Bibek Kc

Hassan Alkhwaildi
email: hassan.alkhwaildi@siu.edu

Multi-Objective TLBO and GWO-based Optimization for Placement of Renewable Energy Resources in Distribution System

Keywords: Distributed Generation, Fuzzy Decision, Hybrid Teaching Learning -Gray Wolf Algorithm, Multi-Objective Optimization, Renewable Energy Sources

The use of renewable solar and wind resources as distributed generation sources in distribution networks has been welcomed by network operators. In order to exploit the maximum benefits of using these distributed products, the location of installation and their capacity should be determined optimally in the distribution network. In this paper, in order to optimize the placement of solar panels and wind turbines in the distribution network with the aim of reducing losses and improving reliability based on Energy Not Supplied subscribers (ENS), a multi-objective evolutionary algorithm based on fuzzy decision method, called the Multi-Objective Hybrid Training Learning Based Optimization-Grey Wolf Optimizer (MOHTLBOGWO) proposed that has a High optimization speed and not trapped at all in the optimal local. At first, the candidate buses are set for the installation of renewable resources using the Loss Sensitivity Factor (LSF). Then the proposed method is used to determine the location and optimal capacity of renewable resources through the candidate bases. Proposed issues have been implemented in a single-objective and multiobjective manner on a 33 bus IEEE radial distribution network. Also, in this paper, the effect of distributing renewable resources on the characteristics of the distribution network is evaluated. The results obtained from the proposed algorithm are compared with the results of other algorithms to demonstrate the superiority of the proposed method in reducing losses, improving reliability, and increasing the financial profit of the network. Simulation results show the better performance of the proposed method in comparison with Teaching-Learning Based Optimization (TLBO) and Grey Wolf Optimiser (GWO) methods and past studies to achieve optimal results. Also, the results show that distributing of the capacity and location of distributed renewable generation leads to a further reduction in losses and a better improvement of the reliability criterion.

Introduction

The growing consumption of electric energy, mainly produced by burning fossil fuels, leads to various issues, such as environmental and financial issues. On the other hand, nearly 15% of active power is produced in large power plants [START_REF] Holttinen | Design and operation of power systems with large amounts of wind power[END_REF][START_REF] Coello-Coello | An Introduction to Evolutionary Multi-Objective Optimization with Some Applications in Pattern Recognition[END_REF]. This power is lost in transmission lines and distribution networks. Reducing power losses is one of the most interesting and most important issues in power system studies. There are several ways to minimize losses in power systems at the level of transmission and distribution networks [START_REF] Hayerikhiyavi | Comprehensive Analysis of Continuously Variable Series Reactor Using GC Framework[END_REF]. DG placement is one of these methods. These methods have advantages such as improving reliability, improving the voltage profile, and reducing the power loss of the active. However, inappropriate placement and inappropriate DG planning can weaken the distribution network characteristics [START_REF] Mehta | Optimal selection of distributed generating units and its placement for voltage stability enhancement and energy loss minimization[END_REF][START_REF] Daud | A review: Optimal distributed generation planning and power quality issues[END_REF]. Several studies have been conducted in the field of exploitation of distribution networks by optimal utilizing the dispersed generation sources in the distribution network. Classical, analytical, and meta-exploratory methods are the methods that have been proposed in this field. Classical methods are methods that can determine optimal response over a short period of time, but with increasing problem dimensions they cannot determine the optimal response. Analysis methods are methods that require additional computations and may not be able to achieve absolute optimal points [START_REF] Jenkinson | Improved optimization for the robust and accurate linear registration and motion correction of brain images[END_REF]. Recently; Metaheuristic methods have been used to solve the problems of distribution network utilization. In [START_REF] Zamzam | Data-driven learning-based optimization for distribution system state estimation[END_REF], the Teachinglearning algorithm has been used and optimization has been achieved as a single-objective or two-objective. Placement of wind turbines and solar cells in the distribution network with the goal of reducing losses and improving the voltage stability conducted as a two-objective issue using the Particle Swarm Optimization algorithm [START_REF] Golestani | Distributed generation dispatch optimization by artificial neural network trained by particle swarm optimization algorithm[END_REF][START_REF] Behbahani | Safety Assessment on Merge and Diverge Areas using Fuzzy Inference System, Artificial Neural Network, and Particle Swarm Optimization[END_REF]. In [START_REF] Prabha | Optimal placement and sizing of multiple distributed generating units in distribution networks by invasive weed optimization algorithm[END_REF][START_REF] Yazdani | Distribution Simultaneous Sizing, Sitting, and Service Area Determination of Sub-transmission Substations and Distributed Generations Considering Load Uncertainty by GSO Algorithm[END_REF], in order to reduce the true power losses in distribution networks, the optimal placement of dispersed generation resources have been used in a combination and single-objective approach. In this study, a sensitivity analysis method was used to determine the best mode for locating dispersed generation sources and capacitors in the network. In [START_REF] Khatod | Evolutionary programming based optimal placement of renewable distributed generators[END_REF], the optimal placement of renewable distributed generation sources is presented using evolutionary planning and its results are compared with the genetic method. The results show that, compared to the proposed method, the genetic algorithm finds the optimal problem at lower speeds. In [START_REF] Sattianadan | Optimal placement of DG in distribution system using genetic algorithm[END_REF], the locating of dispersed generation in distribution networks is provided by considering the voltage stability criteria. In this study, the genetic algorithm is used to find the best answer. In [START_REF] Kaur | Effective Loss Minimization and Allocation of Unbalanced Distribution Network[END_REF][START_REF] Rao | Teaching-learning-based optimization algorithm[END_REF], a new and high-efficiency algorithm is proposed using a firefly algorithm to determine the location and capacity of dispersed generation sources in an unbalanced distribution network in a single-objective optimization. The goal of the problem is to reduce network losses.

The use of Genetic Algorithm (GA) and Simulated Annealing algorithm for optimal allocation of DG in distribution network [START_REF] Gandomkar | A combination of genetic algorithm and simulated annealing for optimal DG allocation in distribution networks[END_REF][START_REF] Tavana | An integrated intuitionistic fuzzy AHP and SWOT method for outsourcing reverse logistics[END_REF] are presented in the form of single-objective optimization with the aim of reducing of losses. In [START_REF] Moradi | A combination of genetic algorithm and particle swarm optimization for optimal DG location and sizing in distribution systems[END_REF][START_REF] Shirai | Configuration of fuzzy membership function circuits using current mode[END_REF], the installation location of the DG is determined by the GA algorithm and its capacity is determined by the Particle Swarm Optimization (PSO). This work has been done on the basis of the weight coefficient method and is presented with the aim of reducing power losses, decreasing voltage oscillation of the bus and improving the voltage stability of the distribution network. In [START_REF] Falaghi | ACO based algorithm for distributed generation sources allocation and sizing in distribution systems[END_REF][START_REF] Shakarami | A new approach for network reconfiguration problem in order to deviation bus voltage minimization with regard to probabilistic load model and DGs[END_REF], the Ant Colony Optimization (ACO) algorithm is proposed to determine the best installation location of the DG in the distribution network. This algorithm is presented in the form of single-objective optimization for reducing losses. Harmony Search algorithm (HS) is presented in [START_REF] Rao | Optimal Placement of Multiple Distributed Generator by Hs Algorithm[END_REF] as an optimization method for solving this problem with the goal of reducing losses based on single-objective optimization. The Artificial Colony Bee (ABC) algorithm has been introduced in [START_REF] Padma Lalitha | Application of fuzzy and ABC algorithm for DG placement for minimum loss in radial distribution system[END_REF][START_REF] Vosoogha | An Intelligent Power Prediction Method for Wind Energy Generation Based on Optimized Fuzzy System[END_REF] to determine the capacity, optimal power coefficient and DG installation location. This algorithm is presented in the form of single-objective optimization for reducing active losses. In [START_REF] Hadidian-Moghaddam | A multi-objective optimal sizing and siting of distributed generation using ant lion optimization technique[END_REF], the Differential Evolution Algorithm (DEA) has been used to optimize single-objective DGs and achieve minimum losses. In [START_REF] Devi | Application of modified bacterial foraging optimization algorithm for optimal placement and sizing of distributed generation[END_REF], the Bacterial Foraging Optimization (BFO) Search Algorithm was used to optimize the planning of DG units in the distribution system with the goal of reducing losses, reducing operating costs, and improving voltage stability. This work is based on the weighting coefficient method and the multi-objective optimization form. The Imperialistic Competitive Algorithm (ICA) is used in [START_REF] Soroudi | Imperialist competition algorithm for distributed generation connections[END_REF] as a singleobjective optimization to minimize losses in the system. The Plant Growth Simulation Algorithm (PGSA) has been used in [START_REF] Prabha | Determining the optimal location and sizing of distributed generation unit using Plant Growth Simulation Algorithm in a radial distribution network[END_REF][START_REF] Rajaram | Power system reconfiguration in a radial distribution network for reducing losses and to improve voltage profile using modified plant growth simulation algorithm with Distributed Generation (DG)[END_REF][START_REF] Khatibi | Comparative Analysis of Power System Model Reduction[END_REF] to determine the unit capacity and the loss sensitivity factor in choosing optimal DG location. Firefly Algorithm (FA) is used in [START_REF] Shakarami | A new approach for network reconfiguration problem in order to deviation bus voltage minimization with regard to probabilistic load model and DGs[END_REF][START_REF] Nadhir | Firefly algorithm for optimal allocation and sizing of Distributed Generation in radial distribution system for loss minimization[END_REF] to optimize singleobjective DGs with the goal of reducing power losses. In [START_REF] Ali | Ant Lion Optimization Algorithm for optimal location and sizing of renewable distributed generations[END_REF][START_REF] Reddy | Ant lion optimization algorithm for optimal sizing of renewable[END_REF], Ant Lion Optimizer (ALO) algorithm is used to determine optimal location of installation and DG size based on renewable resources with the goal of reducing losses and improving the profiles and voltage stability in a multiobjective optimization based on weight coefficient method. In [START_REF] Hasanien | A cuckoo search algorithm optimizer for steady-state analysis of self-excited induction generator[END_REF], the optimal placement of wind turbines in the distribution network is proposed using Cuckoo Search Algorithm (CSA) in a single-objective optimization with the goal of reducing power losses. In [START_REF] Choi | Multi-objective optimization of voltage-stability based on congestion management for integrating wind power into the electricity market[END_REF][START_REF] Shokouhandeh | Optimal Estimation of Capacity and Location of Wind, Solar and Fuel Cell Sources in Distribution Systems Considering Load Changes by Lightning Search Algorithm[END_REF], the locating of wind turbines and solar panels is proposed to reduce power losses and improve voltage stability using PSO algorithm based on multi-objective optimization and weight coefficient method.

As mentioned in most of the previous studies, the problem of positioning is presented as single or twoobjective optimization with the goal of reducing losses and improving the voltage profile, based on the weight coefficients method. In order to achieve a more accurate and realistic exploitation of the distribution network, the problem of the location of distributed generation should be considered as a multi-objective. One of the best ways for solving multiobjective problems is the use of Pareto levels to determine the optimal answer, which in this paper focuses on it and presents a multi-objective hybrid algorithm. On the other hand, the placement of renewable resources from the perspective of reliability, and considering the network failure rate and energy not-supplied network, has been less investigated. In this paper, these concepts are considered. In this paper, the proposed method is based on the combination of Teaching-learning and gray wolfs algorithms The Teaching-learning algorithm was presented in 2012 [START_REF] Rao | Teaching-learningbased optimization: an optimization method for continuous nonlinear large scale problems[END_REF] and the high convergence rate and the lack of control parameters were the features of this method. The gray wolf method is presented in 2014 [START_REF] Mirjalili | Grey wolf optimizer[END_REF] and has been greatly welcomed to solve the power engineering optimization problems. This method has features such as high convergence speed, high computational power, fast and large searches and Avoid Local Optimal. Therefore, in this paper, in order to locating solar panels and wind turbines in a 33-buses radial standard distribution network and reducing losses and improving reliability, Utilizing the benefits of both methods, a multiobjective hybrid algorithm based on a fuzzy decision method called MOTLBOGWO is proposed. The main contribution of this article are following:

• Use of a new cumulative smart method called the HTLBOGWO method • Solve multi-objective problem of locating renewable resources based on fuzzy decision method in MOHTLBOGWO algorithm • Study of the location of renewable energy sources from the perspective of reliability • Assess the dispersal of location and capacity of renewable energy sources over network characteristics The rest of this paper is organized as follows: In Section 2, Loss Sensitivity Factor Formulation is described for determining the candidate buses for the installation of renewable energy sources. In Section 3, the problem formulation including optimization target function and problem constraints is presented. In Section 4, the proposed algorithm, the fuzzy decision method and implementation of the proposed method in problem solving described. In Section 5, the simulation results are presented and the conclusions are presented in Section 6.

Loss Sensitivity Factor

In this study, the Loss-Sensitivity Factor (LSF) is presented to show buses that are sensitive to losses [START_REF] Reddy | Application of loss sensitivity factor and genetic algorithm for capacitor placement for minimum loss in radial distribution system[END_REF][START_REF] Asadi | Optimal placement and sizing of capacitor banks in harmonic polluted distribution network[END_REF]. Also, using this factor can reduce the search area and the time of the optimization process. In other words, the buses that are in trouble for losses are identified by this factor, and thus instead of searching all the network buses for the installation of dispersed generation by the optimization method, the search area is limited to these buses, thereby the time of the calculations is reduced. For a transmission line 'L' connected between the buses "i" and "k", as shown in Figure 1, the active power losses on this line are defined by RI2, defined as Eq. ( 1) [START_REF] Ali | Ant Lion Optimization Algorithm for optimal location and sizing of renewable distributed generations[END_REF][START_REF] Reddy | Application of loss sensitivity factor and genetic algorithm for capacitor placement for minimum loss in radial distribution system[END_REF].

(P Q )R P (V ) - + = (1)
The LSF can be calculated as follows [START_REF] Sardi | A loss sensitivity factor method for locating ES in a distribution system with PV units[END_REF]:

ik loss k ik 2 k k P 2Q R Q (V ) -  =  (2)
The normalized voltage is obtained by dividing the voltage in the base conditions by 0.95 [START_REF] Ali | Ant Lion Optimization Algorithm for optimal location and sizing of renewable distributed generations[END_REF][START_REF] Reddy | Application of loss sensitivity factor and genetic algorithm for capacitor placement for minimum loss in radial distribution system[END_REF]. Buses whose their voltages are less than 1.01 can be considered as the candidate bass for DG installation. It's worth noting that LSFs introduce a sequence of buses for the installation of DG.

Problem Formulation

In this study, multi-objective optimization of location and capacity of solar panels and wind turbines in the distribution network using the MOHTLBOGWO hybrid algorithm is proposed to reduce losses and improve reliability. In order to achieve Pareto set levels, Problem optimization variables, the optimal location and capacity of dispersed wind and solar generation sources are determined using intelligent singleobjective optimization (using the HTLBOGWO method) as well as multi-objective based on decision-making fuzzybased approach.

Objective Function

In this study, the minimization of power losses and improvement of Reliability is considered as an objective function and is described below.

• Line loss

Total network losses are equal to the losses of all network lines. To calculate network losses, you must first get the current of lines. To calculate the current of lines, it is also necessary to solve the load distribution problem and obtain the voltage of the buses [START_REF] Haggi | The effect of rescheduling power plants and optimal allocation of STATCOM in order to Improve power system static security using TLBO algorithm[END_REF]. By calculating the buses voltages, the line currents and network losses are calculated as follows:

(3) [START_REF] Mehta | Optimal selection of distributed generating units and its placement for voltage stability enhancement and energy loss minimization[END_REF] where k is between the buses i and j. Rk and Xk are the resistance and reactance of the k-th line, and Nb is the number of grid lines.

• Reliability

Reliability indicators are distribution system reliability assessment factors that were first introduced by the IEEE in 1998 to evaluate the distribution system. Basic reliability indicators are three load point indicators, a) The average rate of breakdown, b) the average withdrawal, and (c) the annual withdrawal period. A radial distribution system includes a set of series equipment including lines, brackets, fuses, and disconnected switches, and so on. A subsystem connected to the load point of a system requires that all equipment between it and the supply point be in operation. Therefore, the principle of serial systems can be considered directly for these systems as follows.

1

n p i i   = =  (5) 1 n p i i i ur  = =  (6) 1 1 n ii p i p n p i i r u r    = = ==   (7)
In the above equation, n is represent the number of outage events affecting load point p, i  denotes Equipment failure rate I (failure/year) and ri is repair time equip I (hours). Based on the basic indices of the load point and energy consumption at load points, energy not-supplied (ENS) (kWh/year) is calculated as follows [START_REF] Sabpayakom | Power losses reduction and reliability improvement in distribution system with Very Small Power Producers[END_REF].

() 1 nl a j j j ENS L u = =  (8)
where, nl represents the total number of load points, the unavailability of the load point j (hours/year), and the average load connected at the load point j (kW).

Constraints

In solving this optimization problem, a series of equal and unequal constraints is considered, which is expressed in sequence.

• Equilibrium power equations

The sum of the algebraic input and output power in the distribution system should be equal to:

ij k kk VV I R jX - = + 2 1 b N loss k k k P R I = =  DG DG N L N Swing DG Lineloss i 1 i 1 q 1 N L N Swing DG Lineloss i 1 i 1 q 1 P P (i) P (i) Pd(q) Q Q (i) Q (i) Qd(q) = = = = = = + = + + = +       (9)
• Voltage constraint

The value of the voltage in each bus should be between a minimum and a maximum value as follows:

min i max V V V  (10)
In the above relation, Vmin and Vmax are considered to be 0.95 and 1.05 p.u respectively [START_REF] Ali | Ant Lion Optimization Algorithm for optimal location and sizing of renewable distributed generations[END_REF].

• Constraints on the production of DG

To prevent reverse power flow, the installed DG capacity in the network is limited as follows, which should not exceed the power supplied by the post [START_REF] Ali | Ant Lion Optimization Algorithm for optimal location and sizing of renewable distributed generations[END_REF].

DG N L N DG Lineloss i 1 i 1 q 1 3 P (i) P (i) Pd(q) 4 = = =     +        (11) DG N L N DG Lineloss i 1 i 1 q 1 3 Q (i) Q (i) Qd(q) 4 = = =     +        (12)
On the other hand, DGs themselves have the minimum and the maximum production capacity is as follows [START_REF] Sabpayakom | Power losses reduction and reliability improvement in distribution system with Very Small Power Producers[END_REF].

min max DG DG DG P P (i) P   ( 13
) min max DG DG DG Q Q (i) Q   (14)
• Line capacity constraints

The Complex power transmission of each line should be less than the nominal value given in the following equation.

Li

Li(rated) SS 

Overview of Proposed Algorithm

TLBO

The TLBO algorithm is a smart optimization method that was introduced by Rao [START_REF] Rao | Teaching-learning-based optimization algorithm[END_REF] based on the influence of teacher to students to increase scientific level of class. This method is based on this principle that the teacher tries to close class level to himself and students, in addition to exploit the teacher's knowledge with regard to other classmates, use their knowledge to increase level of them. Because of the teacher can't bring level of individual students to himself, so tries to increase the average level of whole class and evaluates the class level based on the exams and students' scores. The mathematical expression of this approach is that first the population of problem variables (teacher and students) are defined randomly. All of these populations are compared together by the objective function and set of variables with best solution are considered as the teacher.

This approach is divided into two phases: teacher phase and student phase.

• Teacher phase

In this step teacher tries to bring class average to himself. But since it is very difficult, teacher tries to increase class average from Mi to M_new. Each set of problem variables are updated based on the difference of these two values. Difference of these two values can be saved by the parameter Diff_Mean as follows:

_ ( _ ) i i f i Diff Mean r M new T M =- ( 16
)
Where Tf is the teacher parameter that is selected randomly between 1 and 2. The ri is a random number between 0 and 1. Using the follow equation each set of variables are updated.

, ,

_ new i old i i X X Diff Mean =+ ( 17
)
• Student phase Students in addition to teacher's knowledge, benefit from each other's knowledge. The mathematical expression of this approach is that in each step and in each repetition each set of variable (student) selects one of students randomly. For example student i selects student j and this i is opposite of j. If the student j has more knowledge respects to student i then the student i updates his status based on the following equation: ,, ()

new i old i i i j X X r X X = + - (18)
The student status is varied as follows:

,, ()

new i old i i j i X X r X X = + - (19)
After the all students changed their status, their level is evaluated by the objective function. Under these conditions the best student is compared with the teacher of previous step and if a better result has, is replaced with previous iteration teacher. This process is continued to obtain convergence conditions.

GWO

One of the population-based intelligent and evolutionary algorithms is the Gray Wolf algorithm (GWO) which was first announced by Mir-Jalili in 2014 [START_REF] Mirjalili | Grey wolf optimizer[END_REF]. In this algorithm, the performance and behaviour of gray wolfs for hunting is simulated. Figure 2 shows that parameters such as α, β, δ, and ω represent the leaders of the group so that α directs the group as leader of the group and has important decisions about hunting, resting place and so on. The second group of leadership belongs to β. In addition to being able to help α due to having a good decision, β members are also the best substitutes for the α wolfs when they are old or dead; ω but is at the bottom of this group. They are the last wolves that are allowed to eat. The other group members that are not α, β and ω are called δ [START_REF] Mirjalili | Grey wolf optimizer[END_REF]. • Investigating, pursuing and following the hunt; • Pursuing, sieging and harassing the hunt until it stops; and • Attacking to the hunt.

In the simulation of the GWO, α is considered as a top answer. After that, the next two responses after α are considered β and δ. Finally, the rest answers are regarded ω.

To model a suitable situation that gray wolves encircle their hunt during hunting are shown as follows [START_REF] Mirjalili | Grey wolf optimizer[END_REF].

(20) [START_REF] Shakarami | A new approach for network reconfiguration problem in order to deviation bus voltage minimization with regard to probabilistic load model and DGs[END_REF] where t represents the repetition, A , C , and P X indicate the coefficients vectors, the position of the bait and the gray wolf respectively. The coefficients vector is obtained from the following equation [START_REF] Mirjalili | Grey wolf optimizer[END_REF]. According to the wolf ability due to finding and surrounding the hunt and in order to having a mathematical simulation of this kind of behaviour, it is assumed that the three top wolves in the group have more knowledge about the hunting place. By storing the position of the three above mentioned wolves, ω wolves have to change their location based on the position of the three top members of the group which can be expressed as follows [START_REF] Mirjalili | Grey wolf optimizer[END_REF]:

1 2 3 , , D C X X D C X X D C X X       = - = - = - ( 24
) 1 2 3 1 2 3 , , X X a D X X a D X X a D       = - = - = - (25) 1 2 3
( 1) 3

X X X Xt + + + = (26)

HTLBOGWO (TLRBO)

The TLBO algorithm is a robust algorithm capable of solving engineering problems. However, a new phase has been added to this algorithm to increase the global and local search capability as well as track the optimal answer. This phase is due to the choice of first, second and third students as the best answers after the student phase. After selecting the top three students, the remaining students will learn from these three students. The process of selection students and their ranking is considered to be the ranking phase, which is called the TLRBO algorithm.

Since the ranking phase and follow up of the students and their learning from the top three students are very similar to the behaviour of the gray wolf algorithm, So in the formulation of TLRBO, method of selection the wolf-alpha, beta, and delta and the method of updating the location of the wolfs of Omega to follow up the top three wolves have been used. Therefore, the proposed algorithm will be a combination of the TLBO and GWO algorithms.

HTLBOGWO (TLRBO) Multi-Objective Algorithm

Multi-objective issues have multiple goals, which are mostly contradictory. The answer to these problems is a set of solutions called Pareto optimal solutions [START_REF] Haggi | Multi-Objective PMU Allocation for Resilient Power System Monitoring[END_REF]. This set includes Pareto optimal solutions that represent the best balance between the objectives. Multi-objective optimization is considered as a minimization problem and formulated as follows [START_REF] Sabpayakom | Power losses reduction and reliability improvement in distribution system with Very Small Power Producers[END_REF]:

  1 2 0 min : F(x)= ( x), ( x),..., ( x), imize f f f ( 27
)
to: g (x) 0, i 1,2,...,

i subject m  = (28)
h (x) 0, i 1,2,...,

i p = = ( 29
) i i i L x U  (30)
where 0 represents the number of targets, m denotes the number of inequality constraints and p is the number of equality constraints. [Li, Ui] are the boundaries variable i. Given the nature of the multi-objective problems, various solutions cannot be compared through mathematical relations operators. In this case, Pareto optimal parental concepts allow us to compare two solutions in a multiobjective search space [START_REF] Sabpayakom | Power losses reduction and reliability improvement in distribution system with Very Small Power Producers[END_REF].

Two key points in finding a suitable set of optimal Pareto solutions for the given problem are convergence and coverage. Convergence refers to the ability of a multiobjective algorithm to determine the exact approximation of Pareto's optimal solution. The coverage reflects the distribution of Pareto's optimal response along the objectives. Since many of the current multi-objective algorithms are deductive, coverage and the number of answers for decision-making after the optimization process are very important. The ultimate goal for a multi-objective optimizer is to find the exact approximation of the optimal Pareto correct solution (convergence) with uniform distribution (coverage) for all purposes.

To solve multi-objective problems using the MOHTLBOGWO algorithm, it first equipped to an archive to store and restores the best approximation of the optimal Pareto solution. The position updating of the search factors for MOHTLBOGWO is the same, but the student's position is selected from the archive. In order to find a suitable expansion for the Pareto optimal frontier, a place from the low-density Pareto optimal frontier, similarly for multiobjective particle swarm optimization algorithm (MOPSO) [START_REF] Robles-Rodriguez | Multi-objective particle swarm optimization (MOPSO) of lipid accumulation in Fed-batch cultures[END_REF] is selected. To find the low-density area of Pareto optimal frontier, the search space should be divided. This is accomplished by finding the best and worst objectives of Pareto's optimal solution, the definition of the hyper-sphere to cover all the solution, and the division of the hyper-sphere into sub-hyper-sphere in each repetition. After the creation of the section, the choice is made by a roulette wheel mechanism with the following probability for each section proposed by Coello Coello [START_REF] Coello-Coello | An Introduction to Evolutionary Multi-Objective Optimization with Some Applications in Pattern Recognition[END_REF].

i i c P N = (31)
where c is a constant number greater than one, and Ni is the number of obtained Pareto's optimal response in the i-th section. This allows MOHTLBOGWO algorithm equations with higher probability to choose positions from low population sections.

Fuzzy Decision Making

The ultimate goal of a multi-objective optimization algorithm is to identify solving in the Pareto optimal set. However, identifying the entire Pareto optimal set is not possible due to its wide dimensions to prove the optimality, and therefore not recommended. Therefore, to investigate the feasibility of having Pareto optimal sets in multiple optimization problems, there is a practical approach. In the present study, a fuzzy approach is applied to select the best solution of the Pareto set. The j-objective function of a solution in Pareto set fj is defined by a membership function j as follows [START_REF] Taghavirashidizadeh | A Genetic algorithm for multi-objective reconfiguration of balanced and unbalanced distribution systems in fuzzy framework[END_REF]:

f f f f f f f f         =           - - (32)
where min j f and max j f are the minimum and maximum values of the objective function j. For each i solution, the membership function is calculated as follows [START_REF] Shirai | Configuration of fuzzy membership function circuits using current mode[END_REF]:

1 1 1 n i j j j m n i j i j    = = = =   ( 33
)
where n is the number of objective functions and m is the number of solutions. The answers have the maximum value of μi for the best compromise answer.

Implementation of MOHTLBOGWO

The steps to implement the proposed method in problem solving are as follows:

• Step 1: Random generation of the initial population from the set of variables including the location of the installation and the capacity of solar and wind units as well as the power factor of wind turbines.

• Step 2: the value of the target function is calculated for each set of variables and the best set is selected in terms of the value of the objective function as the representative of the entire population. • Step 3: Each set of variables is updated by the proposed algorithm, and if the new variables have better results, they will be replaced with the previous set. • Step 4: if the condition for convergence does not exist, go to step 1. Otherwise, go to step 5. • Step 5: Stop the algorithm.

Simulation Results and Discussion

Testing System

As shown in Figure 3, in this paper, the proposed method is implemented on the IEEE standard 33-buses radial network. In the 33-buses network, the total consumption of this network is 3720 kW and 2300 kVAR. The 33-buses Network has 37 branches. System information is presented in [START_REF] Etemad | Exploiting endusers capability in voltage support by means of power electronic transformer[END_REF].

Simulation Strategies

In this paper, the optimal placement of solar panels and wind turbines for the purpose of reducing losses and improving reliability indicators are presented using the proposed method HTLBOGWO. First, simulations were performed in a single-objective optimization. Then, multiobjective optimization was proposed based on fuzzy decision method and the results were compared and analyzed. In single-objective optimization, simulation results obtained from TLBO, GWO, and HTLBOGWO methods are evaluated based on indicators of loss reduction and energy not-supplied subscriber reduction (reliability improvement). In multi-objective optimization, the results of multiobjective methods MOGWO, MOTLBO and MOTLBOGWO are presented. In Figure 4, the LSF curve of the 33-buses network is presented. In this figure, the buses 6, 28, 29, 30, 9, 10, 13, 8, 27, 31 and 26 are based on the LSF curve considered as the candidate buses for installing wind turbines and solar panels Which are similar to Candida buses in reference [START_REF] Ali | Ant Lion Optimization Algorithm for optimal location and sizing of renewable distributed generations[END_REF].

Single-Objective Optimization Results

In this section, the results of single-objective positioning of solar panels and wind turbines are presented for the purpose of reducing losses and reducing ENS for 1, 2 and 3 DGs 1 megawatts. In Table 1, the results are presented with the objective of reducing losses. In the positioning of 3 solar panels, the buses 13, 24 and 30 were selected for installation with a capacity of 996, 938 and 852 kW respectively. The network losses before positioning were 202.68 kilowatts. After locating one, two, and three panels, this value has dropped to 127.28, 86.55 and 72.11 kW, respectively. In locating of 3 wind turbines, the buses 30, 13 and 24 were selected for installation with a capacity of 997, 1000 and 789 kW and with power factors 0.8659, 0.8122 and 0.8726 respectively. With locating 1, 2 and 3 wind turbines, the network losses dropped from 202.68 to 81.43, 32.17 and 13.68 kilowatts, respectively. With 1, 2 and 3 wind turbines, the network losses dropped from 202.68 to 81.43, 32.17 and 13.68 kilowatts, respectively. Also, the minimum voltage is also improved by the use of panels and turbines. The results also show that the ENS value before the locating of solar panels and wind turbines was 6.695 MW, and after locating 3 panels it reached 0.628 MW, and after locating 3 turbines reached 0.671 MWh. The results show that the cost of network losses with the optimal locating of solar panels and wind turbines has decreased and financial benefits from loss reduction have increased. In addition, the results have shown that increasing the number of DGs has led to a further reduction in losses, reduction cost of losses, and ENS, as well as further increase in the minimum voltage and net profit of the network. The results show that the performance of wind turbines was better than solar panels in improving the distribution network characteristics. In other words, in terms of reduction of losses and ENS, as well as the improvement of minimum voltage, it achieves better results due to the injection of reactive power in addition to the active power to the distribution network.

Table 1. Optimal sizing DG's for 33 bus IEEE system (active power loss objective function)

The convergence curve of the combined HTLBOGWO combination method, along with TLBO and GWO methods for single-objective optimization of solar panels and wind turbines with the goal of reducing losses for 3 DGs, is shown in Figure 5 and Figure 6, respectively. As can be seen, in locating solar panels and wind turbines, the HTLBOGWO method has less convergence fluctuations, and achieved a lower loss rate than the TLBO and GWO with a higher convergence rate and less repetition.

Single-objective optimization results with the goal of reducing losses using TLBO, GWO and HTLBOGWO methods for 3DG are presented in Table 2. As can be seen, the proposed method is better than other methods in terms of reducing losses, reducing cost of losses, reducing ENS, improving the minimum voltage and increasing the financial profit of the network.

Table 3 presents the results of single-objective positioning of solar panels and wind turbines with the goal of reducing ENS for 1, 2 and 3 DG 1 megawatts. As can be seen, with the locating of 1 and 2 solar panels, the network losses are decreasing, but in the positioning of the three panels, the losses compared to the positioning of the two turbines increased from 87. [START_REF] Tavana | An integrated intuitionistic fuzzy AHP and SWOT method for outsourcing reverse logistics[END_REF] contrast to the positioning of the three panels, the ENS value was strongly Dropped to 0.0025 MWh. In the positioning of wind turbines, with increasing its number, the amount of losses decreased, the minimum network voltage increased and the amount of ENS decreased, so that it reached 0.002 MW in the positioning of 3 turbines. Also, with the optimal locating of turbines, the cost of losses is reduced and the amount of financial gain in the locating of the three turbines has a maximum value. This table also shows that wind turbines have a better effect on the characteristics of the distribution network than solar panels. Single-objective optimization results with the aim of reducing the ENS obtained from the HTLBOGWO method are presented in Table 4 and compared with the TLBO and GWO methods. The amount of losses by the proposed method was 97.04 kilowatts and the losses obtained from the TLBO and GWO methods were 101.25 and 103.17 kW respectively. Also, the amount of ENS by the proposed method, 0.025 MWh and by TLBO and GWO methods were 0.048 and 0.044 MW, respectively, which indicates the superiority of the proposed method in solving the problem of positioning solar panels. Also, according to Table 4, in the locating of solar panels and wind turbines, the HTLBOGWO method performed better than other methods in terms of reducing losses, reducing ENS, improving the minimum voltage and financial profit of the network.

Assessment of the Renewable Resource Dispersion Effect

In this section, the effect of dispersing the capacity of solar panels and wind turbines has been evaluated in problem solving. In other words, the effect of using a 3 MW DG with the use of three DGs with a capacity of 1 MW on the power loss, reliability index, minimum network voltage, cost of losses and financial profit of the network has been evaluated. The results obtained in Table 5 and Table 6 are presented for the purpose of decreasing losses and decreasing the ENS in a single-objective optimization, respectively. As can be seen, when using three DGs with a capacity of 1 MW instead of using a 3 MW DG The amount of network losses and ENS will be lower and the network obtaining the higher minimum voltage , more financial gain and reduce cost of losses. For example, according to Table 5, in dispersal conditions, the network losses decreased from 103.96 to 72.11 kV and ENS values decreased from 4.379 to 0.628 megawatts / h. According to Table 6, under dispersal conditions, the amount of network losses decreased from 161.26 to 97.04 kilowatts and ENS values from decreased 0.11 to 0.025 MWh. The voltage profile curve of 33-buses network before locating and under dispersion conditions for solar panels and wind turbines is plotted in Figure 7. Also Figure 7 shows the voltage profile curve of 33-buses network before locating and under conditions where there is no dispersion condition. Figure 7 and Figure 8 showed that the distribution and distribution of power in the network buses leads to improvement of the network voltage profile.

889 [START_REF] Vosoogha | An Intelligent Power Prediction Method for Wind Energy Generation Based on Optimized Fuzzy System[END_REF], 903 [START_REF] Khatibi | Comparative Analysis of Power System Model Reduction[END_REF], 994 [START_REF] Prabha | Optimal placement and sizing of multiple distributed generating units in distribution networks by invasive weed optimization algorithm[END_REF] 996/1@ 13, 938/1@ 24, 852/1@ 30

Multi-Objective Optimization Results

In this section, multi-objective optimization of the locating of solar panels and wind turbines is presented based on the fuzzy decision approach using the HTLBOGWO method and the results are compared with the TLBO and GWO multi-objective methods. The Pareto optimal set of solutions for placement of 1 panel and 1 wind turbine with a capacity of 1 MW is shown in Figure 9 and Figure 10, respectively. As shown in Figure 9, the MOHTLBOGWO method, in comparison with the MOTLBO and MOGWO response scattering, offers better results in terms of achieving an optimal response. Also, in the terms of achieving to lower losses, lower ENS, minimum voltage, lower cost of losses and higher financial profit, the proposed method performance was better than the other two methods. Also, according to Table 7 and Table 8, in the multi-objective optimization, items such as the losses, ENS, the minimum voltage, the cost of losses, and the amount of financial gain are located between the single-objective values that aimed at reducing losses and reducing ENS. In other words, in the multi-objective optimization, there is a Compromise between the losses and ENS. In Figure 11, the multi-objective positioning of both panels and turbines simultaneously is presented using various methods. The numerical results are also given in Table 9. The results show that the proposed MOTLBOGWO method offers better Pareto-optimal solution than other methods and has obtained the optimal solution with less dispersion. Also, according to Table 9, can be seen that the simultaneous use of 1 panel and 1 turbine instead of use one panel or one turbine, has led to a further reduction of losses and ENS, a further increase in the minimum voltage and net profit of the network.

Conclusions

In this paper, the new MOHTLBOGWO method was used to determine the location and capacity of solar panels and wind turbines for the purpose of reducing losses and improving reliability in the distribution network. The proposed problem was evaluated based on single-objective and multi-objective optimization based on fuzzy decision making in optimizing the use of renewable resources in the 33 Buses distribution network. The effectiveness of the proposed method in various optimizations was presented and compared with the MOTLBO and MOGWO results. The results showed that in the optimal placement of the solar panels and wind turbines, unlike their single-objective optimization, there is a compromised between the reduction of losses and improved reliability, and the optimal solution was determined from the set of answers of the Pareto levels. In comparison with the MOTLBO and MOGWO methods, the MOHTLBOGWO method has a better convergence in Pareto levels and achieves optimal solutions. Also, the ability of the proposed method in single-objective optimization In comparison with previous studies in reducing losses, improving the minimum voltage and increasing network profits was confirmed. The results also showed that the dispersal of renewable resources in the distribution network would result in more reduction of losses, greater improvement on reliability, and more financial gain on the network.

Figure 1 .

 1 Figure 1. Distribution Network Equivalent Circuit [32] 22 k k ik ik loss 2 k

Figure 2 .

 2 Figure 2. Leader hierarchy in gray wolves group The principles of GWO function are as follows:

  vectors of random numbers at a distance are shown by and that are selected from [0, 1] area and vector a decreases from 2 to 0 during repetitions.

Figure 3 .

 3 Figure 3. IEEE Standard Radial 33-buses Distribution Network

Figure 4 .

 4 Figure 4. LSF curve of the 33-buses network

Figure 5 .

 5 Figure 5. Convergence curve of different methods with the aim of reducing the losses in the 3 PV positioning

Figure 6 .

 6 Figure 6. Convergence curve of different methods with the aim of reducing losses in the 3 WT positioning

Figure 7 .

 7 Figure 7. Network voltage profile of 33 buses before placing solar panels and under dispersion conditions

Figure 8 .

 8 Figure 8. Network voltage profile of 33 buses before placing wind turbines and under dispersion conditions

Figure 9 .Figure 10 .

 910 Figure 9. Pareto optimal answers set curve in the placement of the solar panels by various methods

Figure 11 .

 11 Figure 11. Pareto optimal answers set curve (PV + WT only with maximum capacity of 3 megawatts)

  to 97.04 kilowatt, but in

			Maximum Size 3MW (kW/pf/@Bus)
		No PV	1PV	2PV	3PV
	Power Losses (kW)	210.98	127.28	86.55	72.11
	ENS (MWh/yr)	6.695	4.158	1.923	0.628
	Minimum Voltage (pu)	0.91308	0.9285	0.9629	0.9667
					996/1@ 13,
				893/1@ 10,	938/1@ 24,
	Size and Location	--	1000/1@30	1000/1@ 30	852/1@ 30
	Total Size (kW)	--	1000	1893
	Losses Cost ($/yr)	110891	66899.8	45491.3	37903.5
	Net Saving ($/yr)	--	43991.2	65399.7	72987.5
		No WT	1WT	2WT	3WT
	Power Losses (kW)	210.98	81.43	32.17	13.68
	ENS (MWh/yr)	6.695	4.158	2.233	0.640
	Minimum Voltage (pu)	0.91308	0.9360	0.9796	0.9892
					997/0.8659 @30,
				861/ 0.8742 @10,	1000/0.8122 @13,
	Size and Location	--	1000/0.8011@30	1000/0.8091@30	789/ 0.8726@24
	Total Size (kW)	--
	Losses Cost ($/yr)	110891	42801	16913.5	7191.6
	Net Saving ($/yr)	--	68090	93977.5	103699.4

Table 2 .

 2 Optimal sizing DG's for 33-bus IEEE system (active power loss objective function-algorithms comparison)

			Maximum Size 3MW (kW/pf/@Bus)
		No PV	TLBO	GWO	HTLBOGWO
	Power Losses (kW)	210.98	74.10	73.29	72.11
	ENS (MWh/yr)	6.695	0.734	0.659	0.628
	Minimum Voltage (pu)	0.9130	0.9621	0.9648	0.9667
			872 (29), 858 (13), 946
	Size and Location	--

Table 3 .

 3 Optimal sizing DG's for 33 bus IEEE system (ENS objective function)

	Total Size (kW)	--
	Losses Cost ($/yr)	110891	38949.0	38525.7	37903.5
	Net Saving ($/yr)	--	71942	72365.3	72987.5
		No WT	TLBO	GWO	HTLBOGWO

Table 4 .

 4 Optimal sizing DG's for 33 bus IEEE system (ENS objective function-Algorithms comparison)

			Maximum Size 3MW (kW/pf/@Bus)
		No PV	TLBO	GWO	HTLBOGWO
	Power Losses (kW)	210.98	101.25	103.17	97.04
	ENS (kWh/yr)	6.695	0.048	0.044	0.035
	Minimum Voltage (pu)	0.9130	0.9694	0.9677	0.9705
			986 (9),	807 (29),	709 (30),
	Size and Location	--	789 (29),	830 (13),	810 (10),
			1000 (13)	1000 (10)	957 (13)
	Total Size (kW)	--
	Losses Cost ($/yr)	110891	53217.5	54228.8	51008.3
	Net Saving ($/yr)	--	57673.5	56662.2	59882.7
		No WT	TLBO	GWO	HTLBOGWO
	Power Losses (kW)	210.98	58.17	59.61	55.43
	ENS (kWh/yr)	6.695	0.018	0.016	0.011
	Minimum Voltage (pu)	0.9130	0.9808	0.9800	0.98248
			893	652	993
			(9) 0.8760, 762	(29) 0.9660, 978	(13) 0.8579, 802
	Size and Location	--	(30) 0.982,	(13) 0.9465, 920	(29) 0.8427, 762
			1000	(30) 0.9824	(30) 0.8209
			(13) 0.9519
	Total Size (kW)	--
	Losses Cost ($/yr)	110891	30577.0	31334.6	29136.6
	Net Saving ($/yr)	--	80314	79556.4	81754.4

Table 5 .

 5 Results of DGs distribufication (SOO-Loss minimization)

	Maximum Size 3MW (kW/pf/@Bus)

Table 6 .

 6 Results of DGs distribufication (SOO-ENS minimization)

	Maximum Size 3MW (kW/pf/@Bus)
	1DG (3000)	3DG (1000)
	(kVA/P.F)	(kVA/P.F)

Table 7 .

 7 Fuzzy multi-objective results for 1 PV placement Maximum Size 3MW (kW/pf/@Bus)

		No DG	1PV (Loss objective)	1PV (ENS objective)	1PV (Loss+ENS bjective)
	Power Losses (kW)	210.98	101.96	161.26	124.62
	ENS (kWh/yr)	6.695	4.379	1.337	1.602
	Minimum Voltage (pu)	0.9130	0.9510	0.9466	0.9486
	Size and Location	--	2585/1@29	2097/1@10	2007/1@30
	Total Size (kW)	--	2585	2097	2007
	Losses Cost ($/yr)	110891	53590.1	84761.3	65505.4
	Net Saving ($/yr)	--	57300.9	26129.7	45385.6

Table 8 .

 8 Fuzzy multi-objective results for 1 WT placement Maximum Size 3MW (kW/pf/@Bus)

		No DG	1WT (Loss objective)	1WT (ENS objective)	1WT (Loss+ENS objective)
	Power Losses (kW)	210.98	61.36	100.09	73.3816
	ENS (kWh/yr)	6.695	4.406	0	1422.4586
	Minimum Voltage (pu)	0.9130	0.9667	0.9564	0.95677

Table 9 .

 9 Fuzzy multi-objective results for 1 PV and 1 WT placement simultaneously Maximum Size 3MW (kW/pf/@Bus)

		No DG	1 PV	1 WT	1PV+1WT
	Power Losses (kW)	210.98	124.6299	73.3816	38.3211
	ENS (kWh/yr)	6.695	1.602	1.422	0.342
	Minimum Voltage (pu)	0.9130	0.9486	0.9567	0.9805
	Size and Location	--	2007/1@30	2078/0.833@30	873/1@13 1405/0.8@30
	Total Size (kW)	--	2007	2078	2278
	Losses Cost ($/yr)	110891	65505.4	38569.3	20141.5
	Net Saving ($/yr)	--	45385.6	72321.7	90749.5


domain: spi info info.info-ce

text:
Keywords: Economie d'usage, Conception de réseaux de service, Optimisation, Réseaux de logistique et transport, Entreprise en croissance Product-Service System, Service networks design, Optimization, Logistics and transport networks, Growing companies

De nos jours, les entreprises proposent de plus en plus d'offres intégrant des produits et leurs services associés plutôt que de vendre uniquement des produits. Les producteurs proposent alors des services comme la reprise, la gestion des consommables et des déchets ou encore la maintenance. Dans ce cas, ils doivent développer des réseaux logistiques pour supporter les activités associées à ces services. L'objectif de ce travail est de mener une étude de conception de réseaux logistiques dans le cadre de l'économie d'usage pour une entreprise en croissance. Pour ce faire, nous avons bâti un modèle de données permettant de représenter le cas étudié, et utilisé un programme d'optimisation afin de concevoir différents scénarios de réseaux logistiques permettant de répondre aux besoins de l'entreprise partenaire. Ce travail a permis de fournir aux entreprises une représentation du réseau logistique en fonction des activités de l'entreprise concernée, ainsi qu'une estimation des coûts globaux du système. Abstract -Nowadays, companies offer more and more not just to sell products, but rather integrated products and services bundles. Producers offer then services as take-back, waste and refill management or even maintenance. In this case, they have to develop logistic networks to support the activities related to these services. The aim of this work is to carry out a study to design logistic networks as part of the Product-Service System for a growing company. To do so, we built a data model to represent the studied case and used an optimization program in order to design a logistic network compliant to the needs of the partner company. This work allowed us to provide a representation of the logistic network according to the activities of the company, as well as an estimation of the global costs of the system.

INTRODUCTION

The aim of this work is to carry out a study, with the help of modelling and optimizing tools, to build a logistics and transport network that will support the activities of a company which has adopted the Product-Service System (PSS) business model. In addition, the network to be built is aimed at an on-growing company, so it will have to evolve according to the expansion of the company's activities. We use a two-year-old start-up company located in Grenoble metropolitan area as a case study for the problem we explored, and they provided a certain amount of data used to experiment the method developed. At the time of the study, the company has one production site in the Grenoble metropolitan area. They have products located on more or less ten towns in France and wish to expand its activities on the French metropolitan territory in a five-years-horizon.

Context and Challenges

The business model studied is based on the PSS concept. This implies that the company does not sell the product, but its functions and services. This type of business model has the potential of improving product and service management for the company and product and service quality for its customers, but also sustainability. Companies are indeed responsible for a larger part of the life cycle of the product, which implies a better resource and waste management. In our case, the product offered by the company is similar to a vending machine. It requires little care, except for maintenance and consumable refurbishment. The company offers a two-year rental agreement, during which the company is responsible for the wellness of the product, and in particular its installation and maintenance. This means that every time a failure occurs on an installed product, the company has to repair it within a certain time span. This business model is, according to the literature [START_REF] Reim | Product-Service Systems (PSS) business models and tactics -A systematic literature review[END_REF], a use-oriented PSS.

All the installation and maintenance activities are currently operated from the production site at the company. This strategy seems to be viable for a small amount of products, but it can quickly be expensive in terms of transport costs as and when the company's activities expand. The company has indeed planned to install a given number of new products every year for a time horizon of five years. To sustain this expansion, the company wants to know how to design its logistics network in order to fulfil the distribution and maintenance functions. Therefore, a method is developed to design a logistics network to be used in such a context. The network will have to support the installation and maintenance activities at each phase of the company's growth while optimizing the overall costs of the system. To do so, the main decisions to take are where to place the facilities serving the maintenance and distribution functions, and how much workforce to hire at every facility. The components of the problem must be clearly modelled in order to meet the requirements of a PSS business model. For instance, the company is required to repair every failure with a full service CIGI 2021 Logistics Network Design in a Product-Service System case AGATHE MÉTAIREAU 1 , VAN-DAT CUNG 1 level since with the PSS business model the company is responsible for the wellness of the product. This work is to help a company with such business model take strategic decisions on its logistics network when designing a PSS offer.

Methodology

In order to help the company make good quality decision, we set up the following methodology. The first step is to study the academic work published on this topic. This will allow to position our work and have an insight on how related problems are handled. This study is presented in Section 2. Then, an important step is to formalize the problem. First, the problem has to be clearly defined. Then, we can express the requirements mathematically by building a data model in Section 3 and an Integer Linear Program (ILP) in Section 4 to represent and solve the problem we address. As the core problem we want to address is locating facilities and allocate customers to these facilities, we wrote the ILP based on an Uncapacitated Facility Location which target is precisely to answer such questions. Next, the relevance of the model has been tested on the data provided by the company. The experimental results on the case study are presented in Section 5. Thus, a sensitivity analysis has been conducted evaluate the robustness of the solutions. This sensitivity analysis also give insight on which parameters can influence the results. This is presented in Section 6. Finally, we explored the possibility of outsourcing some activities in order to suggest recommendations to the company. This is detailed in the Section 7.

RELATED WORK IN THE LITERATURE

The PSS business model studied is based on the fact that the producer keeps the ownership of the product and is responsible for its proper functioning. It is very similar to the business model of vending machines, as in this case the machine is made available in a public place and its owner has to refurbish it and repair it in case of failure. It is also close to the activities implemented in the context of reverse logistics, because in this case a product which has already been sold is reinjected in the supply chain to be resold are reused. After-sales services are also close to use-oriented PSS, because it implies replacing or repairing a product returned by a customer. This is why we chose to explore the literature related to these topics, in addition to articles related to the PSS.

Product-Service System

Several aspects of the PSS have been studied in the literature, and we focused on the ones related to our problem. On the logistics network design, [START_REF] Sun | Research on "location-inventory" problem of spare parts supply chain based on product service system[END_REF] determine the configuration of a multi-level logistics network using a Location-Inventory problem modelled with a Mixed Integer Linear Program (MILP). Concerning costs estimation, [START_REF] Shen | A framework for cost evaluation in product service system configuration[END_REF] suggested a methodology to identify, classify and calculate costs inherent to a PSS business model.

Activities related to maintenance have been studied from different angles. [START_REF] Derrouiche | Approche d'analyse et de simulation des différents scenarii système produit-service (PSS) : cas d'Envie Loire. 10ème Conférence Francophone de Modélisation[END_REF]] designed a method to set up maintenance processes as part of a PSS offer. [START_REF] Kuo | Simulation of purchase or rental decision-making based on product service system[END_REF] studied the parameters influencing the feasibility of such a business model. [START_REF] Kuo | The optimisation of maintenance service levels to support the product service system[END_REF] designed a model based on Multi-Attribute Utility Theory to optimize the service level of a network with several types of maintenance. [START_REF] Rezapour | Reliable product-service supply chains for repairable products[END_REF] used a stochastic approach considering demand and production uncertainties to determine the optimal quantities of spare parts, semi-finished and finished goods to produce in order to satisfy the demand. [START_REF] Xia | Lease-Oriented Opportunistic Maintenance for Multi-Unit Leased Systems under Product-Service Paradigm[END_REF] developed a model allowing to optimize the preventive maintenance planning for leasing contracts. [START_REF] Van Ooijen | Coordinating failed goods collecting and repair capacity policies in the maintenance of commoditized capital goods[END_REF] identified the parameters of the transport between customers and repair centres in order to determine the best strategy to adopt with a transport service provider.

Vending Machines

The literature about logistics aspects of the vending machine business model is mainly focused on tactical aspects. [START_REF] Rusdiansyah | An integrated model of the periodic delivery problems for vendingmachine supply chains[END_REF] built a non-linear mixed integer program called Integrated Inventory and Periodic Vehicle Routing Problem with Time-Window to answer the problem of periodic refurbishment of the vending machines. [START_REF] Kim | The combined manpower planning and preventive maintenance strategies by aggregate planning for the service division of vending machines[END_REF] addressed the manpower question and built a non-linear program to calculate how many permanent and temporary technicians to hire in order to fulfil the tasks related to preventive and curative maintenance.

After-Sales Services

Literature on after-sales services is mainly focused on operations aspects. On another hand there are also a few studies pertaining to the information system required by such a business model. For example, [START_REF] Sagarna | After-sales maintenance service strategies optimization. An offshore wind farm case study[END_REF] studied several scenarios to determine the optimal preventive-curative maintenance strategy for a wind farm. [START_REF] Chen | Probe on networkbased collaborative maintenance model for after-sales equipment[END_REF] focused on the set up of an information system supporting aftersales maintenance.

Reverse Logistics

The literature related to reverse logistics is mainly about take-back activities. Most of the references are focused on the design of logistics networks required for such activities, and the most common approach is to use a model of Facility Location Problem type. Researchers use several declinations of this type of problem, like Uncapacitated Facility Location [START_REF] Srivastava | Network design for reverse logistics[END_REF]), Capacitated Facility Location with a deterministic [START_REF] Melo | Facility location and supply chain management -A review[END_REF] or stochastic [START_REF] Listes | Stochastic approaches for product recovery network design : a case study[END_REF] approach to optimize the positioning of the facilities.

Other approaches have also been used. [Cruz-Rivera and Ertel, 2009] used a Fixed Charge Facility Location model to place waste collecting facilities. This problem is also addressed with different strategies like discrete event modelling [START_REF] Kara | Simulation modelling of reverse logistics networks[END_REF] or continuous optimization ( [START_REF] Fleischmann | Reverse Logistics Network Structures and Design[END_REF]).

About maintenance activities, [START_REF] Amini | Designing a reverse logistics operation for short cycle time repair services[END_REF] use a What-if analysis to decide where to stock spare parts, and a Facility Location based Integer Linear Program (ILP) to place technicians dedicated to maintenance.

Conclusion and Positioning

To the best of our knowledge, articles studying maintenance and PSS either concentrate on preventive maintenance, or search to optimize the parameters of an existing system, rather to build a new system supporting maintenance activities for a PSS business model. Articles pertaining to the other topics we identified as relevant are more focused on tactical or operational problematics than on strategical ones.

The problem addressed by our study is designing a logistics network for maintenance and distribution as part of a PSS. These three aspects (i.e. maintenance, logistics network design and PSS) have all been studied, but not altogether to the author's knowledge.

Furthermore, we need to consider the growing aspect of the network for a start-up company. To the best of our knowledge, the literature about this is rather scarce and does not apply to the case we study.

Facility location problems are sometimes extended to consider other logistics problematics. We can cite Location-Inventory, where facility location questions are integrated with inventory management decisions. We can also cite Location-Routing, where the routing between facilities is jointly addressed with their location. In our case, these aspects are not taken into account, mostly because of the lack of data provided by the case study company. In fact, as the company is still relatively young, the current available data they have provide small amount of maintenance, installation and refurbishing demand.

DATA MODEL

To address the problem identified, we choose to adapt an Uncapacitated Facility Location (UFL) based Integer Linear Program (ILP) to our study. The UFL-ILP model lends well to the case study. As we stated before, the company currently operates all of the distribution and maintenance activities from its production site, in the Grenoble metropolitan area. But with the expansion of its activities, this strategy will be very expensive, mostly in terms of transport costs. As a result, the problem we address is how to locate maintenance and distribution sites on the covered territory so that the overall costs of the system will be optimized. This requires building a data model which will represent the system and be the input of the UFL-ILP set up. The aim of this section is to explain this model.

Geographical repartition

To decide where to place facilities, there is a need to know where the customers -respectively the products -will be located. The start-up company does not have this information, at least not in long term. We propose to build an expansion scenario based on their commercial strategy over the French metropolitan territory. With the business plan on five years the company provided, this time horizon has been selected as well.

The initial state for the expansion was the roster of cities in which the company had already placed products in 2019. All these cities have been classified by region, and then the roster has been completed with the most populated cities of each French region, so that it contains three cities per region (Figure 1). The repartition of cities obtained is rather consistent with the French population density in 2019 (Figure 2). To be as close as possible of this repartition, several big regional cities such as Clermont-Ferrand, Limoges, Perpignan and Chambéry have been added to the roster and obtain the final geographical scenario (Appendix 1).

Figure 1. Map of the selected cities Figure 2. French population density in 2019

To decide in which year the products will be placed in the cities for the first time (i.e. activation year; in other words, year in which there is new clients in these cities), we apply a random draw to these cities and obtain a classification of the cities per activation year (Appendix 2).

Products repartition

To design an efficient logistics network, we also have to determine how much products will be located in the cities each year. To do so, the repartition of the products is modelled based on the initial state, communicated by the company. We estimate the number of products to be placed in every city each year using two parameters, that are the occupation rate (i.e. number of products in the city on total number of commercialised products the year before) and the population rate (i.e. population of the city regarding to the total population in the activated cities of the year in question). For each city , every year , let and be respectively those parameters, which are positive if the city is activated and zero otherwise. Those parameters are weighted by the proportions for the population rate and for the occupation rate. For every year , let be the total number of products in all the cities (given by the company). So, for the city , the year , the number of products will be calculated as follows:

. Let us take a simple example to illustrate this formula. For a year , let's assume we will have 150 new products on the entire territory. Let's assume there was 50 products installed the year 1, and that the total population of the territory is 10000. Let's select a city in which there is already 10 products. This city has 1000 inhabitants. As a result, its occupation rate and population rate will be the following: 10 50 0.2, 1000 10000 0.1. Let us weight those parameters equally, in other words 0.5. Finally, the number of products to be placed in the city j at year t will be: 150 0.5 0.1 0.5 0.2 22.5. We chose to round down non-integer numbers to the nearest integer, so here: 22.

Product ageing and breakdown modelling

We choose to set up a model in which the products will have an evolutive failure rate according to their ageing. Three age categories are defined for the products: young products (from 0 to 1 year old), medium-aged products (from 1 to 2 years old) and old products (more than 2 years old). This choice of categories is also defined regarding the 2 years rental duration.

The failure rate will be shared in two types of failures: the short ones and the long ones. Each failure type has its own component cost, repair duration and proportion of the failure rate. This proportion will also evolve with the age of the product (i.e. the older the product will go, the more long or serious failures it will have). Let be the type failure rate of a product of age , and ! the proportion of failure of type for a product of type . The number of failures of type for a product of type will be as follows: " ! .

Cost structure

To define the cost estimation purpose of our work, we had to set up a cost modelling of the system. To do so, all the costs that the system could entail are cataloged and classified into categories. This allows to identify which activity would be the most expensive. Two types of costs were distinguished: structural costs, which are related to the design of the network and are calculated by the UFL-ILP, and functional costs, which are calculated from the network obtained by the solving of the UFL-ILP. Each one of these cost types are subdivided into three categories: facility cost, installation cost and maintenance cost. These costs are detailed in Table 1. Figure 3 summarizes schematically the inputs and outputs of the model.

Figure 3. Diagram of the inputs and outputs of the model 4 INTEGER LINEAR PROGRAM

To model our logistics network design problem, we choose to formulate it as an Uncapacitated Facility Location based ILP (UFL-ILP) as follows.

Problem Data

+ -Time horizon. , ⟦1, ,⟧. , ⟦2, ,⟧. / -Set of potential facilities. 0 -Set of customer cities. 1 -Set of product types.

-Set of failure types. (9)

Constraints ( 1), ( 2), ( 3) and ( 4) define the different costs (facility, installation, maintenance) of the problem while constraint (5) set the number of technicians necessary. Constraint (6) ensures that the customer cities are served only by opened facilities. The customer cities are served by one and only facility is ensured by constraint ( 7). Constraints ( 6) and ( 7) are the constraints coming from the classic UFL model. Constraint (8) allows to respect the action range, and finally constraint (9) ensures that an opened facility stays open the next year.

EXPERIMENTAL RESULTS

The problem has been modelled and solved using the data characterizing the company. The UFL-ILP have been run on CPLEX (12.6.2 Version), with an Intel Core i7-8550U CPU and 8Gbytes of usable RAM. The runs lasted less than one second for each data instance.

Data Generation

A time horizon of five years, an action range of 48 hours (quality of service), an installation time of half an hour are used. These parameters are deduced from the data provided by the partner company. The annual technician's availability of 1470 hours is used, calculated from the mean annual days of work of a technician worker. The charged wage per hour of the technicians is set to 19.45€, based on the mean wage of a technician. Three age categories have been defined for the products, and two failure types, again based on the data of the company (Tables 2 and3). For the data pertaining to the facilities, we choose to locate facilities only on the cities where products are located (cf. section 3.1), except for Luxembourg for which we could not find sufficient information. The number of client cities is 41, and the number of candidate cities for facilities is 40. For each candidate city to locate a facility, we search for an available suitable facility and use its annual rent as opening cost. If the facility is opened for the first time, the real estate agency costs are also considered in the opening cost.

For the functioning cost of the facilities, the annual electricity consumption cost are calculated and added to the annual charges paid to the real estate agency.

Centralized Solution

The first step is to solve the problem using the strategy currently in process at the company. It consists in operating all the activities from the production site (centralized solution). In this part, there is only one possible facility, and the UFL-ILP will not decide where to locate the facilities. It will just calculate the costs and the number of technicians to hire.

Figure 4 shows a representation of the results per cost category and per year.

Figure 4. Centralized solution's cost repartition

In this solution, there is no structural facility cost, because no facility is opened, so there is no rent fee. We observe that the most expensive costs are the structural installation cost and the structural maintenance cost, which represent the transport costs of the system.

Decentralized solution

In this part, the program is run with the possibility of opening several facilities, to answer the problem first defined (i.e. design the logistics network).

Figure 5 shows a representation of the results per cost category and per year. Maps showing the network obtained each year are available in Appendix 3. After we ran the program for the two solutions and calculated all the costs, the results have been compared to identify which solution would be the most interesting for the company. Figure 6 shows the cost comparisons for each activity and for the total costs over 5 years of the business plan.

The centralized solution is more interesting in terms of facility cost. Indeed, only the Grenoble site is opened every year, but its opening cost is set to zero because the site already exists. Regarding this, the facility cost is reduced in the centralized solution. But this facility cost savings is low compared to the savings made on installation and maintenance costs in the decentralized solution. As the facilities are closer to the customers thanks to the decentralized logistics network, the transport costs are indeed much lower than in the centralized solution. Finally, the total costs (bottom right chart) of the decentralized system are lower (and even three times lower in 2023) when compared to those of the centralized one.

SENSITIVITY ANALYSIS

A sensitivity analysis has been conducted to identify which parameters could influence the results. We have chosen to vary four parameters: the action range, the products repartition in the cities, the failure rate, and the failure types proportion regarding the failure rate.

Parameters

The action range was initially 48 hours, which is a specification of the company's rental contracts. We choose to run the program with an action range of 24 hours, 20 hours and 10 hours.

The product repartition depends on two parameters, the population rate and the occupation rate. These parameters are respectively weighted by the values and . These values are initially set to 0.1 and 1 -1 0.9. The program is run using 0.2 to 0.9 incremented of 0.1 each time and with the corresponding values for .

Results

The results of the sensitivity analysis are detailed in Table 6. A '0' means that none of the variations influences the result. A '+' and a '++' mean that respectively one and two variations influence the result. A '+++' means that at least three variations influence the result. Looking at the results, it is to note that the most influencing parameters are the products repartition and the failure rate. Each variation of these parameters has indeed a significant impact on most of the cost types.

About the action range, this parameter impacts the result only when it is set to 10 hours (otherworldly divided by nearly 5 from 48h). Thus, we can conclude that the solution is not very sensitive to this parameter, except if this constraint becomes very strong, that is to say in the hypothesis of a high quality service. Finally, the failure types proportions impact only the functional maintenance cost. This can be explained by the fact that these parameters do not appear in the UFL-ILP, and hence have no influence on the structural costs.

OUTSOURCING AND RECOMMENDATIONS

For the start-up company, different configurations (centralized vs. decentralized, with outsourcing or not) of the logistics network are designed. We try to find which one is the most interesting for the company in terms of costs. The first step is the identification of the network configuration, the different service activities and the outsourcing options available for each one.

Logistics Network Structure

As stated before, the logistics network can be centralized or decentralized. To compare both options, we totalize of the structural and functional facility costs.

Installation Service

This concerns the installation of the products at the clients' premises. This includes the transport of the product from the company to the installation site, and the installation intervention. This can be outsourced or not. To compare both situations, an offer made by a logistics service provider is used. We classify the costs of the provider's offer into categories and calculate the invoice for the company. Then, we calculate what it would cost to the company if it were internalized, using the same cost classification.

Maintenance Service

This is about the products maintenance at the clients' premises (i.e. failure repair). This includes the intervention cost, the component cost, and the technician's transport cost. This activity is necessarily internalized because it is a core component of the company's service and product offer.

Transport of Products

The transport of products is subdivided in two components.

-The upstream transport includes the way from the company to the facility inventory. This subcomponent is considered only when we choose a decentralized network.

-The downstream transport includes the way from the facility inventory to the customer. In case of a centralized network, this is the way from the production site to the customer's premises.

If the installation service is outsourced, the service provider manages this part, and so we do not have to make a decision on this. Otherwise, we can choose to outsource it or not. To estimate the cost invoiced by a transport provider, the transport costs we calculated for the UFL-ILP are used, and are increased by 15% to consider the functioning fees and the margin of the carrier.

Recommendations

Six different scenarios are built using all the possibilities we enumerated and calculated the overall costs of each one. Based on this comparison, the least expensive configuration was the one with a decentralized network, internalized installation service and outsourced transport. In this configuration, the company is in charge of the facility, installation and maintenance activities. The service provider will manage the upstream and downstream transports. The cost of this configuration is close to the one of the configurations in which we have a decentralized network, with outsourced installation.

As the outsourced transport costs are an estimation, the study could be more precise if we considered a real carrier's offer, so that the choice between those two scenarios could be more reliable.

CONCLUSION

The aim of our work was to design a logistics network dedicated to a growing company which uses a PSS business model.

To reach this goal, a complete methodology have been built based on a data model representing the system, the product life cycle and the expansion strategy of the company over its 5 years business plan. This data model has been used as an input for our adaption of an Uncapacitated Facility Location based ILP which allowed to design optimized logistics networks and estimate the overall system costs.

We completed the study by a report on the different strategies that the company could adopt. The comparison of these strategies leads to recommendations for the company regarding outsourcing possibilities.

The goals of this study have been globally answered, but the work we carried out can be extended.

First, we built a linear life cycle model for the products. As the product of the company are still young, there is a lack of data about the way they will work with the time. A more complete life cycle analysis on the products could help to understand better how they evolve, and then offer a more precise model in terms of maintenance activities.

Then, with the upcoming expansion of the company, more data will be available. This can allow to consider other aspects of the problem which are currently overlooked, such as vehicle routing for simultaneous installations or maintenances at the clients' premises or spare parts and consumable refurbishment management at the facilities. We could use more sophisticated models as Location-Inventory-Routing Problems to address these aspects altogether.

Furthermore, as stated before, the outsourced transport costs are estimated, this can be further refined with real offers to better specify our recommendations.

&23-

  Installation time. ℛ -Action range (i.e. maximal duration between a failure and its repair). 5 -Annual availability of a technician in hours. ∀ ' ∈ /, #$ & -Opening cost of the facility ', (* & -Agency fee of the facility '. ∀ ' ∈ /, ∀ ∈ 0, # & -Transport cost from ' to , 5 & -Transport duration from ' to . 58 -Mean time to do a direct round trip from a facility to a customer (this is the sum of all transport durations on the number of possible trips). ∀ ∈ ,, ∀ ∈ 0, -Number of products in the city the year . ∀ ∈ ,, ∀ ∈ 0, ∀ ∈ 1, -Number of products of type in the city the year , especially, ∀ ∈ ,, ∀ ∈ 0, ∀ ∈ 1, 9 -Number of new products in the city the year . ∀ ∈ , ' -Repair time for a failure of type . ∀ ∈ , ∀ ∈ 1, " -Number of failures of type for a product of type . 4.2 Decision Variables ∀ ∈ ,, ∀ ' ∈ /, %#ℎ & -Number of technicians to be hired the year at the facility 'ℎ% (*#'=' ; ' )%JM%) ℎ% #8) $ %J ℎ% ;%*J , 0 $ ℎ%JK')%. , ∀ ' ∈ /, ; & ≥ ; & .

Figure 5 .

 5 Figure 5. Decentralized solution's cost repartition In this solution, the most expensive costs are the functional maintenance cost and the structural facility cost.

Figure 6 .

 6 Figure 6. Comparison of the two solutions

Table 1

 1

			. Costs details
	Cost	Notation	Detail
	Structural facility cost Structural	#$% & for each facility '	Opening cost of a facility (one-year rent and agency fee on the first year), calculated by the UFL-ILP Transport costs related to
	installation cost	# '	installation (one direct round trip per new product installed), calculated by the UFL-ILP
	Structural		Transport costs related to
	maintenance cost	#	maintenance (one direct round trip per failure), calculated by the UFL-ILP
	Functional facility cost Functional installation cost Functional	each #(' & for facility ' #' )	Depreciation costs of the technician's trucks, rental expenses, electricity fees Technician's wage during the installation Component cost, technician's
	maintenance cost	# *'	wage during the maintenance

Table 2 . Failures' Characteristics

 2

	Failure type	Short	Long
	Repair time	1h	2h
	Component cost	32€	120€

Table 3 . Products' Characteristics

 3

	Age category	Young	Medium Old
	Failure rate	0.33	0.38	0.45
	Long failure proportion	0.8	0.75	0.7
	Short failure proportion	0.2	0.25	0.3

  Table 4 details the values used for the failure rate depending on the products age category.

Table 4 . Variations of the failure rate

 4 Table 5 details the values of ! used in the sensitivity analysis depending on the products' age category.

	Age category	Young	Medium Old
	Variation 1	0.25	0.30	0.37
	Variation 2	0.30	0.35	0.42
	Variation 3	0.35	0.40	0.47
	Variation 4	0.40	0.45	0.52
	The failure types proportions, ! and ! , are related by the formula ! ! 1.

Table 5 . Variations of the failure types' proportions

 5

	Age category	Young	Medium Old
	Variation 1	0.60	0.55	0.50
	Variation 2	0.70	0.65	0.60
	Variation 3	0.80	0.75	0.70
	Variation 4	0.90	0.85	0.80

Table 5 . Variations of the failure types proportions

 5

			Structural costs			Functional costs
		Facilities	Installation Maintenance	Facilities	Installation Maintenance
	Action range	+	+	+	+	0	+
	Products repartition	+++	+++	+++	+++	++	++
	Failure rate	+++	+++	+++	+++	0	+++
	Failure types proportions	0	0	0	0	0	+++

Univ. Grenoble Alpes, CNRS, Grenoble INP*, G-SCOP * Institute of Engineering Univ. Grenoble Alpes 38000, Grenoble, France agathe.metaireau@grenoble-inp.org, van-dat.cung@grenoble-inp.fr