t. : Maximum capacity of the supplier f to deliver the component c in period t. : Transport maximum capacity of the supplier f for the component c in period t.

Fig. 3 .

 3 Fig.3.Nomenclature of the three proposed alternatives The set of suppliers for each component are as follows: C1= {F1, F2, F3}; C2= {F2, F3}; C3= {F1, F2}; C4= {F1, F4}; C5= {F2, F5}; C6= {F4, F5}; C7= {F3, F4};

Fig

Fig 5 .

 5 Fig 5. Production necessary machines

TABLE 15 .

 15 RESULTS TABLE.

	MILP	Sol.time	variables	constraint Coef.
	Obj.	(s)
	P1 6.1848	810.71	266	734	4206
	e+004
	P2 6.9082	931.54	274	742	4222
	e+004
	P3	921.39	319	855	5855
	e+004

TABLE 6 .

 6 DEMAND FOR COMPONENTS

TABLE 7

 7

	. DISTRIBUTOR VOLUME

APPENDIX . NUMERICAL EXAMPLE DATA


Driss Serrou
email: d.serrou@gmail.com

Abdellah Abouabdellah
email: a.abouabdellah2013@gmail.com

Mesure de la performance de la chaîne logistique hospitalière en intégrant les dimensions : Coûts, Sécurité et Qualité : Application en cas du regroupement des pharmacies

Keywords: Regroupement, Sécurité, Qualité, Logistique hospitalière, Analyse fonctionnelle, indicateurs de performance I

Suite à la multiplicité des services de soins qu'offre un hôpital et suite à des facteurs qui entrent en jeu lors de ses fonctionnements tels que la maitrise des coûts, l'assurance qualité et la garantie de sécurité, sa mission reste complexe et très difficile à gérer. La maîtrise des dépenses hospitalières reste une préoccupation majeure chez la majorité des managers des systèmes hospitaliers, ce qui les conduit toujours vers la recherche d'une solution rationnelle et optimale des flux physiques et informationnels liés à leurs activités. Ces flux résument le vocable logistique hospitalier. Dans ce papier, nous nous intéressons à la mise en place d'un système d'aide à la décision permettant l'analyse de la performance du stock hospitalier via les trois dimensions 1 coût, qualité et sécurité. La première partie de l'article montre l'intérêt de la logistique hospitalière dans un hôpital ainsi que la revue de la littérature concernant l'évaluation de la performance d'un système hospitalier. La deuxième partie décrit les étapes de mise en place de notre système d'aide à la décision. La troisième partie explique l'apport de note démarche d'aide à la décision pour l'analyse de la performance de la chaine logistique. Nous terminons notre travail par l'application du système d'aide à la décision à un centre hospitalier au Maroc

INTRODUCTION

Les managers des centres hospitaliers, doivent faire face à des contraintes de plus en plus complexes. Ils doivent trouver de nouvelles solutions pour répondre à un environnement en pleine de transformation et innovation. Ils doivent donc développer de nouveaux outils de management et d'aide à la décision pour mieux piloter leur établissement avec une pression budgétaire accrue. La place de la chaine logistique hospitalière et son impact sur les performances des établissements de santé sont bien reconnus [START_REF]EHCR, Efficient Healthcare Consumer Response: Improving the Efficiency of theHealthcare Supply Chain[END_REF] [2], Ainsi la mesure de performance des hôpitaux est aujourd'hui considérée comme un élément indispensable du processus d'amélioration de la qualité des soins [START_REF] Barney | Organizational Culture: Can it be a Source of Sustained Competitive Advantage?[END_REF] [4] [START_REF] Groene | The World Health Organization Performance Assessment Tool for Quality Improvement in Hospitals (PATH): an analysis of the pilot implementation in 37 hospitals[END_REF]. Actuellement la maîtrise des dépenses conduit les établissements de santé à raisonner et à optimiser les flux physiques et les flux d'information correspondants en termes de performance globale de leurs chaînes logistiques [START_REF] Hassan | Logistique hospitalière : organisation de la chaîne logistique pharmaceutique aval et optimisation des flux de consommables et des matériels à usage unique[END_REF]. La logistique peut contribuer fortement à la performance de l'hôpital. Partout les réseaux de la santé sont confrontés à l'impossible triade de la performance : coût, qualité et sécurité. L'évaluation et l'amélioration de la performance des hôpitaux s'imposent pour un meilleur management des processus. Les experts du domaine confirment que le choix des indicateurs de performance n'est pas un exercice facile [START_REF] Morgan | How effective are your measurement systems[END_REF].Le secteur de la santé au Maroc constitue un chantier de changement mobilisateur d'engagements, de partenariats et de moyens. La réforme hospitalière jugée lourde et coûteuse a permis l'encadrement des hôpitaux dans un esprit d'amélioration de l'offre de soins et de celle de l'image de l'hôpital public auprès de la population. L'extension de la couverture médicale de base via les projets 2 RAMED, AMO et INAYA est un exemple de cette réforme. L'objet de ce papier est de mettre en place un système d'aide à la décision permettant l'analyse de la performance de la logistique hospitalière. Notre contribution est d'intégrer les trois axes Coût, Qualité et Sécurité. La première partie de l'article décrit l'intérêt de la logistique hospitalière et montre les recherches antérieures concernant la mesure de performance dans le secteur industriel et hospitalier. La deuxième partie décrit notre démarche pour l'analyse de la performance de la logistique hospitalière basée sur le système multicritères. La troisième partie présente les résultats obtenus et l'apport observés après la mise en place du système multicritères d'aide à la décision sur la chaine logistique hospitalière d'un centre hospitalier au Maroc.

II. INTERET DE L'ETUDE

A. Définitions D'après FREMONT la logistique hospitalière est une fonction complexe qui gère des flux de Produits et des circuits de distribution très différents [START_REF] Fremont Frédérique | la logistique hospitalière[END_REF]. Ainsi Hassan 2006 a défini l'ensemble des activités de conception, de planification, de gestion d'approvisionnement, de fabrication (bien et service), de livraison et de gestion des retours (logistique inverse), du fournisseur jusqu'au bénéficiaire (patients), tout en prenant en compte les trajectoires des patients au sein de l'hôpital sans lesquels il n'y a pas de flux de produits (pharmaceutiques) [START_REF] Hassan | Logistique hospitalière : organisation de la chaîne logistique pharmaceutique aval et optimisation des flux de consommables et des matériels à usage unique[END_REF]. Dans notre article, nous retenons la définition de la logistique comme « la satisfaction des besoins patients (produits ou services) à travers une optimisation des divers fonctions de l'hôpital». La figure 1 illustre la chaîne logistique hospitalière et met en évidence ses acteurs clés et leurs spécificités [START_REF] Martinelly | Chaîne logistique en milieu hospitalier : modélisation des processus de distribution de la pharmacie[END_REF] : Plusieurs experts ont estimé l'importance des coûts logistiques dans les établissements de santé, Les évaluations de [START_REF] Housley | Hospital Materiel Management[END_REF] arrivent à une estimation de 46% pour les centres hospitaliers nord-américains [START_REF] Housley | Hospital Materiel Management[END_REF].D'après [START_REF] Henning | The Financial Impact of Materials Management[END_REF] en reprenant une démarche similaire évaluant que la logistique hospitalière prend 42% des dépenses totales d'un centre hospitalier [START_REF] Henning | The Financial Impact of Materials Management[END_REF].

Ainsi CHOW et HEAVER (figure 2) arrivent à une estimation 46% [START_REF] Chow | Logistics performance: Definition and Measurement[END_REF]. Cette part importante des coûts logistiques montre que les démarches logistiques au sein des hôpitaux sont devenues un des vecteurs importants du processus de réduction des dépenses de santé. Ces données peuvent appuyer la prise de décision d'une amélioration de cette fonction dans l'hôpital.

C. Intérêt de la qualité dans la logistique hospitalière

La norme ISO 9000 définie3 la qualité comme «aptitude d'un ensemble de caractéristiques intrinsèques à satisfaire des exigences » (ISO 9000). La gestion de la qualité est un élément du système de management de l'organisme qui se concentre sur l'obtention de résultats, en s'appuyant sur les objectifs de qualité pour satisfaire selon le cas les besoins, les attentes ou les exigences des parties intéressées (ISO 9001) . La qualité et la qualité des soins ont fait l'objet de nombreuses définitions au cours des dernières décennies et la littérature sur le sujet est abondante. Depuis les années huitante, la qualité des soins a souvent été synonyme d'efficacité des soins pour le patient. Donabedian définissait la qualité comme suit : « des soins de haute qualité visent à maximiser le bien-être des patients après avoir pris en compte le rapport bénéfice/risques à chaque étape du processus de soins » [START_REF] Donabedian | Explorations in quality Assessment and Monitoring, vol. 1, The definition of quality and approaches to its assessment[END_REF]. La pression est mise sur les hôpitaux pour l'amélioration de la qualité et ils devront produire des indicateurs destinés à fournir de l'information sur la qualité de leurs prestations et à améliorer la transparence.

Dans la littérature on trouve plusieurs méthodes telles que, six Sigma, AMDEC, MSP, plans d'expériences,… ont été utilisées pour améliorer et optimiser la qualité des produits et/ou processus.

D . Intérêt de la sécurité dans la logistique hospitalière

La mission d'un hôpital a évolué au fil du temps, il est de plus en plus caractérisé par un environnement étoffé d'activités où le risque zéro n'existe pas. Le système hospitalier se doit de maîtriser, de gérer et de prévenir le risque, mais la sécurité hospitalière est de nature très variée, ainsi la gestion des risques s'inscrit aujourd'hui comme une composante essentielle de la stratégie d'un système hospitalier. Le terme « sécurité des patients » est l'appellation la plus utilisée et provient de la traduction de l'anglais des termes « patient safety ». L'OMS 4 , dans sa récente Classification Internationale pour la Sécurité des Patients (CISP) précitée propose la définition suivante : « La sécurité des patients est définie comme étant l'absence, pour un patient, d'atteinte inutile ou potentielle associée aux soins de santé. Une atteinte associée aux soins de santé est une atteinte découlant de, ou associée à des projets formulés ou à des analyses prises pendant que les soins ont été dispensés et qui ne résulte pas d'un traumatisme ou d'une maladie sousjacente ».

Plusieurs travaux de recherche ont été menés ces dernières années sur la gestion des risques dans les chaines logistiques hospitalières. On trouve les travaux Pons et al 2005 ont proposé l'intégration d'une démarche de gestion des risques à une structure d'achat de dispositifs médicaux [START_REF] Pons | Gestion liés à l'achat des dispotifs médicaux[END_REF]. Ainsi, on trouve les travaux de Aloui 2007 qui proposé un système de maitrise de risque [START_REF] Aloui | Contribution à la modélisation et l'analyse du rique dans une organisation de santé au moyen d'une approche système[END_REF]. Roussel 2008 a fait une étude sur l'enjeu d'intégrer une démarche de gestion des risques à une structure d'achat adaptable à toutes les organisations [START_REF] Roussel | Moll ,Methods and tools for risk management in heathcare organisations[END_REF]. Ces travaux ont montrées l'importance de l'apport sécurité dans la performance de la logistique hospitalière. Dans la littérature on trouve plusieurs méthodes telles que, AMDEC, HAZOP, HACCP,… ont été utilisées pour de la gestion des risques dans les établissements de santé.

E . Intérêt Importance des concepts CQS

F . Intérêt de la pharmacie dans les établissements de santé

La pharmacie occupe un rôle indispensable pour le fonctionnement d'un établissement de santé. Elle ne participe pas directement à l'acte de soins mais elle est impliquée dans de nombreuses activités qui concourent à la bonne réalisation de cet acte [START_REF] Rakotondranaivo | Supplychain et innovation : quelles perspectives pour l'organisation des flux des médicaments anticancéreux de l'hôpital à domicile ?GISEH[END_REF]. Il présente l'intersection des flux des produits pharmaceutiques (médicaments, dispositifs médicaux, objets de pansements et équipements). Selon DELOMENIE 1996 Ce service représente près de 15% du budget de l'hôpital [START_REF] Delomenie | Dépenses de médicaments à l'hôpital, la documentation française[END_REF]. Sa maîtrise et sa rentabilité sont donc vitales et passent par une productivité forte ainsi qu'une utilisation efficace des ressources pour améliorer la qualité des soins. Il convient d'optimiser l'organisation des flux physiques et d'information, de mieux répondre aux attentes des utilisateurs des prestations de service, de favoriser la qualité, la sécurité, la traçabilité, de minimiser les coûts. D'après Di Martinelly et al., 2005, la pharmacie hospitalière représente une part non négligeable des dépenses d'un établissement de santé [START_REF] Martinelly | Chaîne logistique en milieu hospitalier : modélisation des processus de distribution de la pharmacie[END_REF]. Elle fait partie intégrante des activités de logistique hospitalière qui sert de support à l'activité de soins apportés aux malades. Il ne faut pas considérer la pharmacie comme « isolée » dans l'hôpital mais comme le maillon central de la chaîne logistique pharmaceutique dont le but est de mettre les produits pharmaceutiques à disposition du patient.

F . Problématiques de la logistique hospitalière

D'après la revue de la littérature et les résultats questionnaire que la priorité de la analyse de performance de la chaine logistique hospitalière via les axes CQS, les managers des hôpitaux doivent se focaliser à l'intégration de ces axes dans l'évaluation de la chaine logistique dans le secteur de santé figure 4: Dans cette perspective, nous avons proposé une démarche d'analyse de performance du stock. Notre apport est l'intégration des concepts CQS. Le travail se déroule en deux phases 'Figure 5'.La première consiste à l'analyse de processus pilote de la chaine logistique. La seconde consiste l'analyse de la performance via les concepts CQS dans le cadre de la situation réelle du travail :

A .2 Cartographie des scénarios:

Dans la chaine logistique hospitalière pharmaceutique aval et amont deux types de structure peut être existe centralisée et décentralisée dans les centres hospitaliers en générale. La figure 6 montre les flux logistiques pour les deux scénarios : La période passé en stock des produits j au mois i La durée de vie par mois du produit j Coût d'achat unitaire urgentdes produits en rupturej durant le mois i Nombre des produits en rupture à acheter des produits j durant le mois i Coût de transport en urgence des produits en rupturej durant le mois i Coût de conditionnement unitaire des produits j durant le mois i : chauffage, refroidissement.

Nombre des produits à conditionner des produits j durant le mois i Cc locaux Coût fixe de conditionnement de la salle: climatisation ; refroidissement Coût d'achat unitaire des produits périmésj durant le mois i Nombre des produitspérimés à acheter des produits j durant le mois i Enfin, le modèle de calcul via les coûts du processus de stock est :

B.2 Description de l'analyse de performance en intégrant les

concepts CSQ Pour aborder notre analyse de performance dans toute sa complexité, nous avions choisi une approche proactive afin de permettre aux acteurs du processus de stock d'identifier les différents facteurs clés de performance. Une étude AMDEC (Analyse des Modes de Défaillance, de leurs Effets et de leur Criticité) nous est alors apparue tout à fait indiquée car sur le plan processus, l'AMDEC vise à rechercher de manière systématique les modes de défaillances potentielles, les effets et les causes possibles de ceux-ci. Dans la littérature médicale, des analyses de risque AMDEC ont déjà été utilisées. Elles évaluent Systématiquement un processus dans son ensemble et permettent de déterminer les défaillances Potentielles à chaque étape.

Dans notre travail notre apport est l'intégration des concepts CSQ dans l'analyse de performance du processus de stockage :

 AMDEC vis-à-vis les coûts

En générale un processus se compose d'un ensemble d'activités ou opérations .Chaque défaillance engendré dans chaque activité est lié à des coûts du processus. L'objectif du modèle des coûts présenté précédemment est de facilité la liaison entre les coûts vis-à-vis les activités du processus de stock. Selon Alaa 2010 les coûts engendrés par une défaillance dans l'industrie se divisent en deux types [START_REF] Alaa | Proposition et développement d'une approche pour la maîtrise conjointe qualité/coût lors de la conception et de l'industrialisation du produit[END_REF] :

 Coût interne de l'évènement = Coût de la main d'oeuvre + Coût matériel  Coût externe de l'évènement= Coût de retard + coût de réclamation Pour notre étude dans le secteur hospitalier 'Processus de stockage' :

 Coût interne de défaillance lié à une activité ou opération = Coût de rupture / coût de conditionnement ou Coût de péremption  Coût externe de défaillance de l'activité ou opération = Coût de défaillance ou action en urgence (Transport produit, prix uit du fournisseur élevé) Par exemple pour le mode de défaillance «Rupture des produits», en cas d'apparition de cette défaillance une action de livraison en urgence doivent effectuer. Le coût de rupture des produits est 1251 €, donc Le Coût interne de défaillance lié à une activité ou opération = 1251 €, le coût externe est plu difficile à estimer, cet évènement génère un retard et risque sur le patient. Pour la défaillance «Rupture des produits» le Coût externe de défaillance de l'activité ou opération est 2000 €.

La somme du coût interne et externe de ce mode de défaillance nous donne le coût total qu'engendre cet évènement, qui est dans le cas du mode de défaillance «Rupture des produits» est estimé à 3251 €.

 AMDEC vis-à-vis la sécurité

 AMDEC vis-à-vis la qualité

Dans le secteur de santé, la prise de conscience de la nécessité de piloter la performance gagne du terrain toutefois une difficulté demeure à savoir le nombre d'indicateurs susceptibles d'être intéressants est énorme à tel point que les gestionnaires n'arrivent pas à se repérer.

Selon SMITH, les caractéristiques des bons indicateurs de la performance dans le milieu de la santé se divisent en deux étapes, celle de la conception de l'indicateur et celle de son application [START_REF] &all | Mesure des performances pour l'amélioration des systèmes de santé : expériences, défis et perspectives[END_REF] : Tableau 4 : indicateurs de la performance dans le milieu de la santé [START_REF] &all | Mesure des performances pour l'amélioration des systèmes de santé : expériences, défis et perspectives[END_REF].

Etapes
Dance cette étape nous avons alors mené un brainstorming dans le but de mettre en évidence les différentes problèmes du processus de stockage lié qualité au niveau de chaque défaillance. Nous avons mis en place des indicateurs de performance pour chaque opération ou activité lié à une défaillance ressortie par AMDEC.

V. APPLICATIO DE L'ETUDE

Dans le but de valider notre travail, nous avons appliqué notre démarche sur un centre hospitalier au Maroc qui est constitué de 6 hôpitaux : Les résultats montrent que dans le cas de la SC, les coûts du processus de stockage diminuent par rapport à la SD, ces résultats s'expriment en une amélioration financière au niveau du processus de stockage, cette optimisation est dû à :

 Création de l'échange entre les hôpitaux en cas de rupture ;  Analyser les besoins des médicaments en temps réel existence d'une pharmacie centrale ;  Optimiser et minimiser le stock par le regroupement des médicaments ;  Amélioration de l'efficacité de la traçabilité des produits ;  Meilleur rotation des médicaments.

2

  RAMED : régime d'assistance médicale AMO : couverture médicale obligatoire INAYA : assurances maladie obligatoire au profit des travailleurs indépendants, des personnes exerçant une Profession libérale et les aides artisans.

Figure 1 :

 1 Figure 1 : Chaine logistique en milieu hospitalier

Figure 2 :

 2 Figure 2 : Proportion de la logistique dans les dépenses totales d'un établissement de santé [13].

7 :

 7 : Résultats d'un questionnaire Dans le but d'évaluer l'importance du concept CQS dans la performance de la chaine logistique hospitalière. Un questionnaire a été soumis à huit hôpitaux marocains à des spécialités différentes. Pour des raisons de confidentialités, On appellera ces hôpitaux de H1 au H8.Nous avons élaboré un questionnaire structuré pour évaluer les sept axes cidessous : Compétences technique & médicale Pour chaque axe, un ensemble de questions a été défini afin d'obtenir les informations pertinentes. Le questionnaire a été soumis aux responsables des processus logistiques dans les hôpitaux concernés au niveau : Stratégique, Tactique et Opérationnel. A travers ce questionnaire, nous visons principalement à évaluer l'importance de chaque axe dans la mesure de performance de la chaine logistique hospitalière.

Figure 3 :

 3 Figure 3 : Niveau de performance par axe et par hôpital D'après les résultats de cette questionnaire on trouve que le niveau de performance des 3 axes axe CQS est plus importants au niveau des huit hôpitaux. Pourtant, nous avons constaté que le coût présente le meilleur axe de performance pour les responsables. Les autres axe de performance est très importants mais n'est pas au même niveau que CQS.

Figure 4 .

 4 Figure 4. La logistique hospitalière via les dimensions Coût, Qualité et Sécurité. Ainsi Hassan 2006 [9] et Fateh Mebrek 2008 [20], arrivent à identifier les problématiques de la logistique hospitalière et se répartissent en trois :  Problèmes à caractères Organisationnel ;  Problèmes liés à la mesure de la performance ;  Problèmes liés au système d'information. Dans l'étude courante, nous nous focalisons sur l'aspect organisationnel cas du regroupement des pharmacies pour le circuit médicamenteux. Dans ce contexte, le regroupement des stocks à l'hôpital consiste à mutualiser les ressources et maitriser les stocks, limiter les gaspillages et fournir une meilleure gestion de stock centralisée avec une traçabilité visible. Les dépenses sur les produits pharmaceutiques représentent une partie importante des dépenses totales sur laquelle il semble possible d'agir rapidement. L'obligation de maîtrise les dépenses est donc en elle-même une raison supplémentaire et suffisante pour entreprendre une démarche de regroupement des pharmacies. Dans la majorité des cas, le regroupement a pour objectif de réduire les coûts d'exploitations et d'augmenter l'efficience des systèmes [21][22].

Figure 5 :

 5 Figure 5 : Etapes de la Démarche d'intégration des concepts: Coût, Qualité et Sécurité

Figure 6 :

 6 Figure 6: Structures décentralisée et centralisée d'un centrer hospitalier en générale [44].A .3 Description des processus logistique pour les deux sénarios:Nous avons résumé les descriptions de chaque processus logistique pour les deux structures* :

Figure 7 :

 7 Figure 7: Importants coûts du processus de stockage

  En générale l'AMDEC une évaluation qualitative : modes, causes et effets d'une part et une évaluation quantitative (occurrence O, gravité G et la probabilité de nondétection D) d'autre part. L'Indice de Criticité avec Ic = O x D x G permet d'évaluer le risque engendré par la défaillance de l'activité.

Tableau 4 :

 4 Part de la logistique hospitalier dans les 4 hôpitaux A. Choix de meilleurs scénarios Dans cette partie, nous comparons les coûts totaux de stockage de la pharmacie du centre hospitalier pour les deux scénarios SD et SC sur une durée d'une année. Les résultats trouvés sur le processus de stockage sont les suivants:

Figure 8 :

 8 Figure 8 : comparaison entre les 2 senarios

Auteurs Objet de travail Méthodes utilisées (Di MARTINELLY 2008)[34]

  III. RECHERCHES ANTÉRIEURES : ANALYSE DE LA PERFORMANCEA. Mesure de la performance dans le domaine industrielLa mesure de la performance dans le milieu industriel est actuellement un élément principal au pilotage efficace de l'entreprise. Le tableau ci-dessous présente les grandes courantes méthodes trouvées dans la littérature concernant la mesure de la performance dans le secteur industriel : La plupart des travaux concernant la mesure de la performance effectuée dans secteur hospitalier est basée sur l'approche de modélisation. Le tableau ci-dessous résume les travaux existes dans la littérature :

		Logistique hospitalière	ADSI
		(pharmaceutique+ patients)
	(DI MARTINELLY, and al. 2009) [35]	Logistique hospitalière (pharmaceutique+ patients)	SCOR
	(HASSAN 2006) [9]	Circuit pharmaceutique	SCOR, ARIS	Méthodes	Objectifs	Performan	Nive	Références
						ce	aux *
	(TRILLING, and al. 2004) [36] (BON VOISIN 2011)[37]	bloc opératoire bloc opératoire	ARIS GRAI	Target Costing ABC / ABM	Gain financier Affectation des charges	Coûts Coûts	S / T / O S / T	(Kato, 1993) [23] (Kaplan et Bruns, 1987) [24]
				EVA	Calcul de bénéfices	Bénéfices	S	(Albony, 1999) [25]
				TQM	Assurance de la qualité	Qualité	S / T / O	(Hill, 1977)[26]
				QFD	Assurance de la qualité	Qualité	S / T / O	(Akao, 2004) [27]
				Navigateu r Skandia	Déterminer le capital humain possédé	Capital intellectuel	S / T	(Edvinsson et Malone, 1997) [28]
				BSC	Evaluer la performance globale	4 axes du BSC	S	(Kaplan, 1992) [29]
			Tableaux de	GIMSI	Concevoir un tableau de bord	Indicateurs définis	T / O	(Fernandez, 1998) [30]
	bord Tableau.2 Analyse de la performance dans le secteur de santé	ECOGRA I	Concevoir un système d'indicateurs	Indicateurs des objectifs	S / T / O	(Ducq et Vallespir, 2005) [31]
	IV. DÉMARCHE D'INTÉGRATION DES CONCEPTS: COÛT, QUALITÉ ET SÉCURITÉ L'intégration des concepts CQS dans la analyse de performance de la chaine logistique hospitalière jeu un rôle très important dans l'amélioration de la performance d'une	SCOR PRISM Benchmar	Analyse de performance Globale Analyse de performance des processus Performance par rapport aux	Indicateurs Définis les parties prenant Indicateurs des	S / T / O S S / T	SCC 5 1996 Neely et al., 2001[32] Anderson et al.,
	organisation de santé. Pour la conduire, il est indispensable	king	organisations	objectifs	/ O	1999 [33]
	d'élaborer une démarche structurée et flexible qui répond aux		références
	enjeux relatifs à leurs exigences.
	Cette démarche se veut d'abord pragmatique et
	expérimentale. Elle s'inspire d'expériences existantes, en
	ayant pour but :
	-la mise en évidence de convergences d'opinions issues
	d'un groupe de travail,
	-et l'obtention d'un consensus avec un groupe d'experts.
	Un groupe de travail a été constitué autour des
	coordonnateurs et 2 experts en sciences des organisations
	du travail, il comprenait des pharmaciens ayant été
	impliqués dans une expérience de développement
	d'indicateurs d'activité en pharmacie hospitalière.

* S : Stratégique, T : Tactique, O : Opérationnel Tableau 1 : Analyse de la performance dans le secteur Industriel B. Mesure de la performance dans le domaine hospitalier (MEBREK 2012) [38] Logistique hospitalière ADSI (JLASSI 2009) [39] Bloc d'urgence IDEF (STACCINI, and al. 2005) [40] Les processes de soins IDEF0/SADT (Imane IBN EL FAROUK ,and al 2012) [41] Logistique hospitalière (pharmaceutique+ patients) SCOR (Fateh MEBREK 2008) [20] la logistique hospitalière Simulation (JOBIN Marie-Hélène and al 2003 [42] la logistique hospitalière Axes de performance (SMITH.C &All ; 2008) [43] Secteur de soin en générale

  B. Analyse de performance en de la structure centralisée en intégrant les concepts CSQ :Pour détecter les causes, un diagramme d'Ishikawa a été réalisé pour chaque mode.

								Evaluation
	Activité du processus	Mode de Défaillance	Effets		Causes	O D G	Ic	Coût Total = Interne	Indicateur qualité à mesurer dans la	Actions d'amélioration
										+Externe	future
	Saisie & Introduction du stock centrale	Etablissements Etablissement H1 Etablissement H2 Etablissement H3 -Détérioration du produit -Erreur des donnés de saisi -Non livraison à la %de la logistique dans le budget 33% 27% 29% distribution -Décalage entre le stock réel et le système Main-d'oeuvre 4 1 3	12	2030 €	Taux d'erreur l'inventaire (Trimestriel) trouvé pendant	Sensibiliser les responsables de la saisie (manuel d'aide à la saisie)
	Suivi la livraison dans les fiches individuels des stocks	Etablissement H4 Etablissement H5 Etablissement H6 -Erreur des donnés de saisie -Non livraison à la distribution -non adéquation entre le stock physique et le système	33% 17% 44% Main-d'oeuvre	4	1 3	12	3187 €	(Trimestriel) Taux d'erreur l'inventaire trouvé pendant	Sensibiliser les responsables de la saisie (manuel d'aide à la saisie)
	Stocker les produits dans les conditions requises par le fabricant	-Détérioration du produit	-Non livraison à la distribution -Produit en stock non conforme (perte financière)	Main-d'oeuvre Milieu	4	4 4	64	8752 €	Taux des produits mal conditionnés (Mensuel)	-Stock les produits un à un suivant les conditions de stock demandé -Contrôle préventif mensuel des conditions de stockage des produits livrés du moi -Sensibiliser les ressources humaines.
	Ranger la livraison FEFO	-Détérioration du produit (risque de préemption)	-Produit en stock non conforme (perte financière)	Main-d'oeuvre	Méthode	4	3 3	36	4132 €	Taux des produits périmés en stock (Mensuel)	-Sensibiliser les responsables de rangement à suivre la méthode FEFO -Contrôle préventif mensuel du classement de stockage des produits livrés du moi par date d'expiration
	Recevoir BCSS de distribution	-BCSS illisble -Erreur sur les quantités -Destinataire	-Retard de livraison -Non-livraison		Main-d'oeuvre	2	3 2	12	1654 €	Taux des livraisons en retard (Mensuel)	-Sensibiliser les responsables de la -Saisie de l'importance du contrôle des bons de commande -Sensibiliser les fournisseurs de refaire le contrôle avant l'envoie des marchandises
	Opérations de gestion des ruptures	-Rupture dues produits	Non-livraison	Main-d'oeuvre	Méthode	2	3 2	12	3251 €	Taux de rupture (Mensuel)	-Suivre en rigueur la politique Min / Max pour sécuriser le stock
	Valider la											-Sensibiliser les responsables de stock
	commande dans l'application et dans les fiches individuelle	-Erreur dans la validation	-Retard de livraison -Livraison non conforme	Main-d'oeuvre		4	1 3	12	1234 €	Taux des livraisons en retard (Mensuel)	de l'importance du mise à jour entre donnés du casier et le système -Contrôle préventif mensuel par un inventaire pour correction des décalages constatés
	de stock
	Livrer la commande	Détérioration du produit	-Produit en stock non conforme (perte financière)	Main-d'oeuvre	Matière	4	5 5	100	761 €	Taux des produits (Mensuel) périmés en stock	-Instaure une maintenance préventive systématique mensuelle des chariots du magasin avant les pannes
			Conclusion							de santé , ainsi que l'analyse de la performance via les couts ,sécurité et la qualité ,
	Les systèmes hospitaliers doivent d'une part assurer une qualité de service irréprochable vis-à-vis des patients, et d'autre part ils doivent optimiser leur chaîne logistique. Ils sont contraints à mieux organiser et à innover pour maîtriser les dépenses tout en garantissant aux patients la qualité et la sécurité des soins.Le présent article a permis de mettre la lumière sur logistique hospitalière, nous		Aussi, l'objectif de ce travail a été de jeter les bases d'une réflexion plus globale sur les systèmes de mesures de la performance de la logistique hospitalière. La démarche de mise en oeuvre d'un système de gestion de la performance peut être une occasion de valider les objectifs ou les résultats du service par les niveaux supérieurs du management.
	avons montré l'importance des coûts des activités
	logistiques dans les établissements

L'identification des causes de défaillances nous a permis de construire le tableau AMDEC pour le processus de stockage du centre hospitalier dans le cas centralisé on se basant sur l'historique d'une année. Le seuil de l'indice de criticité d'acceptabilité a été fixé à 10 par le groupe :

Coût, Qualité et Sécurité : CQS Xème Conférence Internationale : Conception et Production Intégrées, CPI

2015, 2-4 Décembre 2015, Tanger -Maroc. Xth International Conference on Integrated Design and Production, CPI 2015, December 2-4, 2015, Tangier -Morocco.

Organisation internationale de normalisation