1. INTRODUCTION
There is an everincreasing complexity in today's business environment (Handfield and Nichols, 2009), which is caused by various factors, including market expansion, a wide range of suppliers, increasing competition and customer demand, and ultimately the performance of a company, especially waiting time, cost and product quality. However, a supply chain optimization model should be designed if the supplier to the market domain is considered among these factors. In general, a supply chain is a complicated network of suppliers to customers and involves people, technologies, activities, resources, and information. The main goal of the design and management of such a model is to attain the best global performance under the criteria of union performance (Aslam and Amos, 2010). A common supply chain comprises suppliers, factories, warehouses, distribution centers, customers, and markets (Mastrocinque et al., 2013). As such, supply chain optimization plays a key role in the competitiveness of the entire chain, in a way that research on the supply chain has increased in the past two decades. Nevertheless, most studies on this topic have a simple structure (e.g., singlelevel, monoproduct, oneclass). Meanwhile, this matter needs to be assessed from a broader perspective in structure, such as the dynamism of the demand system in the market, which makes the problem more similar to the real world. Deciding about facility location problem (FLP) and the physical structure of the network, especially in the field of the retail market, are some of the factors effective supply chain competitiveness. It is worth noting that some of the articles performed in this area have overlooked the impact of customer demand on supply chain competitiveness. Nevertheless, competitive facility location only models the distribution section in the supply chain. Even if they had the specific features of the chain, they would have analyzed the competitive market supply chain (Bilir et al., 2017;Dziatkovskii and Hryneuski 2021;Roozitalab and Majidi, 2018).
The present study considers a more novel model, compared to previous studies, which makes the supply chain more competitive, and the innovation of pricedependent demand changes modifies the design of the network’s physical structure. The main objective is integration in the design of a competitive supply chain, where pricedependent demand changes are taken into account. Demand is considered to be fixed and as the product price in supply chain research. The current research primarily aims to add an elasticity function to the demand parameter, which will affect supply chain strategic decisions. In this study, the demand considered is in the form of price elasticity and profit function. We consider scenarios to deal with pricedependent demand changes, and a robust optimization approach is employed to handle uncertainty. To this end, we evaluate supply chain strategic decisionmaking under demand and pricechanging conditions. In addition, risk factors are also taken into account due to their overlooking in most previous studies.
2. THEORETICAL FOUNDATION AND RESEARCH LITERATURE
In a research, Kung and Liao (2018) constructed a discrete location model for profit maximization with endogenous consumer demands and network effects. When the function was linear, they designed a polynomialtime algorithm to find an optimal solution. When it was nonlinear, they showed that the problem was NPhard, developing an approximation algorithm based on demand function approximation, linear relaxation, decomposition, and sorting. Numerical studies are conducted to demonstrate the average performance and general applicability of their algorithms. In another study, Nasiri et al. (2018) introduced the capacitated competitive FLP. In order to consider a more realistic environment, they presented a problem that enables the follower to partially (due to the capacity limitation of the facilities) satisfy the demand of a customer that is supposed to be met by the leader. These scholars developed two algorithms (GA and PSO), which solve an IP (MIP) model for evaluation of the fitness function. Moreover, Afify et al. (2019) provided an analysis on the effects on facility location by prioritizing customer demands and adopting geographic distance calculation, which allows fast generation of costeffective and complete solutions using reasonable computing power. Furthermore, the underlying technique is customizable offering a tradeoff between solution quality and computation time. Beresnev and Melnikov (2019) investigated a bilevel optimization program that modeled a two parties’ competition in the form of a Stackelberg game. They implemented a branchandbound algorithm where the introduced constraints improved the upper bound’s quality. In the experimental part of the paper, they tuned the parameters of the algorithms and investigate their performance on artificially generated input data. Dan and Marcotte (2019) considered the problem faced by a service firm that makes decisions with respect to both the location and service levels of its facilities, taking into account that users patronize the facility that maximizes their individual utility, expressed as the sum of travel time, queueing delay, and a random term. The situation could be modeled as a bilevel program that involves discrete and continuous variables as well as linear and nonlinear (convex and nonconvex) functions. In the end, these scholars designed an algorithm based on piecewise linear approximation as well as a metaheuristic that exploits the very important structure of the problem.
3. RESEARCH METHODOLOGY
The risk model considered between routes presented by GhomiAvili et al. (2021) is used to take the supply chain risk factor into account. In route modeling, there is a possibility of route failure in the input and output flows of the distribution center.
In this formula, the first parameter is μ, which shows the possibility of correct transportation of products from the supplier. This parameter is equal to 0.5% in the designed parameter. The second parameter is δ, which demonstrates the relocation of products in distribution centers without damage. The mentioned parameter is considered to be 1% in the present study. Finally, the third parameter is ϕ, which shows the possibility of transporting products from the distribution warehouse to customers without damage (equal to 2% in the present study). In general, damage occurs when one of the nodes of the network stops working. Since a part of sales is lost due to improper performance of the supply chain caused by damage to products, the shortage parameter will be considered in the model. Notably, the cost of shortage is calculated based on the difference in the number of net sales and the product unit cost. Damage costs will be calculated as the probability of selling products at the time of possible damage at the cost of shortage.
The presented model includes three objective functions, and the first and second of which are maximizing profit and maximizing the level of services and accountability, respectively, and are not computed. In addition, the third objective function is the risk problem.
4. DATA ANALYSIS
4.1 Multiobjective Problemsolving Method
The general form of a multiobjective decisionmaking (MODM) problem is shown below.
Assume that the first objective is considered as the main objective, and other objectives are constrained to the upper bound of Epsilon and applied in the conditions of the problem. In this case, the EC method is used and the singleobjective model (24) is obtained.
where the first objective is considered as the main objective, and the second to the nth objectives are bound by the maximum amount of e_{i} . Different solutions are obtained in the model (24) by changing the values of e_{i} , which might not be efficient or have poor efficiency. The mentioned problem can be solved by partial correction and completion of the model (24), which is known as the AEC method (Mavrotas, 2009). In the AEC method proposed in the present study, we first determine the ${e}_{i}\in [Min(f),Max({f}_{i})]$ range based on Lex technique for mentioned objectives. The singleobjective model (24) is solved after valuing e_{i}s, the solution of which is an efficient one, and the values of objectives are placed in Pare to Front per this solution. Note that a change in eis in the related range leads to another efficient solution and another point on Pareto Front.
The application of the AEC method to solve the proposed biobjective model is explained below.
The AEC process includes important steps, such as:

1. Determining the outcome matrix

2. Estimation of the minimum, maximum and scope of changes of objectives (i=1, 2)

3. Epsilon initialization for the second objective Epsilon=Min( f_{2})

4. Partitioning the amplitude of Epsilon changes by N

5. Determining the size of the step for Epsilon change $StepSize=\frac{R({f}_{2})}{N1}$

6. Defining the conditions of the AEC method for the second objective ${f}_{2}+slac{k}_{2}=Epsilon$
where slack_{2} is the negative auxiliary variable corresponding to the second objective

8. Defining the objective function of the AEC method

9. Defining a loop to solve the Norder optimization problem with the eightstep function while taking the sixstep condition into account along with other conditions per N different Epsilon values
4.2 Implementation of the EpsilonConstraint Method
To implement the problem, the mathematical model is considered for a clothing manufacturing company in Tehran, which has about 150 retailers in Iran and three large agencies, and 500 sale points across the country. The company is currently just a distributor or middle warehouse in Tehran, which covers the entire sales. However, the company has aimed to establish middle warehouses in Mazandaran and Isfahan with increasing sales and lack of company capacity. The model is solved in GAMS and CPLEX, and the process took 66.96 seconds. After solving the model, the method of allocating each strategy to each risk is determined, the results of which are reported in the following tables. In general, 10 points are created on the Pareto Front after solving the model, where the values related to the objective functions (cost, time, and quality) are determined for each point.
According to the results, the higher the accountability rate, the higher the profit and the lower the risk, which indicates the accuracy of the model.
4.3 Multiobjective Genetic Algorithm Solution
The NSGAII algorithm is one of the most widely used and robust algorithms available for solving multiobjective optimization problems with proven efficiency in solving various problems. The main features of this algorithm include:
Defining densitybased distance as an alternative feature to practices such as fit sharing
Using the binary tournament selection operator
Saving and archiving the nondominant solutions obtained in the previous steps of the algorithm.
In the NSGAII algorithm, a number of solutions are selected in each generation using the binary tournament selection method, where two solutions are randomly selected from a population and compared and the more efficient solution is ultimately selected. The selection criteria in the NSGAII algorithm are solution rank in the first order and densitybased distance in the second order. The lower the rank and the higher the densitybased distance, the more favorable the solution. A series of members of a generation are selected for participation in crossover 1 and mutation 2 by repeating the binary selection operator on the population of each generation. The crossover operator is used on a part of selected individuals, and the mutation operator is applied to the other people, which leads to the formation of a population of offspring and mutants. Following that, the population will be integrated with the main population. The members of the newly formed population are arranged first based on rank and then in ascending order. Members of the population with the same rank are sorted based on densitybased distance and in descending order. Now, the members of the population, who are sorted based on rank and then the densitybased distance are equal to the number of people in the main population. Afterwards, some members are selected from the top of the sorted list, and the rest of the population is discarded. The selected members make up the next generation population, and the cycle mentioned in this section is repeated until the termination conditions are met.
4.4 NSGAII Algorithm Implementation
In order to validate the problem data in this research, we design 10 datasets with different dimensions to show that the model is able to solve all the data in a correct process, which is introduced in the following dimensions of the 10 sample problems.
According to the results, GAMS software and the genetic algorithm have converged in example number “one”, which means that the performance of the algorithm is correct in other dimensions and has reported a nearoptimal solution.
4.5 Algorithm Sensitivity Analysis
To analyze the sensitivity of the algorithm, we evaluate the online criteria of the algorithm, such as the convergence rate of the algorithm with respect to the iterations of the problem and the time to reach the final solution. This problem has reached convergence in the very first iterations and shows that the algorithm has reached the optimal convergent solution very quickly, which indicates the efficiency of the algorithm.
4.6 Robust Optimizer Implementation
The robust optimization approach is one of the strongest methods to solve problems under uncertainty (Aghaei et al., 2011). Since the problem is solved definitively in the first case, but the amount of customer demand is not always known in advance and has fluctuations in the real situation, therefore scenarios should be defined against the uncertainty of the problem. In the present study, we consider nine scenarios for the amount of demand, and the probability value of each scenario is determined according to the demand level. In some places, one parameter is fixed and another is changed and vice versa. Accordingly, we consider nine different scenarios. As observed, the demand is considered in the definite state of 4000, which is considered as 3600 and 4400 tolerances with 10% uncertainty.
According to the results, since robust optimization is a pessimistic solution, it is a low bound for the problem in the first objective function and has the same function in the second objective function. On the other hand, it is a high bound in the third objective. Therefore, the lowest level of profit and service and the highest risk are calculated by the robust optimization approach. However, the problem is analyzed to evaluate changes in the amount of profit using a middle warehouse, two middle houses, and three middle houses. In the end, the highest profit value is obtained when using three middle warehouses. As observed in the present study, the problem is solved using the Epsilonconstraint method, where profit and yield are maximized and risk is minimized. According to the results, the risk is minimized at a high return rate and when the most deliveries are made to the customer. In addition, the highest profit is obtained at the level of return of 0.92, which indicates 0.92% of accountability toward customer demand.
5. CONCLUSION
The present study aimed to evaluate the effect of network strategic decisions, such as the number, location, and capacity of supply chain nodes on sales volume and profit and chain. In addition, the model proved that oneobjective mathematical models are not able to provide presentable solutions in the supply chain because the results change with different purposes, which is due to the multiobjective nature of the supply chain. In addition, the model proved that the designed supply chain changes with changes in the price and the number of warehouses. Nonetheless, changes in demand and input and output flows had little effect on the network. Moreover, control of damage risk will increase sales and overall profit and decrease sales lost. To develop the model in future research, it is suggested that factors such as customer service level and customer distance from demand points, which can affect the level of strategic decisionmaking of the chain, be considered. In addition, it is recommended to consider the model in a multiperiodic form instead of a oneclass form. In the current study, the model is assessed statistically but changes in the price and number of warehouses can also be evaluated in the form of different periods. In addition, while a linear mathematical model is designed in the present study, the problem can be assessed in a nonlinear way by considering other objectives.