Muhammad Akbar
email: muhammad@eagle.sophia.ac.jp

Dual resource constrained scheduling considering operator working modes and moving in identical parallel machines using a permutation-based genetic algorithm

Keywords: DRC scheduling, working modes, moving, makespan

This paper proposes a novel dual resource constrained (DRC) scheduling problem under identical parallel machine environment that consider operator working modes and moving activity between machines with regards to the makespan minimization objective. We define the working modes as all operator activities when the operators interact with the machines such as loading, setup, controlling, and unloading. Firstly, we provide the mathematical model of the problem using Mixed Integer Linear Programming (MILP). We add unloading activity beside setup to be included in the model. Also, we consider the moving activity that is usually neglected in DRC scheduling problem. Moreover, we propose a permutation-based genetic algorithm (PGA) to tackle the computational burden of the bigger size problem. Then, we run a full factorial experiment with replication to compare the solution quality and computational time of our PGA to the solver and random search method. The results show that our proposed PGA could solve the problem in a reasonable time that is faster than the solver with a good quality solution that is better than random search.

Introduction

Recently, many industries use partially automated machines for producing products which operators can leave them in the machining time. The operators are necessary for such only activities like the loading and unloading jobs, sometimes controlling or doing the setup [START_REF] Baptiste | FPTAS for the two identical parallel machine problem with a single operator under the free changing mode[END_REF]. The total idle time of operators becomes the highest if they only operate a machine each. However, assigning an operator to two or more machines results in some machine waiting time that increases the makespan or the tardiness. Dual resource constrained (DRC) scheduling considers both machine and operator resources as limiting resources [START_REF] Elmaraghy | Scheduling of Manufacturing Systems under Dual-Resource Constraints Using Genetic Algorithms[END_REF]. Most research in DRC scheduling deals in a condition that the operator number is not less than the number of machines, e.g. [START_REF] Hu | Minimizing total flow time for the worker assignment scheduling problem in the identical parallel-machine models[END_REF] and [START_REF] Chaudry | Minimizing total tardiness for the machine scheduling and worker assignment problems in identical parallel machine using genetic algorithms[END_REF]. On the next level, we find articles that deal with fewer operators, but they cannot supervise many jobs at the time [START_REF] Agnetis | A job-shop problem with one additional resource type[END_REF], [START_REF] Paksi | Flexible Job-Shop Scheduling with Dual-Resource Constraints to Minimize Tardiness Using Genetic Algorithm[END_REF]. Only a little research considers an operator can supervise several machines simultaneously [START_REF] Baptiste | Solving the two identical parallel machine problem with a single operator[END_REF] as in [START_REF] Baptiste | FPTAS for the two identical parallel machine problem with a single operator under the free changing mode[END_REF], [START_REF] Costa | A hybrid genetic algorithm for job sequencing and worker allocation in parallel unrelated machines with sequence-dependent setup times[END_REF].

There are several approaches to solve the DRC scheduling with each operator can process many jobs simultaneously. One approach uses a given finite set of working modes as a reference to estimate the job processing time using multipliers [START_REF] Baptiste | FPTAS for the two identical parallel machine problem with a single operator under the free changing mode[END_REF]. The other approach uses mixed-integer linear programming (MILP) model allowing an operator to do many setup activities and leave the machine while processing the job to minimize the makespan [START_REF] Costa | A hybrid genetic algorithm for job sequencing and worker allocation in parallel unrelated machines with sequence-dependent setup times[END_REF]. In this work, we combine the advantages of both to propose a new approach by applying MILP model to get a more accurate solution and considering many working modes such as loading, setup and unloading activities. Also, this research considers transportation time between machines.

Problem statement

Figure 1 illustrates the proposed DRC scheduling problem with three identical parallel machines and two same-skill operators with five jobs. It must consider not only the sequence of jobs in each machine but also the activity/task sequence of jobs and moving sequence performed by each operator that makes this problem becomes harder to solve. Therefore, we must include the operators' assignment on the Gantt chart to describe the schedule. The new consideration of task allocation causes the job assignment to the operator becomes more flexible in which one job can be performed by different operators, e.g., setup performed by an operator and unloading by another operator. We only consider setup (that includes loading) and unloading activities in the model. This contribution do not appear in the traditional scheduling problem since the operators always control the same machine. The other contribution related to moving route and time makes the computation of makespan more precise. We describe the problem statement of this DRC scheduling problem as follows. The production system consists of a set M of m identical parallel machines and a set W of w identical operators where w ≤ m. This production system must produce a set N of n jobs aiming at the minimization of the makespan. Each job needs three sequence activities, which are setup, machining, and unloading performed on a unique machine. Each operator can contribute to any b activities of working modes from a set B. In our case, the b value is two consisting setup and unloading activities. Thus, each Operator moving from machine h to machine i operator could move from one machine after finishing one activity b to the other machine to perform any activity in set B. Any activity b of job i starts if both the assigned machine j and operator k are available.

The mathematical model

We refer to the previous research [START_REF] Costa | A hybrid genetic algorithm for job sequencing and worker allocation in parallel unrelated machines with sequence-dependent setup times[END_REF] then adjust and add some new constraints to build our own MILP model. We adjust some constraints in several ways by adding new activity indices (1 for setup and 2 for unloading) to the decision variables and place the operator indices as the main resource instead of the machine. It is because the operator assignment is more complicated than the machine since two operators are possible to execute the same job. We also include transportation time between machines as a new parameter. The mathematical formulation is reported as follow.

Indices

𝐶 𝑚𝑎𝑥 the makespan Model minimize 𝐶 𝑚𝑎𝑥 (1) subject to: ∑ ∑ ∑ ∑ ∑ 𝑋 𝑘ℎ𝑎𝑗𝑖𝑏𝑙 𝑚 𝑖=1 𝑛 𝑗=0 2 𝑎=1 𝑚 ℎ=1 𝑤 𝑘=1 = 1 ∀𝑏 = 1,2; 𝑙 = 1,2, … , 𝑛 (2)
∑ ∑ ∑ ∑ ∑ 𝑋 𝑘ℎ𝑎𝑗𝑖𝑏𝑙 𝑛 𝑙=1 2 𝑏=1 m 𝑖=1 𝑚 ℎ=1 𝑤 𝑘=1 ≤ 1 ∀𝑎 = 1,2; 𝑗 = 1,2, … , 𝑛 (3)
∑ ∑ ∑ ∑ 𝑋 𝑘ℎ20𝑖𝑏𝑙 𝑛 𝑙=1 2 𝑏=1 𝑚 𝑖=1 𝑚 ℎ=1 ≤ 1 ∀𝑘 = 1,2, … , 𝑤 (4)
∑ ∑ ∑ ∑ 𝑋 𝑘ℎ10𝑖𝑏𝑙 𝑛 𝑙=1 2 𝑏=1 𝑚 𝑖=1 𝑚 ℎ=1 = 0 (5) ∑ ∑ ∑ ∑ 𝑋 𝑘ℎ𝑎𝑗𝑖1𝑙 𝑛 𝑗=0 2 𝑎=1 𝑚 ℎ=1 𝑤 𝑘=1 -∑ ∑ ∑ ∑ 𝑋 𝑞𝑔𝑐𝑓𝑖2𝑙 𝑛 𝑓=0 2 𝑐=1 𝑚 𝑔=1 𝑤 𝑞=1 = 0 ∀𝑖 = 1,2, … , 𝑚; 𝑙 = 1,2, … , 𝑛 (6)
∑ ∑ ∑ 𝑋 𝑘ℎ𝑎𝑗𝑖𝑏𝑙 𝑛 𝑗=0 2 𝑎=1 𝑚 ℎ=1 ≥ ∑ ∑ ∑ 𝑋 𝑘𝑖𝑏𝑙𝑔𝑐𝑓 𝑛 𝑓=1 2 𝑐=1 𝑚 𝑔=1 ∀𝑘 = 1,2, … , 𝑤; 𝑖 = 1,2, … , 𝑚; 𝑏 = 1,2; 𝑙 = 1,2, … , 𝑛 (7) 𝑂 𝑏𝑙 𝑐 -𝑇 𝑏𝑙 𝑐 ≥ 𝑂 𝑏𝑙 ∀𝑏 = 1,2; 𝑙 = 1,2, … , 𝑛 (8) 𝑇 𝑏𝑙 𝑐 -𝑂 𝑎𝑗 𝑐 ≥ ∑ ∑ ∑ 𝑇 ℎ𝑖 • 𝑋 𝑘ℎ𝑎𝑗𝑖𝑏𝑙 𝑤 𝑘=1 𝑚 𝑖=1 𝑚 ℎ=1 -𝐵 • (1 -∑ ∑ ∑ 𝑋 𝑘ℎ𝑎𝑗𝑖𝑏𝑙 𝑤 𝑘=1 𝑚 𝑖=1 𝑚 ℎ=1 ) ∀𝑏 = 1,2; 𝑙 = 1,2, … , 𝑛; 𝑎 = 1,2; 𝑗 = 0,1, … , 𝑛 (9)
𝑂 2𝑙 𝑐 -𝑃 𝑙 𝑐 ≥ 𝑂 2𝑙 ∀ 𝑙 = 1,2, … , 𝑛 (10)
𝑃 𝑙 𝑐 -𝑂 1𝑙 𝑐 = 𝑃 𝑙 ∀ 𝑙 = 1,2, … , 𝑛 (11)
{ 𝑂 1𝑙 𝑐 -𝑂 2𝑓 𝑐 ≥ ∑ ∑ ∑ ∑ 𝑂 1𝑙 • 𝑋 𝑘ℎ𝑎𝑗𝑖1𝑙 𝑛 𝑗=0 2 𝑎=1 𝑚 ℎ=1 𝑤 𝑘=1 -𝐵 • (2 -∑ ∑ ∑ ∑ (𝑋 𝑘ℎ𝑎𝑗𝑖1𝑙 + 𝑋 𝑘ℎ𝑎𝑗𝑖1𝑓 ) 𝑛 𝑗=0 2 𝑎=1 𝑚 ℎ=1 𝑤 𝑘=1 + 𝑄 𝑓𝑙 ) 𝑂 1𝑓 𝑐 -𝑂 2𝑙 𝑐 ≥ ∑ ∑ ∑ ∑ 𝑂 1𝑓 • 𝑋 𝑘ℎ𝑎𝑗𝑖1𝑓 𝑛 𝑗=0 2 𝑎=1 𝑚 ℎ=1 𝑤 𝑘=1 -𝐵 • (2 -∑ ∑ ∑ ∑ (𝑋 𝑘ℎ𝑎𝑗𝑖1𝑙 + 𝑋 𝑘ℎ𝑎𝑗𝑖1𝑓 ) 𝑛 𝑗=0 2 𝑎=1 𝑚 ℎ=1 𝑤 𝑘=1 + 1 -𝑄 𝑓𝑙 ) ∀ 𝑖 = 1,2, … 𝑚; 𝑓 = 1,2, … , 𝑛; 𝑙 = 𝑓 + 1, 𝑓 + 2, … , 𝑛 (12)
Constraint ( 2) ensures the assignment any activity of specific job to only one operator and one machine, and there is only one activity of one job which precedes. Constraint (3) forces that each activity of one job precedes at most one other activity of one job conducted by the same operator. Constraint (4) denotes each worker starts by unloading of job 0. Constraint (5) ensures that there is no assignment for setup of job 0. Constraint [START_REF] Paksi | Flexible Job-Shop Scheduling with Dual-Resource Constraints to Minimize Tardiness Using Genetic Algorithm[END_REF] forces that setup and unloading activities of one job must perform on the same machine. Constraint [START_REF] Baptiste | Solving the two identical parallel machine problem with a single operator[END_REF] ensures the feasibility of sequence of activity by each operator: if activity b of job l precedes activity c of job f, it must have a predecessor of activity a of job j. Constraint [START_REF] Costa | A hybrid genetic algorithm for job sequencing and worker allocation in parallel unrelated machines with sequence-dependent setup times[END_REF] states that the minimum time lag between the operation completion time of and the moving completion time before activity b of job l must be equal to its operation time. Constraint [START_REF] Abedinnia | Machine scheduling problems in production: A tertiary study[END_REF] denotes that the difference between the moving completion time to do activity b of job l and the completion time of previous activity a of job j is at least equal to the moving time required by itself. Constraint [START_REF] Holland | Adaption in Natural and Artificial Systems[END_REF] ensures, on each machine, that the unloading activity is possible after the machine finishes processing the job. Constraint [START_REF] Zhong | Comparison of Performance between Different Selection Strategies on Simple Genetic Algorithms[END_REF] forces that each machine starts processing the job immediately after the setup activity. The twofold constraints [START_REF] Razali | Genetic Algorithm Performance with Different Selection Strategies in Solving TSP[END_REF] accommodates the feasibility sequence on each machine: if setup activity of job l and unloading activity of job f processed on the same machine, then unloading activity of job f must be completed before setup activity of job l starts, or vice versa. Constraint (13) fixes there is no time for unloading activity of job 0. Constraint (14) defines the makespan value. Finally, Constraint (15) and ( 16) define the corresponding binary variables.

4

The proposed permutation-based GA One of the most common meta-heuristic technique used in scheduling problem is Genetic Algorithm (GA) [START_REF] Abedinnia | Machine scheduling problems in production: A tertiary study[END_REF]. Since it is proven and easier to develop, we consider GA to solve our problem at first that can perform as the basic comparator to other techniques for the future research. Genetic algorithm (GA) that is found by Holland in 1975 mimics the biological processes [START_REF] Holland | Adaption in Natural and Artificial Systems[END_REF]. This meta-heuristic procedure works with a set of solutions (chromosomes) called as population. A chromosome, which contains alleles, represents one solution that is evaluated by its fitness value that indicates the objective function. The initial population usually comes from a random process. At every iteration, the selection mechanism chooses a couple of chromosomes (parents). The parents follow the crossover mechanism to generate new solutions (offspring) by combining their structure. Moreover, each chromosome can experience changing of allele sequence based on the mutation scheme to prevent the solution trapped into local optima. Finally, this algorithm will stop to iterate after it meets the stop criterion such as the maximum iteration number (generation number).

The encoding scheme plays a vital role to yield the effectiveness and the efficiency of the algorithm [START_REF] Baptiste | Solving the two identical parallel machine problem with a single operator[END_REF]. On the other hand, our DRC scheduling deals with three kinds of assignments: sequence of activity between jobs, operator to each activity, and machine to each job. We use a simple single-string as one chromosome containing n alleles that represent the sequence of jobs. In decoding phase, this sequence becomes a reference in resulting those three assignments to get the fitness value (the makespan). In the mathematical formulation, let 𝑙 ̅ = 𝜋 (𝑖) becomes the job on the i-th allele to represent a job sequence chromosome (see Fig, 2).

𝜋 ( 1) 𝜋 ( 2) 𝜋 ( 3) 𝜋 ( 4) 𝜋 ( 5)

4 1 5 3 2
Fig. 2. An example of a chromosome represents a job sequence (4-1-5-3-2) with n = 5 jobs

Our decoding algorithm consists of seven steps (as follow) that need an iterative process as many as the number of activities, which is twice of the jobs number. 18) and ( 19) and back to step 2.

Procedure of decoding

𝑻𝑴 𝒊 * = { 𝒔 𝒍 * + 𝒎𝒂𝒙{𝑻𝑴 𝒊 * , 𝑻𝑴𝑾 𝒌 * } + 𝒑 𝒍 * , 𝒊𝒇 𝒃 = 𝟎 𝒖 𝒍 * + 𝒎𝒂𝒙{𝑻𝑴 𝒊 * , 𝑻𝑴𝑾 𝒌 * } , 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆 (18)
𝑻𝑾 𝒌 * = { 𝒔 𝒍 * + 𝒎𝒂𝒙{𝑻𝑴 𝒊 * , 𝑻𝑴𝑾 𝒌 * }, 𝒊𝒇 𝒃 = 𝟎 𝒖 𝒍 * + 𝒎𝒂𝒙{𝑻𝑴 𝒊 * , 𝑻𝑴𝑾 𝒌 * } , 𝒐𝒕𝒉𝒆𝒓𝒘𝒊𝒔𝒆 (19)
We use the binary tournament as our selection method since it is more efficient than rank method and more effective than roulette wheel method [START_REF] Zhong | Comparison of Performance between Different Selection Strategies on Simple Genetic Algorithms[END_REF] [START_REF] Razali | Genetic Algorithm Performance with Different Selection Strategies in Solving TSP[END_REF]. Moreover, we choose two-point crossover that has been largely adopted in combinatorial problem and block swapping scheme [START_REF] Costa | A hybrid genetic algorithm for minimizing makespan in a flow-shop sequence-dependent group scheduling problem[END_REF] for our crossover and mutation schemes. Finally, the stop criterion is the number of generations.

Before comparing, we set GA parameter using a full factorial experimental design without replication for each case and analyze the result using graphical descriptive statistics to find the convergence point that represents the optimal generation number and Tukey test with 95% confidence interval to find the least population size from the best. Then, both parameters are used in another full factorial experimental design to find the optimal crossover and mutation probability in each case.

The number of strings needed to reach convergence point becomes higher when the case becomes more complex. The algorithm needs only 200 strings in the small-sized problem and needs more strings of 7,500 and 30,000 strings respectively for medium and big-sized problems. On the other hand, the generation number is always smaller than the population size in all cases. Also, in our experiments, we acknowledge that the crossover probability never becomes lower when the case becomes more complex, which needs to be analyzed more deeply in the future.

We implement a full factorial experiment design with five replication for PGA and RS and without replication for the solver. To evaluate the solution quality, we use relative percentage deviation (RPD) for each method i according to the equation (20):

𝑅𝑃𝐷 𝑖 = 100 • 𝑇𝐶𝑇 𝑖 -𝑇𝐶𝑇 𝑖 𝑚𝑖𝑛 𝑇𝐶𝑇 𝑖 𝑚𝑖𝑛 (20)
Where 𝑇𝐶𝑇 𝑖 is the total completion time (makespan) resulted from method i and 𝑇𝐶𝑇 𝑖 𝑚𝑖𝑛 is the best makespan among all methods. Table 1 also shows that PGA and RS can yield the optimal solution in the smallsized problem except for subcase 4 x 4 x 2 and 5 x 4 x 2. We acknowledge that our decoding algorithm always assigns a resource immediately after it is free, but, in that subcase, the optimal solution has different sequence logic. Our meta-heuristics also have better computational time than the solver in the small-sized problem.

The PGA outperforms other methods for average RPD in the medium-sized problem respectively with only 0.72% compared to RS with 1.55% and solver with 43.31%. Also, in the big-sized problem, the average deviation of PGA solution from the best is only 0.73% compared to the RS with 4.73%. By running for 5 minutes, the Gurobi solver can only reach 57.94%, on average, of the difference between its upper and lower bounds in the medium-sized problem. We also acknowledge that the solver cannot reach the optimal solution after one day running. Moreover, the computational (run) time of PGA is very reasonable compared to the RS that the difference is not more than 15 seconds even in the big-sized problem.

Conclusions

In this paper, we propose a novel DRC scheduling under an identical parallel machine environment that considers operator working modes and moving activity concerning the makespan minimization objective. We develop a model at first, but it can only solve the small-sized problem in reasonable time. Therefore, we propose a permutation-based genetic algorithm (PGA) to tackle the computational burden. To test its performance in solution quality and computational time, we compare the PGA to the solver and RS. Firstly, we set the PGA parameter using statistical approaches. We acknowledge that the appropriate parameters depend on the case. The comparison results show that the PGA could solve the problem in a reasonable time that is faster than the solver with a good quality solution that is better than random search. There are several ideas for improvement for the next potential research. First, to involve a new social objective function such as operator's productivity or workload balance. Second, to extend the model into more complex machine configuration, e.g., flow shop or job shop. Third, to implement other meta-heuristics methods.

Fig. 1 .

 1 Fig. 1. An illustration of a Gantt chart of the proposed DRC scheduling problem with 5 jobs

  𝑓, 𝑗, 𝑙 = 0,1,2, … , 𝑛 jobs 𝑔, ℎ, 𝑖 = 1,2, … , 𝑚 machines 𝑘, 𝑞 = 1,2, … , 𝑤 workers 𝑎, 𝑏, 𝑐 = 1, 2 activities Parameters 𝑃 𝑙 the processing time of job l 𝑂 𝑏𝑙 the operation time of activity b of job l 𝑇 𝑔𝑖 the moving time between machine g and i 𝐵 a big number Decision variables 𝑋 𝑘ℎ𝑎𝑗𝑖𝑏𝑙 a binary variable that result in 1 if worker k is assigned to do activity b of job l on machine i after finishing activity a of job j on machine h. 𝑄 𝑓𝑙 a binary variable that result in 1 if setup activity of job l performs before unloading activity of job f in the same machine. 𝑂 𝑏𝑙 𝑐 the operation completion time of activity b of job l 𝑃 𝑙 𝑐 the processing completion time of job l 𝑇 𝑏𝑙 𝑐 the transportation/moving completion time before doing activity b of job

  𝑋 𝑘ℎ𝑎𝑗𝑖𝑏𝑙 ∈ {0; 1} ∀𝑘 = 1,2, … , 𝑤; ℎ = 1,2, … , 𝑚; 𝑎 = 1,2; 𝑗 = 0,1, … , 𝑛; 𝑖 = 1,2, … , 𝑚; 𝑏 = 1,2; 𝑙 = 1,2, … , 𝑛 (15) 𝑄 𝑓𝑙 ∈ {0; 1} ∀ 𝑓 = 1,2, … , 𝑛; 𝑙 = 𝑓 + 1, 𝑓 + 2, … , 𝑛

1 .

 1 Set parameters for the zero (y = 0): setup number (z) = 0; assigned activity (b*) = ∅; assigned job (l*) = ∅; operator k expected moving completion time (TMWk) = 0 ∀𝒌; assigned operator (k*) = ∅; assigned machine (i*) = ∅; unloading waiting list in machine i (WLi) = ∅ ∀𝒊; busy machine matrix (B) = ∅; operator k earliest assigning time (TWk) = 0 ∀𝒌; operator k last machine location (Lk) = ∅ ∀𝒌 and machine i earliest assigning time (TMi) = 0 ∀𝒊. 2. Add y by 1. If y > 2n stop the iteration and compute makespan that is equal to the maximum value of TWk of all k. Otherwise, continue to step 4. 3. If 𝒛 < 𝒏, set i* = i ∃𝒊 = 𝟏, 𝟐, … , 𝒎 | 𝑻𝑴 𝒊 = 𝐦𝐢𝐧 𝒊 𝑻𝑴 𝒊 . Otherwise, set 𝒊 * = 𝒊 ∃𝒊 ∈ 𝑩 | 𝑻𝑴 𝒊 = 𝐦𝐢𝐧 𝒊∈𝑩 𝑻𝑴 𝒊 4. Compute expected moving completion time to machine i* of all operator k using equation (17). 𝑻𝑴𝑾 𝒌 = 𝑻𝑾 𝒌 + 𝒎 𝒊𝒋 ∀ 𝒌 = 𝟏, 𝟐, … , 𝒘, 𝒊 = 𝑳 𝒌 , 𝒋 = 𝒊 * (17) Then, set k* = k ∀ 𝒌 = 𝟏, 𝟐, … , 𝒘 𝒊𝒇 𝑻𝑴𝑾 𝒌 = 𝐦𝐢𝐧 𝒌 𝑻𝑴𝑾 𝒌 and update 𝑳 𝒌 * = 𝒊 * 5. Set b* = 1 if 𝒊 * ∉ 𝑩 ∪ 𝒏 𝒔 < 𝒏. Otherwise, b* = 2 6. If b* = 0, add z by 1, l* = 𝝅 (𝒛) , add j* to the B, and update WLj* = l*. Otherwise, set b* = 2, l* = WLj*, remove j* from the B and update WLj* = ∅. 7. Update TMi* and TWk* using equation (

5

Numerical examples and computational results

The objective of this benchmark is to compare the performance of the solution quality and run time between solver (SLV) using Gurobi 7.5.2, PGA, and random search (RS) which are executed on 16-GB RAM PC powered by an octa-core 3.6-GHz processor.

The PGA and RS have been coded in RUBY ® language. The RS uses same encoding and decoding scheme as in PGA to get the fitness value of a string. The stop criterion for RS is the number of evaluated strings as many as in PGA.

Our experiment consists three cases based on the number of jobs (n), machines (m), and operators (w)small, medium, and big-sized problem (see Table 1). We generate all parameters from uniform distributions which are U [START_REF] Baptiste | FPTAS for the two identical parallel machine problem with a single operator under the free changing mode[END_REF]79], U [START_REF] Baptiste | FPTAS for the two identical parallel machine problem with a single operator under the free changing mode[END_REF]99], U [START_REF] Baptiste | FPTAS for the two identical parallel machine problem with a single operator under the free changing mode[END_REF]20], and U [START_REF] Hu | Minimizing total flow time for the worker assignment scheduling problem in the identical parallel-machine models[END_REF][START_REF] Holland | Adaption in Natural and Artificial Systems[END_REF] respectively for setup, machining, unloading, and moving time. The solver is time limited in the medium-sized problem for 300 seconds and not run in the big-sized problem despite memory problem.


Songi Kim

Bongju Jeong
email: bongju@yonsei.ac.kr

Mass Customization Capability Planning with Additive Manufacturing

Keywords: Mass Customization Capability Planning, Mass Customization, Additive Manufacturing

Mass customization aims to manufacture large quantities of customized products at low costs comparable to that in mass production. However, the two operational objectives of mass customization, production flexibility and cost-efficiency, conflict with each other. In this circumstance, one of the famous prototyping technologies, additive manufacturing (AM), began to draw attention with its multiple function in the production system, which enables mass customizers to achieve the two contradictive objectives. This study defines mass customization capability planning (MCCP) as a production planning process which balances between production flexibility and cost-effectiveness. Also, the mathematical planning model of MCCP is developed to support it. Since the MCCP model includes stochastic parameters, a heuristic method is applied to the solution searching process. After, the MCCP model was validated by the experiment analysis.

Introduction

The term mass customization was firstly mentioned as a process to provide product variety and customization with flexibility and quick responsiveness [START_REF] Davis | From 'future perfect': mass customizing[END_REF]. Among the various definitions, the predominant features of mass customization include product variety, flexibility, and cost-efficiency [START_REF] Pine | Mass customizing products and services[END_REF]. Early papers on mass customization try to classify mass customization into several levels [START_REF] Duray | Approaches to mass customization: configurations and empirical validation[END_REF][START_REF] Silveria | Mass customization: literature review and research directions[END_REF] and more recently, the optimal location of customer involvement in the production system [START_REF] Carr | Optimal admission control and sequencing in a make-to-stock/maketo-order production system[END_REF][START_REF] Rudberg | Mass customization in terms of the customer order decoupling point[END_REF]. However, as the product variety increases, the mass customizer confronts the difficulty to balance two contrasting operational goals: production flexibility and costefficiency. From this viewpoint, operational capability of mass customization is understood as balancing trade-offs between the two operational goals [START_REF] Sawhney | Implementing labor flexibility: a missing link between acquired labor flexibility and plant performance[END_REF]. Production flexibility, the ability to respond effectively to changing circumstances, enables mass customizer to change production setups in a short time, with a little effort. The second objective, cost-efficiency, of the mass customization comes from the mass production strategy. In the view of economy of scale, homogeneous items require less attention to managing them. In contrast, mass customization requires a much higher number of production set-ups and more diverse resources to produce various kinds of products.

Regarding this, this study deals with one of the most flexible manufacturing technology, additive manufacturing (AM). Adding materials enables to produce objects with a much more complex design so the technology is expected to play a crucial role to provide the manufacturing flexibility to the production system [START_REF] Gero | Recent advances in computational models of creative design[END_REF]. Initially AM was used to create prototypes before the products were developed [START_REF] Gibson | Additive manufacturing technologies: rapid prototyping to direct digital manufacturing[END_REF]. However, AM processes recently broaden its functional boundary to the rapid tooling (RT) area to create tools which are necessary for the traditional fabrication procedure, injection molding, and to the rapid manufacturing (RM) area to manufacture end-use products right away. Most of the previous papers focused on figuring out which, among the three functions, could be the optimal choice for the production system. On the other hand, this study puts more weight of its ability to switch between the three functions freely, which can contribute to increasing the production system's flexibility.

In the previous research, most of the studies with mass customization capability focused on defining the term and investigating its relationship with other managerial factors such as with product modularity [START_REF] Tu | Measuring modularitybased manufacturing practices and their impact on mass customization capability: a customer-driven perspective[END_REF], organizational flatness, coordination, and product modularity [START_REF] Zhang | The effects of organizational flatness, coordination, and product modularity on mass customization capability[END_REF], absorptive capacity [START_REF] Zhang | Absorptive capacity and mass customization capability[END_REF], and quality management [START_REF] Kristal | The effect of quality management on mass customization capability[END_REF]. Instead of adopting qualitative manner, this study understands mass customization capability planning (MCCP) as a production planning issue. With this approach, the mathematical model is developed to support it. Also, a simple experimental analysis was carried out to validate the mathematical model.

Mass Customization Capability Planning

The concept of mass customization has emerged from the convergence of the two contrasting strategies: mass production and one-of-kind production (OKP). The first strategy, mass production, focuses on achieving cost-effectiveness with a few types of standard products. Since the number of product types is somewhat limited, it is able to forecast demands for the standard products with proper forecasting techniques. Under the OKP circumstance, however, there can exist an infinite number of product types.

In addition, the customization level of each product may vary depending on the customer's requests and the firm's capability to produce customized products. As a combination of the two strategies, mass customization produces both types of products. On the one hand, mass customizer must forecast the future demands of the standard products and establish a proper production plan for the products and the parts. On the other hand, the mass customizer must prepare its capability to deal with the customized demands since the customers' specific requirements are unknown until the actual demand occurs. This gives rise to the necessity for the mass customizer to include the customization capability planning as a new production planning step.

In this respect, MCCP aims to give a guideline so as to support the mass customizer's decision-making on its customization capability. As the nature of custom order bears uncertainty, the customization capability planning does not suggest an exact solution for the mass customizer. Instead, it offers a range of customization capability levels which helps to understand the impact of the custom demands and its proper capability levels to deal with it.

There is a significant difference in the decision variables between the MCCP model and the traditional capacity planning model. In addition to the capacity-related decision in the traditional models, the MCCP model decides the proper customization capability according to the custom demand forecast. Therefore, the important decision variables of the MCCP model are related to its customization capability: the customization level and the custom order fulfillment ratio.

A mass customizer decides its level of product variety by setting a proper customization level. By setting the customization level, the firm is able to produce customized products of which customization level locates within the customization limit. However, if there is a new order requiring a product with being more customized than the firm's customization limit, the firm faces a difficult situation where putting most of its capacity on that order. Second, the custom order fulfillment ratio depends on the number of customized products manufactured in the planning horizon.

The customization level and the custom order fulfillment ratio are related to each other. For example, a firm can either produce a large quantity of customized products with a low customization level or produce a small number of high-customized products. Therefore, it is difficult to evaluate which of the two strategies represents the higher customization capability since they are in the two different dimensions.

3

Mass Customization Capability Planning Model

Assumptions and Notations

Since the mathematical representation of MCCP does not exist before, this very first model is developed based on the detailed assumptions. First, demand information of both typical and custom order is known by long-term forecasting. However, only typical orders include detail profile of the products, such as bill-of-materials and part specifications. Long-term forecasting for custom orders is available only to predict customers' tendency to customize their products. The products are customized from the standard products. Parts can be customized, while BOM information for the final products is fixed. In addition, it is assumed that customers can customize both common parts and differentiated parts as well. Customized products are comprised of common parts, differentiated parts, and customized parts while standard products consist of common parts and differentiated parts. Regarding AM, it is assumed that all parts can be additively manufactured. The building time of AM machines is assumed to be affected by the building technique of the AM machine and the part design. Indices, parameters, and decision variables are represented in Table 1-3, respectively. Service level (order fulfillment ratio) for custom orders at period t

Mathematical Model

The objective functions of MCCP model are to maximize the economic benefit during the entire planning periods as in Equation ( 1), at the same time to maximize the total customization level of the products as in Equation ( 2). (2)

Subject to

𝐼 𝑗𝑡 = 𝐼 𝑗,𝑡-1 + 𝑌 𝑗𝑡 𝑁𝐶 -∑{𝑛 𝑖𝑗 × 𝑋 𝑖𝑡 𝑆𝑇 + 𝑛 𝑖𝑗 × 𝑋 𝑖𝑡 𝐶𝑈 -𝑌 𝑗𝑡 𝐶 } 𝐼 𝑖 ∀𝑗, 𝑡 (3)
𝑌 𝑗𝑡 𝐶 = ∑ 𝑛 𝑖𝑗 × 𝑋 𝑖𝑡 𝐶𝑈 𝐼 𝑖 ∀𝑗, 𝑡 (4)
𝑋 𝑖𝑡 𝑆𝑇 = 𝑑 𝑖𝑡 𝑆𝑇 ∀𝑖, 𝑡 (5)
𝑋 𝑖𝑡 𝐶𝑈 ≤ 𝑑 𝑖𝑡 𝐶𝑈 ∀𝑖, 𝑡 (6)
∑ 𝑋 𝑖𝑡 𝐶𝑈 𝐼 𝑖 = ∑ 𝑑 𝑖𝑡 𝐶𝑈 × 𝛽 𝑡 𝐼 𝑖 ∀𝑡 (7)
𝑌 𝑗𝑡 𝐶 ≤ 𝑊 𝑗𝑡 × 𝑏𝑖𝑔 𝑀 ∀𝑗, 𝑡 (8)
𝐶 𝑖𝑡 𝐶𝑈 = ∑ (𝑛 𝑖𝑗 × 𝑊 𝑗𝑡 ) 𝑗 ∑ 𝑛 𝑖𝑗 𝑗 ∀𝑖, 𝑡 (9)
𝐶 𝑖𝑡 𝐶𝑈 ≤ 𝐶 𝑈𝑃 ∀𝑖, 𝑡 (10)
𝑀𝑂𝐿𝐷 𝑗𝑡 𝑁𝐶 ≥ 𝑌 𝑗𝑡 𝑁𝐶 𝑛 𝐷𝑀 ∀𝑗, 𝑡 (11)
∑ 𝑍 𝑗𝑙𝑘𝑡 𝐾 𝑘=1 = 1 ∀𝑗, 𝑙, 𝑡 (12)
𝑀 𝑚𝑡 𝐷𝑀 = 𝑀 𝑚,𝑡-1 𝐷𝑀 + 𝑃𝑀 𝑚𝑡 𝐷𝑀 ∀𝑚, 𝑡 (13)
𝑀 𝑘𝑡 𝐴𝑀 = 𝑀 𝑘,𝑡-1 𝐴𝑀 + 𝑃𝑀 𝑘𝑡 𝐴𝑀 ∀𝑘, 𝑡 (14)
𝑊𝑇 𝑚𝑡 𝐶_𝐷𝑀 = ∑ ∑ (𝑡 𝑗𝑙𝑚 𝐶_𝐷𝑀 × ∑ 𝑠𝑡𝑎𝑟𝑡 𝑗𝑠 𝑚+1 𝑠=1 ) 𝑌 𝑗𝑡 𝐶𝑈 𝑙=1 𝐽 𝑗=1 ∀𝑚, 𝑡 (15)
𝑊𝑇 𝑘𝑡 𝐴𝑀 = ∑ ∑{(𝑡 𝑗𝑙𝑘 𝐶_𝐴𝑀 + 𝑡 𝑘 𝑆𝑒𝑡_𝐴𝑀 + 𝑡 𝑘 𝑃𝑜𝑠𝑡_𝐴𝑀 ) × 𝑍 𝑗𝑙𝑘𝑡 } 𝑌 𝑗𝑡 𝐶𝑈 𝑙=1 𝐽 𝑗=1 ∀𝑘, 𝑡 (16)
𝑊𝑇 𝑚𝑡 𝐷𝑀 = ∑(𝑡 𝑗𝑚 𝑁𝐶 𝑀𝑂𝐿𝐷 𝑗𝑡 𝑁𝐶 + 𝑡 𝑚 𝑆𝑒𝑡_𝐷𝑀 ) 𝐽 𝑗=1 + 𝑊𝑇 𝑚𝑡 𝐶_𝐷𝑀 ∀𝑡 𝑚 = 1 (17) 𝑊𝑇 𝑚𝑡 𝐷𝑀 = ∑(𝑡 𝑗𝑚 𝑁𝐶 𝑌 𝑗𝑡 𝑁𝐶 + 𝑡 𝑚 𝑆𝑒𝑡_𝐷𝑀 )𝑡 𝑗𝑚 𝑁𝐶 𝐽 𝑗=1 + 𝑊𝑇 𝑚𝑡 𝐶_𝐷𝑀 ∀𝑡 𝑚 = 2 (18)
𝑊𝑇 𝑘𝑡 𝐴𝑀 ≤ 𝑤 𝑡 × 𝑀 𝑘𝑡 𝐴𝑀 ∀𝑘, 𝑡 (19)
𝑊𝑇 𝑚𝑡 𝐷𝑀 ≤ 𝑤 𝑡 × 𝑀 𝑚𝑡 𝐷𝑀 ∀𝑘, 𝑡 (20)
The customization level of the product 𝑖 at period 𝑡 is calculated from Equation ( 9). Equation [START_REF] Tu | Measuring modularitybased manufacturing practices and their impact on mass customization capability: a customer-driven perspective[END_REF] ensures that the value of customization level can't be over than the upper bound of the customization level. Equation [START_REF] Zhang | The effects of organizational flatness, coordination, and product modularity on mass customization capability[END_REF] ensures the number of molds used to fabricate un-customizable part 𝑗 must be higher than the number of uncustomizable part 𝑗 divided by the mold life n 𝐷𝑀 . Equation [START_REF] Zhang | Absorptive capacity and mass customization capability[END_REF] ensures that only one of AM techniques is selected to proceed customized part 𝑙 from part 𝑗 at the period 𝑡. Equations ( 13) and ( 14) represent the number of machine 𝑚 at period 𝑡 is the sum of the number of machines at the previous period 𝑡 -1 and the number of machines purchased at the start of the period 𝑡. Equations from (15) to (20) are the time-related capacity constraints of the manufacturing processes.

Solution Algorithm

The MCCP model requires a specific solution searching procedure since it includes probabilistic parameters and multi objectives, and the range of index l (index of customized part) is decided by the decision variable 𝑌 𝑗𝑡 𝐶 . The solution searching procedure is divided into two parts: (1) to decide optimal MCCP plan and (2) to check the time-related capacity constraints of machines (Fig. 1). In terms of solving multi-objective problem, the algorithm controls the upper limit of the second objective (total customization level), finds optimal plan satisfying feasibility condition with the given value of the second objective, and relaxes the boundary of the second objective if the resulting solution is infeasible. To address the solution algorithm, an index 𝑝 is defined as the iteration number. One of the key elements of this algorithm is 𝐶 𝑈𝑃 , the upper bound of customization level. The value of 𝐶 𝑈𝑃 is renewed at every iteration 𝑝. The solution searching algorithm starts with 𝑝 = 0. The first stage focuses on deciding optimal customization level which satisfies 𝐶 𝑝 𝑈𝑃 . In this stage, the mathematical model is applied except the equations which include index 𝑙 such as Equations ( 12

Experimental Analysis

To validate the MCCP model, a simple experimental analysis was carried out. It reflected the situation where the custom demand increased with linearly. Also, three manufacturing steps were considered: prototyping, tooling, and fabrication with consideration of the AM's possible function in production system. It was assumed that dedicated manufacturing technology corresponds to a certain manufacturing step. In this case, injection molding was assigned to fabrication, and machining was assigned to tooling. Meanwhile, AM processes were assumed to be capable of operating in all manufacturing steps. And, the five different AM processes included selective laser sintering, electron beam melting, laser metal deposition, fused deposition modeling, and stereolithography apparatus. The lengths of processing time, setup time, and postprocessing time were assumed based on the characteristics of the processes. There were two types of products which consisted of two common parts and the other differentiated part. The demand of each product was randomly generated from normal distribution with its mean and standard deviation (which was set as 10).

The result showed that the customization level stayed same due to the lower demand increasing rate (0.2% per period). Meanwhile, the ratio of the number of customized products to the total number of products increased as the custom demand increases. In terms of the machines, three AM machines with SLS process were purchased to correspond to the increasing trend of custom demand.

Conclusion

To implement mass customization successfully, the mass customizer should balance between the two contrasting objectives: production flexibility and cost-efficiency. This study argues that the mass customization capability, defined as the ability to balance between the two objectives, must be planned as a long-term planning step.

Based on the argument, the MCCP model is developed to support the mass customizer's decision-making process on its appropriate level of production flexibility, as well as the resulting profits. Also, heuristic method is used to search optimal boundary of the decision variables, especially the customization level and order fulfillment ratio.

Maximize 𝑓 1

 1

Fig. 1 .

 1 Fig. 1. Solution algorithm of the MCCP model

Table 1 .

 1 Indices

	𝑖	Index of product (𝑖 = 1, 2, … , 𝐼)
	𝑗	Index of part (𝑗 = 1, 2, … , 𝐽)
	𝑙	Index of customized part originated from part 𝑗 (𝑙 = 1, 2, … , 𝑌 𝑗𝑡 𝐶 )
	𝑘	Index of AM machine type related to building technique(𝑘 = 1, 2, … , 𝐾)
	𝑚	Index of dedicated machines' possible function (𝑚 = 1, 2, … , 𝑀) (in this model, 1 for
		tooling and 2 for fabrication)

Table 2 .

 2 Parameters

	𝑇𝑂𝑇𝐴𝐿 𝑑 𝑖𝑡	Forecasted total demand including the standard product i and customized product modified from the standard product at period t
	𝑆𝑇 𝑑 𝑖𝑡 𝐶𝑈 𝑑 𝑖𝑡 𝑛 𝑖𝑗	Forecasted demands of the standard product i at period t Forecasted demands of the customized product i at period t (stochastic value) The number of the part 𝑗 to manufacture a unit of standard product i
	𝑆𝑒𝑡_𝐷𝑀 𝑡 𝑚 𝑆𝑒𝑡_𝐴𝑀 𝑡 𝑘 𝑃𝑜𝑠𝑡_𝐴𝑀 𝑡 𝑘 𝑡 𝑗𝑚 𝑁𝐶	Setup time of dedicated machine with function 𝑚 Setup time of AM with building technique k Post processing time of AM with building technique k Processing time of non-customized part 𝑗 at dedicated machine 𝑚
	𝑡 𝑗𝑙𝑚 𝐶_𝐷𝑀	Processing time of customized part (𝑗, 𝑙) at dedicated machine 𝑚
	𝐶_𝐴𝑀 𝑡 𝑗𝑙𝑘	Processing time of customized part (𝑗, 𝑙) at AM machine with building technique k (stochastic value)
	𝐴𝑆𝑆𝐸𝑀 𝑡 𝑖 𝑠𝑡𝑎𝑟𝑡 𝑗𝑠	Assembling time of product 𝑖 Binary parameter whether customized part 𝑗 starts at manufacturing step 𝑠 (sto-
		chastic value)
	𝑛 𝐷𝑀	Mold life made by dedicated tooling machine
	𝐴𝑀 𝑛 𝑘 𝑝 𝑖 𝑆𝑇	Mold life made by AM technique 𝑘 Unit price of standard product 𝑖
	𝑐 𝑗	Unit cost of manufacturing part 𝑗
	𝐷𝑀 𝑘 𝑚 𝐴𝑀 𝑘 𝑘 ℎ	Purchasing cost of a unit of dedicated machine 𝑚 Purchasing cost of a unit of AM machine 𝑘 Holding cost of a part unit
	𝑤 𝑡 𝐶 𝑟𝑚 𝑗𝑙𝑟	Available working time in period 𝑡 Binary parameter whether customized part (𝑗, 𝑙) is supposed to be made with raw material 𝑟 (stochastic value)
	𝐷𝑀 𝑏 𝑚𝑟 𝐴𝑀 𝑏 𝑘𝑟 𝛼 𝑗𝑙	Whether dedicated machine at manufacturing step 𝑚 can handle raw material 𝑟 Whether AM with building technique 𝑘 can handle raw material 𝑟 Effective design vector for customized part (𝑗, 𝑙) (stochastic value)
	𝑠 𝑗𝑙𝑛	Effective design subfactor 𝑛 of customized part (𝑗, 𝑙)
	𝐷𝑀 𝑀 𝑚,0 𝐴𝑀 𝑀 𝑚,0 𝐶 𝑈𝑃	Initial number of dedicated machines 𝑚 Initial number of AM machines 𝑘 Upper bound of customization limit

Table 3 .

 3 Decision variables

	𝑆𝑇 𝑋 𝑖𝑡 𝐶𝑈 𝑋 𝑖𝑡	Number of standard product 𝑖 manufactured in period 𝑡 Number of customized product transformed from standard product 𝑖 manufac-tured in period 𝑡
	𝑌 𝑗𝑡 𝑁𝐶	Number of part 𝑗 manufactured in period 𝑡
	𝑌 𝑗𝑡 𝐶	Number of customized part 𝑗 manufactured in period 𝑡
	𝑍 𝑗𝑙𝑘𝑡	Whether customized part (𝑗, 𝑙) at period 𝑡 is fabricated by AM machine 𝑘


Keywords: Electrochemical chloride extraction, reinforced concrete, carbonation, Raman microspectroscopy

The increasing international interest in contemporary architecture has drawn attention to the numerous listed buildings made of reinforced concrete in Europe, and especially in France. The main source of deterioration of this cultural heritage is the corrosion of rebars through carbonation or chloride contamination, but also often by a combination of both. The present study explored this combined corrosion mechanism in reinforced concretes, and investigated Electrochemical Chloride Extraction (ECE) as a technique to stop or decrease corrosion. The analytical approach was based on physico-chemistry, electrochemical measurements, Raman spectroscopy and SEM examinations. The results evidenced the aggressiveness of the combined carbonation and chloride-induced corrosion, and demonstrated the efficiency of the ECE treatment in terms of chloride extraction and reduction of corrosion rate. It appears that ECE treatment only reduces corrosion activity by increasing pH to a value of 10. Nevertheless, the long term durability of the treatment is questionable as the return to a sound concrete passivity is not obtained.

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 1 Introduction

Concrete is now part of the world cultural heritage landscape, as evidenced by the recent Unesco listing of the famous German Bauhaus architecture, the Polish Centennial Hall in Warsaw and the center of the French city Le Havre (rebuilt by Auguste Perret) for their outstanding universal value [1].

The Redmonest European Project revealed that at least 1500 buildings made of concrete are now registered in Belgium, France, and Spain. The survey performed within the project shows that the protection of this contemporary heritage is exponential in France, where the number of listed concrete monuments increased from 200 in the 1990's to more than 800 in the 2010's [START_REF] Marie-Victoire | Concrete cultural heritage in France: inventory and state of conservation, 4th international[END_REF][START_REF] Marie-Victoire | Water-repellents as alternative carbonation-induced corrosion treatments for reinforced concrete cultural heritage 14th international conference on durability of buildings materials and components[END_REF]. This architectural heritage is unfortunately affected by several types of deterioration, the most deleterious of which is certainly rebars corrosion. Several phenomena are involved in this process. The oldest of these historic concretes were cast at a time when mix design or casting were still a new and developing technology, meaning that poor initial concrete quality or insufficient concrete covers can sometimes be encountered. It is usual to measure carbonation depth of several centimeters in concrete made in the 1920s or 1940s, with open porosity of up to 20% [START_REF] Hergenroeder | Investigations on the statistics of carbonation depths in concrete[END_REF][START_REF] Marie-Victoire | Carbonation and historical buildings made of concrete, NUCPERF 2006: Corrosion and long term performance of concrete in NPP and waste facilities[END_REF]. When those carbonated concretes are subjected to marine chlorides or to de-icing salts, the double contamination can contribute to severe corrosion. In historic concrete, this leads to a massive and unacceptable loss of original materials.

The standard technique to cure this deterioration is patch repair. However, the 2007 CONREPNET European project showed that patches for repairing reinforced concrete corrosion were not efficient over time [START_REF] Tilly | CONREPNET -Concrete repairs -Performance in service and current practice[END_REF]. Among the reasons for this lack of durability, the compatibility of the patch materials with the parent historic concrete

M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT

4 was the main reason for early failure (within 2 years). The authors suggest that longer term failure could be attributed to the location of the repair patch, which only concerns the spall area and not the surrounding concrete, which is still carbonated or chloride polluted. There was therefore a need for additional treatments to address degradations induced by corrosion. Electrochemical realkalization and chloride extraction were studied for this purpose [START_REF] Pocock | Chloride extraction and realkalization -six years on, Corrosion and protection of reinforced concrete[END_REF][START_REF] Pocock | Chloride extraction and realkalization -six years on, Construction Repair[END_REF][START_REF] Bertolini | Conservation of historical reinforced concrete structures damaged by carbonation induced corrosion by means of electrochemical realkalization[END_REF][START_REF] Mietz | Electrochemical realkalization for rehabilitation of reinforced concrete structures[END_REF][START_REF] Mietz | Electrochemical rehabilitation methods for reinforced concrete structures -a state of the art report[END_REF].

Corrosion has been extensively studied in chloride-polluted concrete [START_REF] Angst | Critical chloride content in reinforced concrete -A review[END_REF][START_REF] Alonso | Chloride threshold values to depassivate reinforcing bars embedded in a standardized OPC mortar[END_REF][START_REF] Poupard | Corrosion by chlorides in reinforced concrete: Determination of chloride concentration threshold by impedance spectroscopy[END_REF][START_REF] Melchers | A comparative study of chlorides and longer-term reinforcement corrosion[END_REF][START_REF] Bouteiller | Mathematical relation of steel thickness loss with time related to reinforced concrete contaminated by chlorides[END_REF][START_REF] Arya | Effect of cement type on chloride binding and corrosion of steel in concrete[END_REF][START_REF] Glass | The influence of chloride binding on the chloride induced corrosion risk in reinforced concrete[END_REF][START_REF] Ann | Chloride threshold level for corrosion of steel in concrete[END_REF][START_REF] Angst | Chloride induced reinforcement corrosion: Rate limiting step of early pitting corrosion[END_REF][START_REF] Pradhan | Rebar corrosion in chloride environment[END_REF][START_REF] Bouteiller | Corrosion initiation of reinforced concretes based on Portland or GGBS cements: Chloride contents and electrochemical characterizations versus time[END_REF] or in carbonated reinforced concrete [START_REF] Stefanoni | Corrosion rate of carbon steel in carbonated concrete -A critical review[END_REF][START_REF] Glass | Factors affecting the corrosion rate of steel in carbonated mortars[END_REF], but the combined effect of the two contaminants has rarely been investigated.

The primary aim of the present study was to investigate the corrosion mechanism resulting from combined carbonation and chloride contaminations. This issue was explored using artificially carbonated concrete with either endogenous (chloride added to the mix) or exogenous (wet and dry cycles) chlorides.

In a second step, an electrochemical chloride extraction was studied. Chloride content, pH evolution, and corrosion rates were characterized. Special attention was paid to the evolution of corrosion products during treatment using an analytical approach that combined Raman micro-spectroscopy and SEM observations.

Materials and methods

Samples and ageing procedures

The reinforced micro-concrete samples were cylinders (10 cm high and 4 cm diameter) with a central rebar. Two cements were studied, namely an ordinary Portland cement (CEM I) and a blast furnace slag cement (CEM III/A). These two cements are of interest: the former was widely used for many years, and the latter was extensively used between the two world wars and its use is currently increasing.

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5

Rebar was composed of smooth carbon steel with a diameter of 5 mm and an active surface of 10cm² delimited with cataphoretic paint (Fig. SI1-1). A rather high water/cement ratio (0.65) was used for concrete formulation to obtain high porosity and thus accelerate the ingress of contaminants (carbonation and chloride ions). This high water/cement ratio is representative of the ratio used in historic concretes.

Four sample series were prepared based on two criteria, namely:

-Contamination content, i.e. either chlorides added to the mix and followed by carbonation (referenced G), or carbonation followed by wetting/drying cycles in a salted solution (referenced I), and -Cement type (CEM I or CEM III/A, respectively referenced 1 and 3).

Therefore, four series named G1, G3, I1, and I3 were studied A precise description of the sample production and contamination can be found in Supplementary Information 1.

Electrochemical chloride extraction

The electrochemical chloride extraction (ECE) treatment is illustrated in Figure 1. ECE was conducted on 37 specimens of each sample series. A cathodic current density of -100 µA/cm² of steel was applied with a power supply between the rebar and a titanium/platinum grid (counter-electrode) for 8 weeks, corresponding to a total charge of 1344 A.h/m². These current density and duration conditions are in accordance with those reported in the technical specification or standards for chloride extraction [START_REF]Electrochemical re-alkalization and chloride extraction treatments for rein-forced, Concrete Part 2: Chloride extraction[END_REF] and realkalization [START_REF]Electrochemical realkalization and chloride extraction treatments for reinforced concrete -Part 1[END_REF]. A disodium tetraborate solution (25g/L of Na 2 B 4 O 7 10H 2 O) electrolyte was used as a 9 pH buffer corresponding to a carbonated concrete. Moreover, some samples were immersed in the electrolyte then Three samples from each series were analyzed after 3, 7, 14, 28, and 56 days of treatment: two were dedicated to destructive analysis and the third was used for nondestructive electrochemical characterizations.

Analytical techniques

Phenolphthalein test

Phenolphthalein (0.5 % in ethanol) was used to determine realkalization progress during the treatment. A pink color is obtained for a pH of 9 or more, whereas the concrete remains colorless for lower pH values.

Chloride titration

Regarding the chloride extraction evolution, the free and total chloride contents of concrete were measured by AgNO 3 potentiometric titration [START_REF] Castellote | RILEM TC 178-TMC : Testing and modelling chloride penetration in concrete -Round robin test on chloride analysis in concrete Part 1 : Analysis of total chloride content[END_REF][START_REF] Castellote | RILEM TC 178-TMC : Testing and modelling chloride penetration in concrete -Round robin test on chloride analysis in concrete Part 2 : Analysis water soluble chloride content[END_REF] on the first centimeter around the rebar on two of the three samples. The free and total chloride contents of concrete were simultaneously determined on the non-polarized samples after 14, 28 and 56 days.

Electrochemical characterizations

Electrochemical characterizations were conducted at each step of the set-up: after curing, after ageing (chloride or carbonation or reverse) and during ECE treatment (depending on the treatment duration). Linear polarization resistance (LPR) and electrical concrete resistance Re were measured using a 5-channel Bio-Logic VMP2Z potentiostat (details in SI2). Corrosion rate i corr (µA/cm² of steel) was calculated according to the Stern-Geary equation (Eq.1)

i corr = B/(Rp.S) (Eq. 1) M A N U S C R I P T A C C E P T E D ACCEPTED MANUSCRIPT 7
Where [START_REF] Andrade | RILEM TC 154-EMC:Electrochemical Techniques for Measuring Metallic Corrosion -Recommendations -Test methods for on-site corrosion rate measurement of steel reinforcement in concrete by means of the polarization resistance method[END_REF]: B = 26 mV, Rp (ohm) is obtained from the linear polarization resistance and the electrical concrete resistance (Re), and S is the active steel surface (10 cm² in this study).

Raman micro-spectroscopy

The

Initial characterizations

Table 1 shows the characterizations of chloride content, pH, and corrosion rate before treatment.

Levels of chloride content in the samples were sufficiently high compared to critical content to induce corrosion [START_REF] Afnor | NF EN 206-1 / P18-325-1. Béton : spécification, performances, production et conformités[END_REF] and was found to be within the range of chloride threshold provided in states of the art [START_REF] Angst | Critical chloride content in reinforced concrete -A review[END_REF][START_REF] Alonso | Chloride threshold values to depassivate reinforcing bars embedded in a standardized OPC mortar[END_REF].

The pH value of the 17.5 mm concrete cover was close to 9 (phenolphthalein was colorless) demonstrating the complete carbonation of the concrete samples [START_REF] Bentur | Steel corrosion in concrete -Fundamentals and civil engineering practice[END_REF][START_REF] Broomfield | Corrosion of steel in concrete -Understanding, investigation and repair[END_REF][START_REF] Bertolini | Corrosion of steel in concrete: prevention, diagnosis, repair[END_REF].

Corrosion rates indicated a passive state for sound concrete. However, corrosion current in the carbonated and chloride-contaminated samples was close to 10 µA/cm² for all four series, and corresponded to a high level of corrosion in reinforced concrete [START_REF] Andrade | RILEM TC 154-EMC:Electrochemical Techniques for Measuring Metallic Corrosion -Recommendations -Test methods for on-site corrosion rate measurement of steel reinforcement in concrete by means of the polarization resistance method[END_REF]. This value was higher than those observed in samples with a single contaminant, and highlighted the aggressiveness of the combined contamination (Table 1).

Chloride extraction

During the ECE treatment, the negatively charged chloride ions migrated from the rebar to the electrolyte. The efficiency of the electrochemical chloride extraction treatment was considered to be the ratio of the initial chloride content minus the remaining chloride content (after each duration time) divided by the initial chloride content. Figure 3 presents the results of the chloride extraction efficiency versus treatment duration for the I1 series and for the corresponding non-polarized samples.

Chloride ions were in a free form because carbonation induced a release of bonded chlorides (as evidenced by the free and total chlorides content values, which are

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similar in Figure 3). As the four series all showed the same behavior, the results of the three other series can be found in Figure SI3.

For the treated samples, an increase of extracted chloride content with increased treatment duration was observed for the four series. Moreover, the extraction was found to be more efficient during the initial stage of the treatment, as previously described by different authors [START_REF] Herrera | Electrochemical chloride extraction: Influence of C3A of the cement on treatment efficiency[END_REF][START_REF] Swamy | Effectiveness and structural implications of electrochemical chloride extraction from reinforced concrete beams[END_REF][START_REF] Fajardo | Electrochemical chloride extraction (ECE) from steel-reinforced concrete specimens contaminated by "artificial" seawater[END_REF]. After 28 days, the efficiency of the extraction was close to 90% for G1, G3 and I1 and was close to 75% for I3 samples (Figure 3 and Figure SI3-1). These high extraction efficiencies can be explained by a porous and thin concrete cover, and by chloride ions that are likely in the free form. The extraction of chloride ions was also observed for the non-polarized samples, but was attributed to a lixiviation phenomenon.

Chloride extraction resulting from the electrochemical treatment was faster than the lixiviation phenomenon (similar values were obtained only after 56 days).

In an in situ situation involving better quality concrete with better quality (thicker and/or less porous), ECE treatment would require a longer duration. In this case, the end of the treatment correspond to the attaining of a chloride content target, for example.

pH evolution

During treatment, water hydrolysis leads to hydroxyl ion formation. An increase of concrete pH around the rebar is therefore expected. Figure 4a presents the results of the pH evolution (pink ring thickness) versus treatment duration for the four series.

Figures 4b and4c show pictures of the phenolphthalein color after 28 and 56 days for I1 series. The thickness of the realkalized concrete around the rebar increased with time. According to [START_REF]Electrochemical realkalization and chloride extraction treatments for reinforced concrete -Part 1[END_REF], the treatment is efficient if the realkalized concrete around the

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rebar is equal to the diameter of the rebar if the latter measures less than one centimeter in diameter, or 1 cm for larger rebar diameters. The results shown in Figure 4a demonstrate that the realkalization was efficient after 14 days for all four series: the ring thickness was larger than the 5 mm rebar diameter. After 56 days of treatment, it was equal to 9, 10, 12 and 14 mm respectively for G3, G1, I1, and I3

series., As expected, no realkalized ring was observed for the non-polarized samples.

In situ Raman micro spectroscopy

Before treatment, an induction time of 12 hours to 5 days was compulsory to obtain active corrosion around the rebar after immersion in tetraborate solution. Control of the corrosion current gave the same order of magnitude (10 to 50 µA/cm 2 ) as those observed in previously described samples. The higher values were attributed to the rebar cross section that was also exposed to the pore solution.

Raman spectra obtained at this stage are reported on Figure 5a and 5c with reference Raman spectra of Green Rust (GR) grown respectively in chloride (Figure 5b) or carbonate (Figure 5d) solution according to the protocols described in SI1-2.

The four series tested mainly showed spectrum 5a, while some spots on G1 samples indicated spectrum 5c.

The main differences between the two types of Green Rust spectra are the gap and the position between the two main bands, which are respectively 70 cm -1 [500-430]

for GR(Cl -) and 75 cm -1 [510-435] for GR(HCO 3 -), and the presence of two smaller bands at 320 and 360 cm -1 for GR(Cl -). Clearly spectrum a) is linked to GR(Cl -) ; while spectrum 5c is attributed to GR(CO 3

2-

).

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The presence of these compounds attests a fast corrosion process in which chloride is incorporated within corrosion products as the anions in Green Rust structure to counterbalance the presence of iron III. GR(Cl -) are known to be thermodynamically unfavored compared to carbonate (or sulphate)-based GRs [START_REF] Abdelmoula | Conversion electron Moessbauer spectroscopy and x-ray diffraction studies of the formation of carbonate-containing Green Rust one by corrosion of metallic iron in NaHCO3 and (NaHCO3 + NaCl) solutions[END_REF]. The localized observation of GR(CO 3

2-

) on G samples shows inhomogeneous distribution of chloride ion concentration in pore solution.

The stability of GR spectra over several days also shows that our setup efficiently protects the concrete rebar interface from atmospheric oxidation. This reflects the situation in real concrete, where oxygen penetration is a slow process [START_REF] Boucherit | Raman studies of corrosion films grown on iron and iron-molybdenum (Fe-6Mo) in pitting conditions[END_REF].

During treatment, once corrosion was proved to occur by the formation of spots of Green Rust, a cathodic current of -100 µA/cm 2 was added to the system. Raman spectra were periodically recorded during this treatment. The spectra observed during the reduction process are depicted in Figure 6 for I1 sample.

After polarization is turned on, the characteristic band of magnetite Fe 3 O 4 appears at 670 cm -1 . With time, a progressive increase is observed in magnetite bands, causing a decrease in Green Rust bands until they almost completely disappear. All the studied series behaved in the same manner, the only differences being the induction time and the growing rate of magnetite, which both varied from one sample to the other (SI 4). However, magnetite was the predominant band for all samples after 24 hours of polarization.

After longer polarization time (more than one day), new Raman spectra were recorded for a few spots around the rebar. They are depicted in Figure 7a for I1 sample and in Figure 7b for G3 sample. Similar behavior was also recorded for I3 sample (not shown). No information was obtained for G1 sample after 24 hours due

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12 to a high interface fluorescence. Figure 7a presents the evolution of the Green Rust bands, with a rapid decrease in the intensity of the 500 cm -1 band compared that of the 430 cm -1 band. A shift of the 430 cm -1 band towards a lower wavenumber (410 cm -1 ) is also observed. Moreover, after 2 days a new band appears in the 3600 cm -1 range (see insert in Figure 7a) corresponding to O-H stretching vibration at 3575 cm -1 . These values were in accordance with reference [START_REF] Lutz | Lattice vibration spectra. Part LXXXII. Brucite-type hydroxides M(OH)2 (M = Ca, Mn, Co, Fe, Cd) -IR and Raman spectra, neutron diffraction of Fe(OH)2[END_REF] and indicated the formation of Fe(OH) 2 in I1 series. In Figure 7b, after 3 days of treatment, two new bands appeared in the Raman spectrum: 205 cm -1 and 280 cm -1 . They correspond to mackinawite Fe 1-x S [START_REF] Bourdoiseau | Characterisation of mackinawite by Raman spectroscopy: Effects of cristallisation, drying and oxidation[END_REF] in G3 series (also observed for I3 series, not shown). The presence of sulfide is due to the blast furnace material contained in cement 3 (CEM III/A) [START_REF] Bouteiller | Corrosion initiation of reinforced concretes based on Portland or GGBS cements: Chloride contents and electrochemical characterizations versus time[END_REF].

In situ Raman spectroscopy analysis of the chloride extraction treatment made it possible to collect information on corrosion mechanisms. First, as expected in a medium pH range containing anions such as chloride, carbonate, or sulfate, rebar corrosion takes place through the formation of Green Rust [START_REF] Refait | Corrosion and cathodic protection of carbon steel in the tidal zone: Products, mechanisms and kinetics[END_REF]. This iron II hydroxide-based compound contains some iron III ions, and the balanced charge is compensated with anions originating from the solution, mainly chlorides in this case.

A progressive transformation of Green Rust into magnetite was evidenced during cathodic polarization, as pH in the pore solution near the rebar increases due to the reduction process. The literature indicates that a pH of around 10-11 is necessary for this transformation to take place [START_REF] Sumoondur | Green Rust as a precursor for magnetite: an in situ synchrotron based study[END_REF]. Raman spectroscopy showed this process to be relatively fast compared to the treatment duration, and also evidenced the rapid release of chloride anions inserted in corrosion products.

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13 However, the local formation of iron II compounds that can be easily oxidized [START_REF] Lutz | Lattice vibration spectra. Part LXXXII. Brucite-type hydroxides M(OH)2 (M = Ca, Mn, Co, Fe, Cd) -IR and Raman spectra, neutron diffraction of Fe(OH)2[END_REF][START_REF] Bourdoiseau | Characterisation of mackinawite by Raman spectroscopy: Effects of cristallisation, drying and oxidation[END_REF][START_REF] Bourdoiseau | The transformation of mackinawite into greigite studied by Raman spectroscopy[END_REF], (hydroxide in CEM I and sulfide in CEM III/A) during long polarization durations, while GR and magnetite are hardly visible in the Raman spectra, is a clear indication of corrosion that is still active in some spots around the rebar.

Corrosion rate

ECE treatment aims to decrease or even stop reinforcement corrosion. Figure 8 presents the results of corrosion rates versus treatment duration. These measurements were performed 3 months after the end of the treatment period in order to allow the system to recover a stable state (with the exception of time 0). For the four series, the ECE treatment leads to a decrease of the corrosion rates over time, with two or three orders of magnitude (log scale). From days 14 to 56 of treatment (corresponding to durations after which free chloride content was below 0.4%), corrosion rates decreased to values below 0.1 µA/cm².

Corrosion rates remained in the range 1 to 10 µA/cm² in the non-polarized samples, where chloride ions had been removed by lixiviation but were still carbonated.

These results show that chloride extraction and pH increase are both needed to slow down the corrosion of the reinforcement and that realkalization is mandatory.

Raman spectroscopy shows that the chloride ions that are bonded to the corrosion products were released at the beginning of the cathodic treatment and were therefore completely extracted. On the lixiviated samples, the chlorides that were bonded to the corrosion products remained at the rebar/concrete interface. They can be released by the oxidation of GR into iron III oxyhydroxides, and can thus cause further corrosion.

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14 Nevertheless, corrosion rates for after treatment remained one order of magnitude higher than for the sound concrete for all contaminated samples. The passive state of the rebar in the sound concrete was not therefore recovered in the samples. This was confirmed by the presence of iron II revealed by Raman spectroscopy, indicating that corrosion was still active on some spots.

Durability

In a previous study dealing with an impressed current realkalization treatment applied to carbonated reinforced concrete, the pH increased from 9 to 10-11 after treatment (quantitative pH determination from powders in solution), inducing a decrease in the corrosion rates [START_REF] Tong | Efficiency investigations of electrochemical realkalization treatment applied to carbonated reinforced concrete -Part 1: Sacrificial anode process[END_REF][START_REF] Sahal | Durability of impressed current realkalization treatment applied on reinforced concrete slabs after 5 Years DBMC Porto[END_REF]. Although the pH remained constant with time, corrosion rates gradually increased again, and finally reached the corrosion rate values observed for untreated carbonated reinforced concrete 30 months after the end of treatment. This behavior was explained by the fact that the increase in pH was not sufficient, as the sound pH concrete value of 13 was not recovered [START_REF] Sahal | Durability of impressed current realkalization treatment applied on reinforced concrete slabs after 5 Years DBMC Porto[END_REF]. Identical cement (CEM I) and mortar composition and similar experimental conditions were used in this previous study and in the present study. Based on this, the hypothesis of similar behavior can be assumed. Moreover, Tlili et al. [46] observed a limit for the pH increase in carbonated solution due to a buffer effect. Figure 9 presents SEM observations of realkalized samples thirty months and five years after treatment.

They exhibit a doubling of the corrosion layer thickness (15 to 30 µm) over time (30 to 60 months), evidencing a reactivation of corrosion.

Therefore, although the electrochemical treatment applied to reinforced concrete with a double contamination seems to be efficient in extracting chlorides and reducing reinforcement corrosion, the long-term efficiency with regard to pH evolution needs to be examined in greater detail.

  the lixiviation of chloride ions without current (no polarization).

  Raman spectrometer equipment was a HORIBA Jobin Yvon LABRAM consisting of an Olympus BX40 microscope confocally coupled to a 300 mm focal length spectrograph. The latter was equipped with a holographic grating (1800 grooves/mm) and a Peltier-cooled CCD detector (1024 × 256 pixels). The spectra were obtained with 632.817nm radiation from an internal 10mW HeNe laser with neutral density filters and 0.7mW attaining the surface of the sample to avoid any thermal effect. For in situ studies, a 50× ULWD (Ultra-Long Working Distance) allows the recording of Raman spectra with a working distance of 8 mm.Electrodes for in situ Raman spectroscopy were specially designed for this study. As shown in FiguresSI1-2, Raman spectroscopy samples were cut from doublecontaminated concrete samples. A glass window was glued on top of the freshly polished sample shortly before the experiment, as represented in Figure2. The electrode was immersed window-up in disodium tetraborate solution with 5mm left outside the electrolyte to ensure that the steel was polarized in a pore solution that had to cross 17.5 mm of concrete and had no direct contact with the atmosphere. Spectra were recorded solely at the rebar concrete interface. Spectra during corrosion initiation were obtained at open circuit potential. Treatment was then applied with an Autolab galvanostat using the same current density (-100 µA/cm 2 ) as previously described. Spectra were then recorded for each sample subjected to cathodic polarization.

22 [Figure 1 :

 221 Figure captions

Figure 2 :

 2 Figure 2: Top view of the electrode with glass used for in situ Raman spectroscopy.

Figure 3 :

 3 Figure 3: Free and total fraction of extracted chlorides for the internal part

Figure 4 :

 4 Figure 4: Diameter of realkalized concrete around the rebar versus treatment

Figure 5 :Figure 6 :

 56 Figure 5: a), c) In situ Raman spectra of the metal concrete interface after immersion in tetraborate solution; b) reference Raman spectrum of GR(Cl -) and d) reference

Figure 7 :Figure 8 :

 78 Figure 7: In situ Raman spectra evolution with long polarization time; spectra have been offset for sake of clarity, tetraborate solution, cathodic current I=-100µA/cm 2 , a)

Figure 9 :

 9 Figure 9: Corrosion products layers after the realkalization treatment a) 30 months

1 R a m a n w a v e n u m b e

 1 c t i o n o f e x t r a c t e d c h l o r i d e / %T r e a t m e n t d u r a t i o n / d a y s a n I n t e n s i t y / u . a . R a m a n W a v e n u m b e r / c m -1 a n i n t e n s i t y / c o u n t s . s -

Table 1 :

 1 Characterizations before treatment: corrosion rate (µA/cm²), pH value and chloride content (% weight of cement) for the four series.

		sound	Cl -	CO 2		Cl -+CO 2
		concrete	contaminated	contaminated		contaminated
							Free
	series						chloride
			Icorr/ µA.cm -² (standard deviation)		pH	content (%
						weight of
						cement)
	G1	0.00	0.02		10.99 (1.82)	9	1.4
	I1	0.00		2.72	9.34 (3.27)	9	0.9
	G3	0.01	0.06		7.82 (1.07)	9	2.1
	I3	0.01		8.80	9.39

Acknowledgements

Funding for this work was provided by the French Ministries of Culture, Environment, Research and Education.

• Electrochemical chloride treatment is provisionally efficient.

• Long term durability of ECE is questionable (pH increase is insufficient).