Damien Lamy
email: lamy@isima.fr

Nikolay Tchernev
email: tchernev@isima.fr

S Kemmoe-Tchomte
email: sylverin.kemmoe_tchomte@udamail.fr

An Optimization Framework for Job-shop with Energy Threshold Issue With consideration of machining operations with consumption peaks

In this paper the problem of the Job-shop is extended to support energy constraints. The objective is to propose scheduling tools for manufacturing systems considering consumption threshold that must not be exceeded. The operations are supposed to consume more energy at beginning and thus representing a consumption peak that is often present in machine tools. This assumption results in considering that an operation is divided into two sub-operations. The goal is then to propose the best schedule considering the energy threshold, the consumptions of operations and duration of consumption peaks as given data. A Mixed Integer Linear Model (MILP) for the problem solving is proposed; it is based on flow approach to take into account the energy threshold. Since it is difficult to find exact solutions for medium and large size problems, a metaheuristic based on a GRASPxELS is proposed. Small scale instances for the problem have been generated, and results expose the relevance of the metaheuristic approach.

Introduction

For several years, environmental and energy constraints have become essential criteria in decision making inside enterprises or laboratories [START_REF] Gutowski | Environmentally benign manufacturing: Observations from Japan, Europe and the United States[END_REF]. This is also one of the major issues for governments, who care of the ecological impact of the industrial sector on the planet and on society. Thus, constraints such as footprint carbon and energy (fossil or not) consumption are now seriously taken into account. According to the International Energy Outlook proposed by the U.S. Energy Information Administration, companies consumed more than 50% of the global delivered energy in 2010 [START_REF]Energy Administration Information (EIA), International Energy Outlook[END_REF]. However they tend to apply their good practices to their different sites and to their suppliers by banishment of some materials for example, which could lead to the ISO14000 certification [START_REF] Gutowski | Environmentally benign manufacturing: Observations from Japan, Europe and the United States[END_REF]. More than 64% of the allocated energy to the industrial sector was used by non-OECD industry. However, companies' answers to this problem are still limited. Without a doubt, according to Rager et al. [START_REF] Rager | Energy-oriented scheduling based on Evolutionary Algorithms[END_REF] to provide solutions to this problem, two types of measures could be taken: technological and/or organizational. Technological measures are quite expensive since they emphasis on new machines or production process, whereas organizational measures focus on improvements for the existing system, thus leading to energy efficiency. A lot of enhancements can be made on this last point in order to obtain better results, meeting industrial expectations and without investing in new machines. According to [START_REF] Duflou | Towards energy and resource efficient manufacturing: A processes and systems approach[END_REF] three decisions could be made to build an energetically responsible production system. At first, the energy used by inactive machines could be minimized (by switching them off/on or by reducing lazy times). Another solution consists in moving activities from On-peak hours to Off-peak hours. Finally, it is possible to avoid consumptions peak which could lead to an overbilling. In this paper, this last point is treated in a Job-shop like manufacturing environment where a near optimal schedule should be proposed while an energy consumption threshold should not be exceeded. From the best of our knowledge, it is one of the first researches focusing on this problem.

In the next section, a literature review of articles concerning scheduling problems with energy constraints is proposed. In the third section, assumptions used in this study are presented. In the fourth section, the mathematical model of the problem is given. In the fifth section, a GRASPxELS metaheuristic is introduced in order to obtain near optimal solutions of the problem. Results for small scale instances are presented in section six. Finally, the last section consists in a conclusion and research perspectives

2

Related work

The literature is full of industrial problems consisting of minimizing the total treatment time, also called makespan, and other objective functions. Until recently, only a few works dealt with energy optimization as an important constraint in scheduling. However, the "Green Manufacturing" field of research is increasingly studied and hence a non-exhaustive review is proposed in this section. [START_REF] Mouzon | Operational methods for minimization of energy consumption of manufacturing equipment[END_REF] proposed methods and operational tools to minimize the energy consumption of a single machine. A mathematical formulation to minimize simultaneously the total completion time of a set of operations and the total energy consumption is proposed. Their model handles the different states a machine can be in: idle, running, switch ON or OFF. Later the same authors [START_REF] Mouzon | A Framework to Minimize Total Energy Consumption and Total Tardiness on a single Machine[END_REF] extend their previous work and proposed a Greedy Randomized Adaptive Search Procedure (GRASP) which objective is to find a solution minimizing both the total energy used and the total tardiness.

[6] used a Genetic Algorithm associated to a Simulated Annealing in order to provide approach solutions to a Flow-shop problem with consideration of total energy consumption. The power used by the machines according to their state is taken into account. They suggest to turn on/off machines according to the need of the production system and respecting conditions. Thus, a machine will not be turned off if the next operation to be scheduled starts earlier than the duration of the turn off/on process. Their results are given in a Pareto graphic. However, they did not use industrial data and underlined that their model does not handle the possible breakdowns. Considering this last point, [START_REF] Salido | Energy-aware Parameters in Job-Shop Scheduling Problems[END_REF] noticed that an energy efficient system provides robustness and is less sensitive to breakdowns and thus they worked on the correlation between makespan, energy and robustness. In their model a machine may have variable speeds for processing operations. A machine which is processing a task quickly will consume more energy and the treatment time will be reduced, however if the machine is processing the operation more slowly, the consumption will be reduced. In this context if a breakdown occurs, the lost time could be caught up by increasing processing speed of the machine. Their work is one of the first including robustness in the optimization of production systems under energy constraints. The model proposed by [START_REF] Fang | A new approach to scheduling in manufacturing for power consumption and carbon footprint reduction[END_REF] consists in minimizing the carbon footprint, the makespan and the consumption peaks in a Flow-shop context with variable speeds allowed on machines. The market tool they used did not permit to obtain a single point on the Pareto frontier in a calculation day even in the case of a two stage Flow-shop with two possible speeds per machine and 36 jobs. [START_REF] Duflou | Towards energy and resource efficient manufacturing: A processes and systems approach[END_REF] proposed a state of the art of different practices concerning the manufacturing systems with energy constraints. They also stated that is very difficult to obtain data concerning energy consumption. As stressed in their study it is not easy to optimize recently constructed manufacture industries because they are energetically well designed; however, even a smooth optimization in less recent manufactures could lead to a strong improvement. In their work [START_REF] Bruzzone | Energy-aware scheduling for improving manufacturing process sustainability: A mathematical model for flexible flow shops[END_REF] proposed a solution which consists in avoiding consumption peaks on a Flexible Flow-shop. They used an Energy Aware Scheduling (EAS) module on the existing schedule obtained with an APS (Advanced Planning and Scheduling) system. The EAS does not modify the given schedule, but optimizes it from the viewpoint of energy consumption by defining a new timetable for the operations. Two approaches are used: a mix-integer linear program (MILP) and a Randomized Neighborhood Search (RANS). They noticed that the MILP can be used when a large consumption peak is allowed and quickly overtaken when the energy threshold is lowered. The possibility to link the given EAS to an existing APS without changing the system in place for a solution handling both applications at the same time is a strong advantage of their approach. They finally noted the fact that their model could be strengthened, by integration of other objectives such as variability of costs and energy need of machines which is constant in their study (unitary).

[18] took into account the variability of electricity pricing during a day, by inclusion of Time-of-Use (TOU) rates in a Flexible Flow-shop. They noticed that it is better in a flexible production system to have parallelized a fast machine with high energy consumption with a slow but economic one, and high energy machine with a slow and economic one, rather than two medium machines from the viewpoint of speediness and energy consumption. [START_REF] Shrouf | Optimizing the production scheduling of a single machine to minimize total energy consumption costs[END_REF] used a similar approach by taking into account TOU and transitions between machine states in a single machine process. The genetic algorithm they implemented could be used in extension of an MRPII (Manufacturing Resource Planning System). However their model does not modify the sequence given in input in order to find a better makespan, and consideration of machines with variable speeds is mentioned as a future study. [START_REF] Liu | An investigation into minimising total energy consumption and total weighted tardiness in job shops[END_REF] Studied a Job-shop where both the total tardiness and the total energy consumption are minimized by reducing the idle times of machines. [START_REF] Zhang | Energy-conscious flow shop scheduling under time-of-use electricity tariffs[END_REF] Proposed a time indexed linear program which objective is to minimize the energy spending and the carbon footprint under a TOU pricing in a height level Flow-shop.

Finally, [START_REF] O'rielly | Strategies to improve industrial energy efficiency[END_REF] pointed out that the industrial mind-set is still focused on the fact that optimizing energy consumption is time-consuming and too expensive which is a barrier to improvements in energy efficiency that could be made in enterprises. In addition, the recent state of the art proposed by [START_REF] Trentesaux | Sustainability in Manufacturing Operations Scheduling: Stakes, Approaches and Trends[END_REF] underlines the lack of decisional tools relative to energy efficiency of production systems. Their review shows that most of the studies are input-oriented and quite recent and they stress the necessity to develop more output-oriented or mixed methods.

In order to clarify the approaches proposed in the literature review, the different systems under study, the way energy is optimized and the objective functions are centralized in Table 1. While reviewing the literature a lack of study concerning the Job-shop problem with consumption peaks consideration appeared, since all studies conducted so far mainly concern the total energy minimization as seen in [START_REF] Liu | An investigation into minimising total energy consumption and total weighted tardiness in job shops[END_REF], [START_REF] He | A bi-objective model for job-shop scheduling problem to minimize both energy consumption and makespan[END_REF] or [START_REF] Salido | Energy-aware Parameters in Job-Shop Scheduling Problems[END_REF]. In the next section are presented the assumptions used in this paper concerning the Job-shop with an Energy Consumption Threshold (JSECT) where the operations to be scheduled present an electricity consumption peak at their start. 3 Assumptions

Job-shop assumptions

This study is based on the well-known Job-shop theoretical model (A review of the Job-shop problem is given in [START_REF] Jain | Deterministic Job-shop scheduling: Past, present and future[END_REF]) representing workshops with multiple paths. The Job-shop problem consists in scheduling a set of n jobs that have to be sequenced on m machines. Each job Ji (i.e.: i ∈ [1,n]) is composed of m operations Oij (i.e.: j ∈ [1,m]) which are sequenced in a predefined order noted Gi={Oi1, Oi2, ….Oim}. Each operation has to be processed on a given machine μij during a processing time pi and no preemption is allowed (a started operation must not be stopped before its end). The Job-shop problem consists in finding a feasible schedule by managing machine disjunctions as the machines are mutualized between jobs. One of the commonly used objectives is then to find such a schedule with a minimal global duration, also called makespan.

The Job-shop problem has received a huge attention over the years, with several extensions such as transportation constraints, time-lags constraints, or financial constraints. Using the disjunctive graph introduced by [START_REF] Roy | Les problèmes d'ordonnancement avec contraintes disjonctives[END_REF] the operations can be modeled by vertices. Precedence constraints between operations of the same job are represented by an arc. Disjunctive constraints between two operations which require the same machine are modeled by an edge. The cost of an outgoing arc is equal to the duration of the operation. An example of a non-oriented disjunctive graph for a Job-shop scheduling problem where three jobs must be scheduled on three machines is presented on Fig. 1 where dashed edges represent disjunction constraints and each operation is performed by a given machine Mi. [START_REF] Mouzon | Operational methods for minimization of energy consumption of manufacturing equipment[END_REF] 12 [START_REF] Liu | An investigation into minimising total energy consumption and total weighted tardiness in job shops[END_REF] 12 [START_REF] Jain | Deterministic Job-shop scheduling: Past, present and future[END_REF] 9

O 1 O 2 O 4
O 5 O 6 O 8
O 9 O 10 O 12
M 1 M 4 M 2 M 4 M 1 M 2 M 3 M 1 M 2 * O 14 O 1 O 3 10 O 7 7
O [START_REF] Gutowski | Environmentally benign manufacturing: Observations from Japan, Europe and the United States[END_REF] 11

M 3 M 3 M 4
Fig. 1 : A non-oriented disjunctive graph

In the study, the graph representation proposed by [START_REF] Roy | Les problèmes d'ordonnancement avec contraintes disjonctives[END_REF] is extended with new arcs modelling precedence between operations when a task is delayed because of the energy used by previous and non-finished operations.

Energy assumptions

In the literature concerning energy optimization on production systems, the operations are generally represented as a simple energy block [START_REF] Weinert | Methodology for planning and operating energyefficient production systems[END_REF] which representation does not fit the reality. An energy block consists in considering an operation from the energy viewpoint, leading to a rectangle where two contiguous sides respectively represent the duration of the operation and its maximum energy consumption as shown on Fig. 2. Furthermore, in the literature most of the operations are considered from three points of view: basic, cutting, and idle/ready as stressed in [START_REF] Aramcharoen | Critical factors in energy demand modelling for CNC milling and impact of toolpath strategy[END_REF]. These assumptions are used in the work of [START_REF] Liu | An investigation into minimising total energy consumption and total weighted tardiness in job shops[END_REF] when minimizing the total energy consumption. [START_REF] Bruzzone | Energy-aware scheduling for improving manufacturing process sustainability: A mathematical model for flexible flow shops[END_REF] considered that every operation had a unitary consumption because of the lack of industrial data, and thus represented them as a simple energy block, not taking into account the different states of the machine. The time indexed linear model they proposed showed that the lower the energy threshold is the harder it is to find an exact solution for such a problem with a linear solver. Still, their model permitted to lay the foundation of the work presented in this study. However several differences between our approaches must be enlightened. First, the basis of our problem is the Job-shop problem which is more general than a Flow-shop. But the main difference to be noticed concerns the energy assumptions. Indeed, it can be seen in the literature that machine operations have a complex energy behaviour and thus should not be only represented as a single block, especially while considering energy threshold. As stressed in [START_REF] Bruzzone | Energy-aware scheduling for improving manufacturing process sustainability: A mathematical model for flexible flow shops[END_REF] it is quite difficult to obtain real and precise data from the industrial sector. However, some useful information can be found concerning power profiles of machines on works related to green manufacturing, both from the viewpoint of machine or process. Thus, it can be stressed that most of the time an extra energy consumption peak is occurring at the start of the operation as shown in [7; 15] or [START_REF] Kellens | Energy and Resource Efficiency of Laser Cutting Processes[END_REF].

Since the objective of this study is to minimize the makespan while considering an energy threshold constraint, it appears that a simple block representation would imply to loose time during the schedule. Indeed, based on the power profile of a 2kW fibre laser proposed in [START_REF] Kellens | Energy and Resource Efficiency of Laser Cutting Processes[END_REF], it can be stressed that the laser cutting process consumes almost 37kW whereas it needs less than 20kW after the peak. Thus, if a threshold is fixed at 40kW and another operation that consumes less than 15kW must be scheduled, it means that such an operation should start at the end of the laser cutting process since both operations would consume more than 40kW if treated simultaneously (15+37=52kW > 40kW). If the laser cutting process has a long duration (approximately 400s in the given example), a huge amount of time is lost whereas the operation could have been scheduled just after the 37kW peak. Hence, in this paper are considered operations that are divided into two sub-operations in order to represent the consumption peak at the beginning, and a lower consumption during the remaining processing time. However, since operations cannot be stopped in the Job-shop, two sub operations relative to the same global operation must be linked in order to keep the integrity of the given operation. This constraint is modelled using no-wait arcs between such sub-operations, or maximal time-lags between two consecutive operations which values are equal to the opposite duration of the peak's length (i.e.: if peak duration is equal to a, then the time-lag max is equal to -a ; A study on time-lags can be found in [START_REF] Caumond | A memetic algorithm for the job-shop with timelags[END_REF]). A graphical representation of such a problem is presented in the Fig. 3. [START_REF] Van Laarhoven | Job-shop scheduling by simulated annealing[END_REF] 13 1 and to provide the energy needed for each operation. Furthermore, it can be stressed that only two disjunctive edges relative to disjunctive constraints on machines between two operations are presented on the graph, in order to ease its reading (the former operations O6 and O11 in the Fig. 1 which have been transformed into operations O11-O12 and O21-O22). Indeed, since operations cannot be stopped once started, these edges represent the fact that the first suboperation (i.e.: representing the consumption peak) must be scheduled after the end of a previous operation treated by the same machine, and hence must be scheduled after the second suboperation of such an operation. In this example, it means that the operation O11 should be scheduled after the end of the operation O22 or the operation O21 should come after completion of the operation O12. To complete this graph representation, the energy threshold is modelled as an extra vertex with a value corresponding to the available energy that must not be exceeded. Thus, one of the objective is to efficiently allocate the energy to the machines in order to obtain the smallest possible makespan. When there is not enough energy allocable to an operation, because of running operations extra conjunctive arcs are added to model the new precedence between operations due to the energy threshold. These extra conjunctive arcs represent the duration that an operation must wait before enough energy could flow from a finished operation to the one that must be scheduled (arc in bold on Fig. 3). Thus, a conjunctive arc may be present between operations that are not directly related to the same machine. In Fig. 3, it can be easily understood that the available energy will not be enough to schedule all possible operations as the threshold is set to 70. Thus O1 on machine M1 and O9 on machine M2 cannot be simultaneously scheduled as the sum of their energy is equal to 73, which is greater than 70. Hence, if a sequence of operations is given, where the first operation (O1) of job J1 appears before the first operation (O9) of job J2 then it will not be possible to start operation O9 at 0. Indeed, if O1 starts at 0, since the operation O2 is linked to the operation O1 with a maximal time lag equal to -5, the operation O2 must start directly after the end of the operation O1. To start operation O2, 23 energy units are transferred at the end of the operation O1 to the vertex modelling operation O2. Because of the energy threshold, the operation O9 will start at 5 since operation O1 (consumption peak of the operation on Machine M1) has a duration equal to 5. In this configuration, the operation O9 would start at 5. Thus a conjunctive arc (represented in bold) links the operation O1 and O9. When the operation O1 is finished, a flow of 3 energy unit (dashed edge) comes in addition to the 26 units left in the Energy Vertex in order to start the operation O9 (the values could be different depending on the other operations to be scheduled as mentioned before). By doing this repartition, the energy threshold cannot be exceeded during the schedule and thus the constraint is respected.

O
M 1 M 2 M 4 M 2 M 4 M 1 M 1 M 3 M 2 O 5 O 6 2 8 -2 O 13 O 14
In the next section a mathematical formalization of the Job-shop with Energy Consumption Threshold is given. This model includes operations with a consumption peak at their beginning.

Linear programming

The model representing the problem has been built to obtain exact solutions not exceeding a given Energy Threshold by repartition of energy resources among the different machines. It relies on a flow added to the incumbent Job-shop problem.

Emax

: energy threshold that must not be exceeded; Ei : energy required for processing the sub-operation i;

Variables

Cmax : completion date of all operations also referred as the makespan of the schedule; si : starting time of sub-operation i; xi,j : binary variable equal to 1 if sub-operation i is realized before sub-operation j and equal to 0 otherwise; yi,j : binary variable equal to 1 if there is a non-null energy flow from sub-operation i to power the sub-operation j and equal to 0 otherwise; φi,j : denotes the number of energy units directly transferred from sub-operation i to suboperation j ;

Linear Formulation

The first line (1) of the linear program refers to the objective of the problem which is the minimization of the completion time of all operations (makespan): The second set of constraints [START_REF] Balogun | Modelling of direct energy requirements in mechanical machining processes[END_REF] gives the expression of the makespan, which must be greater or equal to the end date of all the operations:

max C p s i i   , V i   (2)
The third set of constraints (3) represents the disjunctions constraints for operations occurring on the same machines. In these constraints, if two operations i and j of different jobs must be treated by the same machine, then i is treated before j, or j is treated before i:

k i l k j i i k i , l k , j , O O , O O , j i , l k , J J / V ) l , k , j , i ( , x x             1 (3)
The fourth set of constraints (4) defines the starting dates of operations of a job according to its sequence of operations.

i i j p s s   , j i J J i j V j i     , / ) , ( (4)
The fifth set of constraints [START_REF] Caumond | A memetic algorithm for the job-shop with timelags[END_REF] ensures that, if i and j are two sub-operations referring to the same global operations, then j is processed directly after the end of the sub-operation i (i.e. no-wait constraints).

i i j p s s   , j i O O j i V j i     , / ) , ( (5)
The next constraints (6) adjust the starting dates of operations that belong to different Jobs but need the same machine, as they can't be processed simultaneously.

1 0           mod(j,2) , mod(i,2) , , O O / V ) j , i ( , H p Hx s s j i j i i j , i i j   (6)
The constraint [START_REF] Duflou | Towards energy and resource efficient manufacturing: A processes and systems approach[END_REF] avoids to exceed the Energy Threshold when processing the operations as it can't be allocated more energy to the operations than Emax.

max , 0 E V j j     (7)
Constraints [START_REF]Energy Administration Information (EIA), International Energy Outlook[END_REF] ensure that the sum of energy flows from sub-operations and initial energy threshold is equal to the energy needed for the sub-operation j.

j V i j i E    ,  , j i V j    / (8)
Constraints [START_REF] Fang | A new approach to scheduling in manufacturing for power consumption and carbon footprint reduction[END_REF] ensure that the sum of energy flows from the considered sub-operation i to the other ones never exceeds the energy that was used for its processing.

i V j j i E    ,  , j i V i    / (9)
Constraints [START_REF] Feo | greedy randomized adaptive search procedure for maximum independent set[END_REF] ensure that if there is an energy flow from i to j yi,j =1 (this variable is then used in Constraints ( 12) ). If yi,j=0 then no flow is possible from i to j.

j , i j , i Hy   , j i / V ) j , i (    (10)
Constraints [START_REF] Gutowski | Environmentally benign manufacturing: Observations from Japan, Europe and the United States[END_REF] stipulate that if there is no need of a flow from i to j (φi,j=0), then necessarily yi,j = 0, if yi,j = 1, then φi,j ≥ 1:

j i j i y , ,   , j i / V ) j , i (    (11)
7th Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2015) 25-28 August 2015, Prague, Czech Republic

Constraints [START_REF] He | A bi-objective model for job-shop scheduling problem to minimize both energy consumption and makespan[END_REF] fix the energy flow between sub-operations of a same global operation according to the energy available:

j i j i j i O O j i V j i E E      , / ) , ( ), , min( ,  (12)
Constraints ( 13) adjust the starting dates of sub-operations which need to wait before the end of previous operations in order to not exceed the energy threshold and receive an energy flow from a previously scheduled operation:

j i i j i i j J J V j i H p Hy s s        / ) , ( , , (13)
Constraints ( 14) stipulate that no flow is possible between two sub-operations i and j, if i and j belong to the same job and if i is processed before j.

0 ,  i j  , j i J J , j i / V ) j , i (     (14)
Constraints [START_REF] Kara | Unit Process energy consumption models for material removal processes[END_REF] imply that if there is a flow from i to j then there must not be flows from j to the predecessors of i in the corresponding product line.

, ,

 

j i k j y y , j i k i J J J J i k V k j i      , , / ) , , ( (15)
Constraints [START_REF] Kellens | Energy and Resource Efficiency of Laser Cutting Processes[END_REF] imply that if operation i and j need the same machine, but i is scheduled before operation j then no flows are allowed from j to any predecessors of i in its product line.

, ,

 

k j j i y x , j i k i j i J J i k V k j i         , , , / ) , , ( (16)
Finally, the set of constraints [START_REF] Liu | An investigation into minimising total energy consumption and total weighted tardiness in job shops[END_REF] avoids cycles between operations occurring on the same machine.

2 , , ,

   i k k j j i x x x , k j i k j i J J J V k j i          , / ) , , ( (17)
As stressed by the results presented in Table 3, the resolution of such a problem as the JSECT is difficult for a solver even for small scale instances, thus an approach using a metaheuristic is proposed in the next section.

GRASPxELS

Principles of the GRASPxELS

The GRASPxELS is a multi-start metaheuristic proposed by [START_REF] Prins | A GRASP x evolutionary local search hybrid for the vehicle routing problem[END_REF] and is relying on a Greedy Randomized Adaptive Search Procedure (GRASP) proposed by [START_REF] Feo | greedy randomized adaptive search procedure for maximum independent set[END_REF] and an Evolutionary Local Search (ELS) proposed by [START_REF] Wolf | Evolutionary local search for the super-peer selection problem and the p-hub median problem[END_REF]. This metaheuristic helped to quickly bring very good results to several problems. Furthermore, the combination of the GRASP and the ELS, aims to propose a better suited metaheuristic which will explore a wider range of solutions. A template algorithm of the GRASPxELS is proposed below. As stressed in the Algorithm 1, a GRASPxELS is divided into three phases: the construction phase, the local search phase and the ELS phase.

During the ELS phase, neighborhood of the previous local optimum solution is explored through mutations and then ameliorated thanks to the local search. The mutation consists in permuting elements in the repetition vector used by [START_REF] Bierwirth | A generalized permutation approach to Job-shop scheduling with genetic algorithms[END_REF] if they belong to different jobs. Finally, the different specificities corresponding to the construction and local search phase are exposed in the next sub-section as they are important part of the metaheuristic. As the main objective is to propose a solution with minimal makespan, a construction rule based on the duration of the activities is chosen. At each construction step, an activity is randomly chosen from a list of activities with small durations. The constructed sequence is then evaluated.

Local search phase:

The construction phase rarely produces local optimum thus it is useful to explore neighborhood of the constructed solution to obtain a better one. The chosen local search is relying on the neighborhood of [START_REF] Van Laarhoven | Job-shop scheduling by simulated annealing[END_REF] which is really fast evidenced by the results obtained in term of computation time (Table 2 and3).

Finally, as one of the most important algorithm of this study is the evaluation of a sequence of operation for the JSECT, this procedure is presented on the next sub-section.

Evaluation of a sequence of operations

As mentioned before, a sequence of the operations relies on a repetition vector. The evaluation of such a sequence is handling both physical and energy constraints. The starting date of an operation is modified inside the evaluation function in order to respect the energy threshold. A principle algorithm of such an evaluation function is given in Algorithm 3. This algorithm returns the makespan, the starting date and the father of each operation. the duration of the consumption peak is taken between 0 and a third of the duration of the operation. An example of an instance is given on Fig. 4. All instances tested in Tables 2 and3 are available online (see : http://damienlamy.com). For each instance, five replications have been made. The results are presented on Table 2 and Table 3. In these tables the column Jobs x Machines represents the number of jobs and machines of the instance. Concerning the CPLEX part of the tables, the Energy Threshold column represents the energy allowed for the schedule. The BKS column refers to the best solution found by the solver. When these solutions are proven optima, an asterisk has been added to the result. The UB-LB columns represent the upper bound and lower bound provided by the solvera dash in UB column means that optimal solution has been found. The Gap column represents the percentage distance between UP and LB. The TT column corresponds to the time needed for the solver to found the BKS -When the computation time reaches 10800s the execution is stopped. In the GRASPxELS part of the tables, the AVG_S column represents the average solution over 5 runs. TT_S refers to the total execution of the metaheuristic while TTB_S refers to the average computation time requested to obtain the best solution found, both in seconds. Finally, the DEV_LB column corresponds to the deviation to the LB and the DEV_UB, in the Table 3, corresponds to the deviation to the best solution found by the solver. The results show that the GRASPxELS provides sound solutions. For the first instances (Table 2) the metaheuristic always found the solution provided by the solver, in less than half of a second, whereas it took more than 18 seconds in average for the solver to prove the convergence. Concerning the instances with 5 jobs and 4 machines, the solver always found the optimal solution, unless for the Inst_3 when considering the lowest energy threshold possible. On this set of instances the metaheuristic always provides a solution which quality is better or equal to the solution proposed by the solver. Concerning computation time, the metaheuristic is quite competitive since it stops in less than a second in average, when the solver needs more than 1500s in average to prove the convergence. When increasing the number of jobs to 6, the solver starts to be overtaken with only 6 proven optima. With these instances, the metaheuristic finds solutions which are always better or equal to the ones provided by the solver (more than 1% of improvement in average) in less than 2 seconds for each replication, which is approximately 6000 times faster than the time needed by the solver in average The results show that the metaheuristic is really helpful when searching for good solutions rapidly. Even if the results are not proven to be optima, their quality are always better or equal to these provided by the CPLEX solver which validates this work.

Conclusion

Nowadays, commonly used objective functions in scheduling problems, such as makespan or total tardiness cannot be considered as the only objectives. Environmental issues and economic reasons lead to also take into account other objectives such as minimisation of greenhouse gas emission or electricity consumption. There exists different ways of increasing energy efficiency of a production system by minimizing the total energy needed, or the consumption peaks. This study focuses on the last point, leading to the formulation of the Job-shop with an energy threshold constraint. In this problem each operation presents two type of energy consumption, thus a model considering sub-operations that correspond to the different energy consumption is proposed. The energy threshold is handled by respecting a maximum energy capacity over the machine-network. The instances generated representing small production systems, with few jobs and machines, are not easily solved exactly. Hence a metaheuristic based on a GRASPxELS has been implemented in order to obtain faster solutions to these small scale instances. The results show that the approach is effective since the GRASPxELS returns really good results which are always equal or better to the ones provided by CPLEX, in a competitive duration. However, exact methods should be further studied, with the use of Lagrangian relaxation for example. In a future work, medium and large scale instances will be addressed in a bi-objective context thus leading to a Pareto graphical representation. It could also be interesting to add other objectives such as decreasing the total energy consumption or include TOU pricing in order to reduce the cost of the production. The possibility to have different energy behaviour for the machines should also be studied as the accuracy of the energy discretization [START_REF] O'rielly | Strategies to improve industrial energy efficiency[END_REF]. Finally, combining the different approaches seen in the literature concerning the energy-efficient production systems could lead to an interesting and complete problem.

Fig. 2 :

 2 Fig. 2 : Energy Block Representation proposed by Weinert et al., 2011[START_REF] Weinert | Methodology for planning and operating energyefficient production systems[END_REF]

Fig. 3 :

 3 Fig. 3 : Graphical representation of a JSECT On the Fig. 3 some extra rectangles have been added to delimitate the global operations presented on Fig.1and to provide the energy needed for each operation. Furthermore, it can be stressed that only two disjunctive edges relative to disjunctive constraints on machines between two operations are presented on the graph, in order to ease its reading (the former operations O6 and O11 in the Fig.1which have been transformed into operations O11-O12 and O21-O22). Indeed, since operations cannot be stopped once started, these edges represent the fact that the first suboperation (i.e.: representing the consumption peak) must be scheduled after the end of a previous operation treated by the same machine, and hence must be scheduled after the second suboperation of such an operation. In this example, it means that the operation O11 should be scheduled after the end of the operation O22 or the operation O21 should come after completion of the operation O12. To complete this graph representation, the energy threshold is modelled as an extra vertex with a value corresponding to the available energy that must not be exceeded. Thus, one of the objective is to efficiently allocate the energy to the machines in order to obtain the smallest possible makespan. When there is not enough energy allocable to an operation, because of running operations extra conjunctive arcs are added to model the new precedence between operations due to the energy threshold. These extra conjunctive arcs represent the duration that an operation must wait before enough energy could flow from a finished operation to the one that must be scheduled (arc in bold on Fig.3). Thus, a conjunctive arc may be present

4. 1

 1 Parameters M : set of machines; V : set of all the sub-operations (|V|=2.|V|); i,j,k,l : indexes representing the different sub-operations to schedule, i,j,k,l ∈ ⟦1;|V|⟧ ; Oi : global operation of the sub-operation i; Ji : job of the operation i; pi : duration of sub-operation i; μi : machine required to process sub-operation i, μi∈M; H : a large positive number.

7th

  Multidisciplinary International Conference on Scheduling : Theory and Applications (

Fig. 4 :

 4 Fig.4: An example of an instance for JSECT

Table 1 :

 1 Different studies concerning energy in production systems

	References	Single Machine	Flow-shop	Flexible Flow-shop	Job-shop	Flexible Job-shop	Carbon footprint	Consummation Pics	Total Energy	Energy Price (TOU)	Makespan	Total Tardiness	Robustness
	Balogun and Mativenga, 2013 [2]								x
	Bruzzone et al., 2012 [4]			x				x			x	x
	Dai et al., 2013 [6]			x					x		x
	Fang et al., 2011 [9]		x				x	x			x
	He et al., 2005 [12]				x				x		x
	He et al., 2015 [13]					x			x		x
	Liu et al., 2014 [17]				x				x			x
	Luo et al., 2013 [18]			x						x	x
	Mouzon et al., 2007 [19]	x							x		x
	Salido et al., 2013 [25]				x				x		x		x
	Shrouf et al., 2014 [26]	x								x
	Xu et al., 2014 [31]			x				x			x	x
	Zhang et al., 2014 [32]		x				x			x

  End 7th Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2015) 25-28 August 2015, Prague, Czech RepublicAlgorithm 3 is focused on evaluating a sequence of operations according to machine disjunctions. The energy aspect of the schedule is handled during the Adjust_Energy_Date algorithm, where the starting date of an operation is updated in order to respect the given energy threshold. The principles of adjusting dates according to available energy is given in algorithm 4.

		7th Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2015)
		25-28 August 2015, Prague, Czech Republic
	Algorithm 4: Adjust_Energy_Date
	Procedure name Adjust_Energy_Date
	Algorithm 3: Evaluation Input/output
	Procedure name Evaluation d: theoretical starting date of the operation
	Input/output father : theoretical father of the operation
	t_S[]: table for energy change dates : sequence to evaluate t_E[]: table for energy available according to dates Input Input n: number of operations op: operation to schedule Variables Variables i: loop index s1, s2, s3: indexes for placing operation according to energy op_M[]: last operation on machine t_Job[]: time job has been treated op_placed: boolean
	Begin t_S[]: table for energy change dates 1. s1≔0, s2≔0, s3≔ 0; t_E[]: table for energy available according to dates job: job treated 2. op_placed ≔ false;
	3. op: operation to schedule WHILE not op_placed DO 4. s1≔ index in t_E with enough energy available for first part of op starting from s1; machine: machine for the operation 5. Check if there is enough energy during first part of op; father, fatherD: predecessor and disjunctive predecessor 6. s2≔ index for end of first part of op if possible; d, dPD: end date of predecessor and disjunctive predecessor 7. IF the first part of op is schedulable THEN
	Begin 8.	Check if there is enough energy during second part of op;
	1. 9.	Init op_M, t_Job, t_S; Init t_E with energy threshold allowed; s3≔ index for end of second part of op if possible;
	2. 10.	FOR i :=0 to n DO IF the second part is schedulable THEN
	3. 11.	job := .sequence[i] ; op_placed ≔ true;
	4. 12.	op := operation corresponding to job's occurence; ELSE
	5. 13.	machine := machine for op; s1≔ s3
	6. 14.	d := 0; dPD := 0; END
	7. 15.	father := -1; fatherD := -1; ELSE
	8. 16.	IF t_Job[job] <> 0 THEN s1≔ s2;
	9. 17.	//Conjunctive father END
	10. 18.	father := vertex -1 ; END
	11. 19.	d:= End[father]; IF t_S[s1] <> d THEN update father according to energy disjunction; END
	12. 20.	END IF d≔ t_S[s1];
	13. 21.	IF (op_M[machine] <> -1) THEN insert d, end date of first and second part of op in t_S;
	14. 22.	//Disjunctive father deduce energy used between s1and s3 in t_E;
	15. End	fatherD := op_M[machine] ;
	16.	dPD:= End[fatherD] ;
	17. 18. 6	END IF IF (dPD > d) THEN update father and d; END IF Computational evaluation
	19. 20. At first, the linear program has been tested using the CPLEX 12.4 solver on a machine Call Adjust_Energy_Date(d, op, father, t_S, t_E); Save d and father into ; 21. embedding a Xeon E7-8870 processor. The previous algorithms have been implemented in C++ Increment t_Job[job]; 22. and have been executed on a computer with an i7-4800MQ processor, running Windows 7 op_M[machine] ≔ op; 23. (Linpack Benchmark: 2277.01 MFLOPS). Parameters used in the GRASPxELS for the number END of restart, the number of ELS and the number of neighbors are respectively 60, 30, 15. The
	24. instances used for the JSECT are composed by four to six jobs and four machines. These Compute final makespan and store it into ;
	instances have been randomly generated by considering that the basic energy consumption and
	the consumption peak of an operation is between 1 and half of the duration of the operation, and

Table 2 :

 2 Results obtained with CPLEX and GRASPxELS on 45 instances -Part I

	CPLEX	GRASPxELS

Table 3 :

 3 Results obtained with CPLEX and GRASPxELS on 45 instances -Part II

					CPLEX						GRASPxELS
	Jobs x Machines	Instances	Energy Threshold	BKS	UB -LB	Gap	TT	AVG_S	TT_S	TTB_S	DEV_LB	DEV_UB
		Inst_1	85	344*	-	344	0	7,42	344	0,44	0,010	0	0
			75	344*	-	344	0	13,02	344	0,53	0,004	0	0
			65	370*	-	370	0	40,4	370	0,73	0,004	0	0
		Inst_2	83	425*	-	425	0	13,75	425	0,55	0,002	0	0
			73	448*	-	448	0	1755,19	448	0,69	0,002	0	0
			63	510*	-	510	0	8606,19	510	0,89	0,014	0	0
		Inst_3	66	366*	-	366	0	70,74	366	0,64	0,028	0	0
	5 x 4		56	375*	-	375	0	274	375	0,99	0,004	0	0
			46	468	468	395	15,6	10800	442	1,70	0,052	11,9	-5,56
		Inst_4	85	309*	-	309	0	32,94	309	0,39	0,008	0	0
			75	336*	-	336	0	389,07	336	0,47	0,016	0	0
			65	343*	-	343	0	227,76	343	0,60	0,230	0	0
		Inst_5	77	320*	-	320	0	6,53	320	0,43	0,022	0	0
			67	331*	-	331	0	83,29	331	0,60	0,008	0	0
			57	367*	-	367	0	591,34	367	0,92	0,042	0	0
	Average:							1527,44		0,71	0,03	0,79	-0,37
		Inst_1	100	406	406	405	0,25	10800	406	0,85	0,076	0,25	0
			90	406*	-	406	0	112,07	406	1,08	0,088	0	0
			80	426*	-	426	0	6022,18	426	1,48	0,054	0	0
		Inst_2	83	477	477	476	0,25	10800	477	0,95	0,010	0,21	0
			73	519	519	499	3,85	10800	519	1,24	0,168	4,01	0
			63	582	582	474	18,56	10800	572	1,71	0,234	20,68	-1,72
		Inst_3	95	433*	-	433	0	44,2	433	0,93	0,018	0	0
	6 x 4		85	463	463	435	6,05	10800	454	1,21	0,082	4,37	-1,94
			75	465*	-	465	0	855,29	465	1,66	0,204	0	0
		Inst_4	85	362*	-	362	0	2140,83	362	0,79	0,006	0	0
			75	411	411	340	17,27	10800	385	0,90	0,098	13,24	-6,33
			65	429	429	363	15,38	10800	429	1,34	0,016	18,18	0
		Inst_5	82	403	403	388	3,72	10800	395	0,88	0,076	1,80	-1,99
			72	408*	-	408	0	2455,89	408	1,24	0,072	0	0
			62	471	471	403	14,44	10800	441	1,92	0,104	9,43	-6,37
	Average:							7255,36		1,21	0,09	4,81	-1,22

7th Multidisciplinary International Conference on Scheduling : Theory and Applications (MISTA 2015) 25-28 August 2015, Prague, Czech Republic

Acknowledgements

This work was financially supported by the French Public Investment Bank (BPI) and granted by the ECOTHER project.


J Macanás

L Ouyang

M L Bruening

M Muñoz

J - C Remigy

Jean-François - F Lahitte
email: lahitte@chimie.ups-tlse.fr

Affiliation

Development of polymeric hollow fiber membranes containing catalytic metal nanoparticules

Keywords: membrane, hollow fiber, metallic nanoparticle, polyelectrolyte multilayer, catalyst

Metal Nanoparticles (MNPs) have unique physico-chemical properties advantageous for catalytic applications which differ from bulk material. However, the main drawback of MNPs is their insufficient stability due to a high trend for aggregation. To cope with this inconvenience, the stabilization of MNPs in polymeric matrices has been tested. This procedure is a promising strategy to maintain catalytic properties.

The aim of this work is the synthesis of polymer-stabilized MNPs inside functionalized polymeric membranes in order to build catalytic membrane reactors. First, the polymeric support must have functional groups capable to retain nanoparticle precursors (i.e. sulfonic), Then, nanoparticles can grow inside the polymeric matrix by chemical reduction of metal ions.

Two different strategies have been used in this work. Firstly, polyethersulfone microfiltration hollow fibres have been modified by applying polyelectrolyte multilayers. Secondly, polysulfone ul-trafiltration membranes were modified by UV-photografting using sodium p-styrene sulfonate as a vinyl monomer. The catalytic performance of developed hollow fibers has been evaluated by using the reduction of nitrophenol to aminophenol by sodium borohydride. Hollow fibre modules with Pd MNPs have been tested in dead-end and cross-flow filtration. Complete nitrophenol degradation is possible depending on operation parameters such as applied pressure and permeate flux.

Introduction

The rejection of synthetic chemicals by man during decades has led to water pollution. Some of these polluting molecules with low molecular weight (pesticides, endocrine disruptor, antibiotics,...) are hardly removed by the conventional water treatment processes [1,2]. Either the oxidation or the reduction of these chemicals by means of soft catalytic reactions might allow the treatment of some polluted water if the derived compounds are more easily removable. Furthermore, the combination of catalysis and membrane processes may change and separate pollutants through a single step [3].

Metal nanoparticles have unique physical and chemical properties which differ from bulk metal and isolated atoms [4][5][6][7]. Catalysis provides a natural application for nanoparticles because their large surface area-to-volume ratio allows effective utilization of expensive metals such as Platinum Group Metals [8]. Without a suitable support, however, metal particles aggregate, reducing their effective surface area and increasing the average particle size which is the key parameter that controls many of the special properties of nanomaterials [START_REF]Nanoparticles -From Theory to Application[END_REF][START_REF] Toshima | [END_REF][START_REF] Pomogailo | Metallopolymer Nanocomposites[END_REF]. To overcome this problem, catalytic nanoparticles have been immobilized on solid supports, e.g., carbon, metal oxides, and zeolites, or stabilized by capping ligands that range from small organic molecules to large polymers [4]. From the above strategies, encapsulation by polymers seems advantageous because in addition to stabilizing and pro-tecting the particles, polymers offer unique possibilities for modifying both the environment around catalytic sites and the access to these sites [START_REF] Kidambi | [END_REF]. Hence, the protective polymer not only influences particle size and morphology but can also have a tremendous influence on catalytic activity and/or selectivity. Thus, including nanoparticles inside polymeric membrane would yield to a useful material for process intensification [3,13,14].

Catalytic polymeric membranes reactor are promising devices for their aptitude to separate the reagents and the products [13,15]. Among the different existing membrane configurations, hollow fibers (tubular membranes of a few millimeters in diameter, with micrometric walls) present the main advantage of having a very high-volume area, which allows the manufacture of modules with a large filter surface but with a reduced volume [16]. Hollow fibers properties can be tailored by surface modification which can be carried out through different techniques such as photochemical modification (photographting), modification by plasma, or coated with polymers or polyelectrolyte [17,18].

For instance, the UV photografting [19][20][21] technique, based on free radical polymerisation initiated from the membrane, permits to obtain various types of grafted polymeric chains. This kind of grafting is very stable due to the covalent bound existing between the grafted polymer and the membrane and it can be very useful for adding chemical functionality at the surface of the membrane. This method was initially used for decreasing membrane molecular weight cut-off by adding charged sites using charged monomers such as acrylic acid (AA) or styrene sulfonate (SS) [18]. As a result, the filtration properties of the membrane were enhanced.

Besides, another surface modification involves sequential deposition of Polyelectrolyte Multilayers (PEMs), originally described by Decher [22]. These multilayers are prepared by sequential deposition (layer by layer deposition) of low molecular weight polymers with ionic charges (eg sulphonic groups, amine groups ...) allowing the presence of either cationic or anionic sites on the external surface of the membrane or in the inside pores [22][23][24]. The layers formed by polyelectrolytes of oppo-site charge are attracted to each other by electrostatic interactions, thus creating dense layers. At first, PEMs were used for the modification of membranes and their application in improved filtration processes, filtered solutes interacting differently with the filtering surface as a function of its electric charge [25].

In the present work, we have loaded the charged groups on the membrane with metal ions and subsequently reduce these ions to obtain metal nanoparticles (MNPs) by inter-matrix synthesis technique [5,[START_REF] Pomogailo | Metallopolymer Nanocomposites[END_REF]26]. This method for preparing nanoparticles has already been successfully tested for the development of new electrochemical sensors [27,28]. Therefore, using polymer grafting or polyelectrolyte deposition, highly active catalytic nanoparticles can be included inside hollow fibers membranes to obtain a catalytic membrane reactor [START_REF] Kidambi | [END_REF]29]. Characterization of the catalytic effect of the fibers was performed using a reaction model widely used in the evaluation of new catalysts for reactions in aqueous phase, the reduction of p-nitrophenol in presence of sodium borohydride and metallic catalyst [23].

Experimental

Photografting set-up

A complete photografting set-up was described in a previous article [20]. Ultrafiltration polysulfone hollow fibers (PS-UF-HF) provided by Polymem SA (Fourquevaux, France) were initially wet by water, dipped in an aqueous monomer solution, and degassed using N 2 . N,N'-methylene-bisacrylamide (crosslinker), sodium p-styrene sulfonate, and 4-hydroxybenzophenone (photoinitiator) were purchased from Aldrich and used as received without further purification.

The fiber was passed through two UV polychromatic lamps with closed elliptical reflectors (model FOZFR 250, λ > 295 nm, I 0 = 338 mW•cm -2 for UVB, Hoenle UV France, Lyon, France). The operating rate can be adjusted between 5 to 20 m•min -1 . After irradiation, hollow fibers were carefully washed with reverse osmosis treated water.

As a consequence of this procedure, the chemical modification only occurs on the hollow fiber outer surface (outside modified PS-UF-HF).

Layer-by-Layer Adsorption of Polyelectrolyte

Polyethersulfone microfiltration hollow fibers (PES-MF-HF) were purchased from MEMBRANA GmbH, Germany (MicroPES TF10) and were modified by the polyelectrolyte multilayer technique, as described previously [22].

A first layer of polyanion (Poltystyrene sulfonate, PSS) was deposited by submerging the PES-MF-HF into an appropriate solution (PSS 20 mM and NaCl 0.5 M). The linking proceeds by a π-π interaction due to aromatic rings. A second layer of polycation (polyallylamine, PAH 20mM and NaCl 0.5M) was deposited after rinsing. In this case, hollow fibers are just modificed on the surface because the polyelectrolytes can not diffuse to the fiber interior (outside modified PES-MF-HF).

Alterantively, the inner part of the fiber can also be modified by pumping the polyelectrolyte through the membrane (inside/outside modified PES-MS-HF).

Metal Loading Metal Loading

The synthesis of MNPs in the grafted polymeric layer of the membrane was carried out in situ by a two-step procedure [28]. First, fibers were dipped in a Pd(NH 3 ) 4 ] +2 0.01M solution what yields to ion loading in the membrane surface by an ion-exchange reaction (Eq 1). Secondly, metal ions load on fibers undergo a reduction with 0.1 M aqueous NaBH 4 solution (Eq 2). It is noteworthy that this modification was done directly on the fibers which were already in filtration modules. Afterwards, fibers were rinsed with pure water.

2R-SO

3 -Na + + [Pd(NH 3 ) 4 ] +2 → (R-SO 3 - ) 2 [Pd(NH 3 ) 4 ] +2 + 2Na + . Eq 1 (R-SO 3 - ) 2 [Pd(NH 3 ) 4 ] +2 + 2NaBH 4 + 6H 2 O → 2R-SO 3 - Na + + 7H 2 + 2B(OH) 3 + Pd 0 Eq 2
Determination of metal concentrations in aqueous solutions was carried out either by Inductively Coupled Plasma Atomic Emission Spectroscopy (ICP-AES) using an Iris Intrepid II XSP spectrometer (Thermo Electron Co.) or by ICP Mass Spectrometry (ICP-MS) using a ThermoElemental ICP-MS, model PQExcell. In all cases, average uncertainty was <2%.

Fibers were also modified by deposition of gold nanoparticles prepared ex situ using the citrate method, in which sodium citrate serves as both reducing agent and stabilizer [31].

Test filtration

Modified PES-MS-HF were tested in a dead-end fi-tration set up using a single-fiber module whereas modified PS-UF-HF were tested in a tangential filtration set up using a laboratory made module of 5 fibers. Figure 1 shows the module conception for both filtration procedures. In deadend filtration set up, the solution was passed through the membrane at constant pressure and permeated through the membrane. In this case, the solutes which are unable to pass through the membrane increase its concentration in solution which may encourage the membrane fouling. In the case of tangential filtration, passage through the membrane is in the perpendicular direction to the flow of solution to be filtered. This will get two effluents: permeate (which crosses the membrane) and retentate (which is retained). The solution tank is driven by a pump and passes through the membrane module (permeate) while the other can be recycled back to the tank. This type of configuration is more interesting to reduce the fouling but needs more energy.

(Figure 1 here)

Catalytic reduction of 4-nitrophenol

The catalytic performance of modified hollow fibers has been evaluated by a model reaction, reduction of 4-nitrophenol to 4-aminophenol by sodium borohydride (Figure 2).

(Figure 2 here)

This reaction is quite simple to follow by UV spectroscopy as the solution of 4-nitrophenol is yellow and has a maximum absorption between 330 and 400 nm (depending on the pH). The decrease in the intensity of this peak is directly connected with the transformation of 4-aminophenol compound which absorbs below 300 nm and therefore is colourless. Furthermore, this reaction does not take place in the absence of catalyst [23,[32][33][34][35].

Results

MNPs content in the membrane

The white hollow fibers turned grey after Pd reduction or pink after Au reduction, which was a good qualitative test of nanoparticle formation. ICP-AES and ICP-MS confirmed that the metal loading was about 1.87 μg Pd/cm 2 for the modified outside PS-UF-HF membranes, 0.82 μg/cm 2 for the outside modified PES-MF-HF and 155 μg Au/cm 2 for the inside/outside modified PES-MF-HF (surface area refers to the surface of the external hollow fiber skin). These data are in agreement with expected results since the modification of membrane inner part with polyelectrolytes allows a higher incorporation of metal nanoparticles inside the membrane compared with the surface modification.

Catalytic reduction of 4-nitrophenol

UV spectra of solutions of pure 4-nitrophenol, with or without reducing agent and with or without bare fiber did not significantly change after 24 hours at room temperature (Figure 3). On the contrary, the analysis of the UV spectra of a nitrophenol solution with reducing agent and a fiber with nanoparticles inside (catalytic surface = 1.6 cm 2 ) demonstrate the catalytic activity of our system because the 4-nitrophenol UV absorption peak clearly disappeared after 24 hours and we obtained a spectra similar to a solution of 4-nitrophenol. Thus, the catalytic activity of modified fibers containing nanoparticles was proved impliying that catalytic sites are accessible to the reagents.

(Figure 3 here)

Catalytic activity test of PSS/PAH/Au inside coated fiber in frontal filtration mode.

Since, microfiltration membranes allow higher fluxes than ultrafiltration membranes, modified PES-MS-HF were tested in dead-end filtration configuration. In this case, fibers were coated using the LBL technique and nanoparticles were deposited both on the outside and the inside of the fiber. -Results of 4-nitrophenol degradation and specific flux over a 2-hour reaction time are plotted respectively in Figure 4 and Figure 5. As it can be seen, a constant yield of more than 95% of 4nitrophenol was obtained during the first hour but the effectivity decreased gradually to about 80% until the end of the experiment. Figure 5 shows the evolution of the specific flux during the experimen and, although the trend is not clear, it looks like the flux slightly increased with the time.

(Figure 4 and figure 5 here)

Catalytic activity test of PSS/PAH/Pd outside coated fiber in dead end filtration mode.

Outside modified PES-MF-HF containing in situ prepared Pd nanoparticles were also tested in a dead-end filtration set up using a single-fiber module. In this case, with this procedure, it is possible to reduce the initial concentration of 4-nitrophenol to less than 5% (95% efficiency) by a single passage through the catalytic membrane (Figure 6). However, in order to achieve this value it was necessary to wait for about 1 hour and catalytic filtration before this time was less successful. By the way, we observed that the catalytic efficiency increased with filtration time when flux decreased.

(Figure 7).

(Figure 6 and Figure 7 here)

Catalytic activity test of PSS/Pd outside coated PS-UF-HF in tangential filtration mode.

In the tangential flow set up, it was possible to reach a conversion of up to 90% in the permeate solution compared with the initial concentration in the tank, demonstrating the catalytic activity of these membranes in an operation mode closer to a real water treatement (Figure 8). The permeate flow rate in this case was quite low (e.g. 0.7 mmol -1 .min -1 .m -2 at 5 bar) and it was found to be constant after 1 hour of operation, this is why a plateau was observed for every applied pressure.

(Figure 8 here)

Discussion

The observed reduction rates in the tangential or dead-end set up demonstrate the catalytic properties of the synthesized membranes. These rates are quite important given the relatively low metal loading of the membrane. These results can be explained by the important catalytic surface due to the absence of aggregation between nanoparticules stabilised by the polymeric matrix and the easy access of nitrophenol to catalytic nanoparticles located at the surface of the membrane which occur here by convection instead of diffusion.

First experiments were carried out with the PES-MF-HF coated inside and outside because we expected high conversion due to the high exchange surface. Although the high conversion obtained (100 %) demonstrated the good efficiency of this set up, the fast decrease observed was not expected.

We account for a possible poisoning of the catalyst due to the by-products of nitrophenol reduction reaction which can interfere with the membrane surface. Indeed, although this reaction has been of-ten used as a model for catalytic test due to its simplicity [23,29], the reaction is actually the result of a series of steps [37] (Eq 3-5):

R-NO 2 +2H + + 2e -→ R-NO + H 2 O Eq 3 R-NO +2H + + 2e -→ R-NHOH Eq 4 R-NHOH +2H + + 2e -→ R-NH 2 + H 2 O Eq 5
The reaction intermediates can interact among themselves leading to unwanted polyaromatic species (Eq 6 and Eq 7) which migh have an affinity to polysulfone or polyethersulfone membranes, yielding to an undesirable absortion.

R-NO + R-NH 2 → R-N=N-R + H 2 O Eq 6 R-NO + R-NHOH → R-N=N(O)-R + H 2 O Eq 7
In this scenario, the higher the conversion, the higher the catalyst poisoning. For this reason, we chose to test a PES-MF-HF only modified in the surface and so less charged in catalyst. The obtained conversion is not so high as in the case of the inside/outside modified PES-MF-HF but superior to 80%. The evolution of this conversion is totally different as we observed an increase of the conversion with the time and a decrease of the flux at the same time. The decrease of the flux with time suggests a pore blocage. This blocage can be due to hydrogen produced during the reduction because hydrogen bubbles from NaBH 4 evolved onto the catalyst surface can possibly block pore and, as a consequence, dry some part of the membrane. Thus, aqueous solutions could not penetreate into the pore due to the high Laplace pressure.

On the other hand, the fact that a decrease of the conversion was not observed suggested that there was not (or only a minor) poisoining of catalyst. If by-products were synthesized, they were not ac-cumuled on the surface (where the catalyst is located) but inside the membrane, participating eventually to the membrane fouling. In fact, it was interesting to compare the conversion evolution in relation to the observed flux. Conversion increased while observed flux decreased (Figure 9). We explain this result by considering the residential time of the solution in the catalysis layer at the surface of the membrane: when the catalyst accessibility is the limiting step, lower fluxes mean higher residential time what corresponds to a higher conversion. Bearing this in mind, one can suggest that our membrane reactor acts as a perfectly agitated reactor where diffusion is negligible compared to convection (here, due to the applied pressure). So, in our experimental conditions, we can assume that the reaction rate is low in front of the value of the flux of reactants.

(Figure 9 here) Finally, tangential filtration mode was expected to prevent fouling and to lead to a more stable process but obtained results didn't show a clear tendance. As observed in Figure 8, the efficiency of the process increased with the applied pressure and so did the permeate flux. Contrary to the deadend filtration configuration, here better efficiencies were obtained for higher fluxes. Moreover, conversion seemed to be stable during the time but the production of hydrogen inside the tank during the experiment (due to the poor stability of NaBH 4 in solution [36,37]) jeopardizes the applicatibility of this configuration in a real water treatment application. Gas-liquid contactors configuration could be a better mode to work with this kind of modified fibers.

Conclusions

Hollow fibers modules have been tested in both dead-end and cross-flow filtration setups, and the experimental results show that complete 4-nitrophenol degradation is possible by optimizing opera-tion parameters such as applied pressure and permeate flux. This reaction was selected just to demosntrate the potentiality of these new modified membranes.

Dead-end filtration appears to be more efficient that tangential filtration mode due to the easiest reaction and filtration control conditions. However, system configuration needs to be improved since it is necessary to purge H 2 bubbles formed inside the module which can displace water avoiding a good contact between the membrane and the solution. Almost total conversion is promising for future applications, but flux must be increased.

List of figures

Fig. 1 Fig. 2 Fig. 4 Fig. 5 Fig. 6 Fig. 7 Fig. 8 Fig. 9

 12456789 Fig. 1 Experimental filtration set up

Acknowledgements

Authors acknowledge «L'Agence Nationale pour la Recherche, ANR» for financial support through the project "Développement de procédés de fabrication de membranes nanostructurées et résistantes aux solvants" and the National Science Foundation (OIS 0530174) for funding this research. J. Macanás is also thankful to the Departament d'Universitats, Recerca i Societat de la Informació de la Generalitat de Catalunya for a postdoctoral fellowship