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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.20 No.4 pp.686-694
DOI : https://doi.org/10.7232/iems.2021.20.4.686

# A Multi-Objective Constrained Optimization Model for Designing a Green Closed Loop Supply Chain Network in Tax System

Sergushina Elena Sergeevna, Kabanov Oleg Vladimirovich*, Grigoryev Andrey Anatolievich, Ruslan V. Lesovik, Natalya P. Khyzhak, Shereuzheva Madina Albertovna, Ushakov Ruslan Mikhailovich, Kamchatova Ekaterina Yurevna, Antonova Irina Sergeevna, Karageziyan Marina Valentinovna, Yatsunova Tatiana Ivanovna, Rustamova Irada Talyatovna, Zhadan Vladimir Nikolaevich
Republic of Mordovia, Saransk, National Research Ogarev Mordovia State University, Russia
Higher School of Physics and Materials Technology, Institute of Mechanical Engineering, Materials and Transport, Peter the Great Saint Petersburg Polytechnic University, Russia
Belgorod State Technological University named after V.G. Shukhov, Russia
Humanitarian and Pedagogical Academy (branch) of Vernadsky Crimean Federal University, Russian Federation, Republic of the Crimea
Russian State Agrarian University, Moscow, Moscow, Russia
Saratov State Academy of Law, Volskaya, Saratov, Russia
State University of Management, Moscow, Russian Federation
I.M. Sechenov First Moscow State Medical University (Sechenov University), Moscow, Russia
Russian University of Transport, Russian New University Moscow, Russia
Department of Criminal Procedure and Judicial Activities, Kazan Federal University, Russia, Republic of Tatarstan, Yelabuga, Republic of Tatarstan, Russia
September 1, 2021 September 12, 2021 September 27, 2021

## ABSTRACT

The multi-objective constrained model proposed for closed green supply chain in the enterprise development. Small and medium businesses make a significant contribution to the economic life of any country and to the maintenance of employment and economic growth. This paper focuses on the pricing problem of a two-stage closed-loop supply chain (CLSC) considering the cross-channel recycling and channel preference based on a single manufacturer and a single traditional retailer in the digital environment. The article analyzes the indicators of taxation of small and mediumsized businesses in the Republic of Mordovia and draws conclusions about the advantages of using a digitalization system for small and medium-sized businesses. Manufacturer’s pricing decreases when channel preferences are constant and cross-channel recovery rates increase. Retailer’s pricing remains stable as the cross-channel recovery rate has less affected on it. This information will be a helpful guideline for the manager to select suitable pricing strategies based on the company scenario.

## 1. INTRODUCTION

One of the most important determinants of the success of rescue and relief operations during a crisis is the level of preparedness of crisis management facilities before the incident (Boronoos et al., 2021;Mohammed et al., 2019). In other words, these facilities must be established and prepared in advance to handle the crises with proper rapid response to problems (Tosarkani and Amin, 2020;Golubev et al., 2021). Many developed countries including Japan, the United States, and South Korea have managed to achieve a high level of disaster preparedness through the use of strategic management and decision support tools. These countries can manage natural disasters with minimal loss of life and property and take action to repair the damages (Rad and Nahavandi, 2018;Sergushina et al., 2018a). One way to improve the response speed and performance of rescue and relief operations is to carefully plan the location of relief facilities. This facility location problem involves placing different relief facilities with different service levels so that they can cover different levels of demand in the affected areas (Akin Bas and Ahlatcioglu Ozkok, 2020). The placement of relief facilities on the transportation network is extremely important for how well they can respond to the demand that will emerge during a crisis. Indeed, proper location of these facilities can significantly reduce the human casualties of a disaster. It should be noted that it takes a large budget to construct these facilities and they cannot be easily moved to another place if it turns out that they are not suitably located (Rajak et al., 2021;Sergushina and Frolova, 2017). Therefore, it is important to do more investigation before starting the process of green supply chain as a strategic level managerial decision (Rajak et al., 2021;Vladimirovich et al., 2019;Sergushina et al., 2018b). Given the importance of this subject, this study tries to find the optimal solution for the supply chain management strategy in the business regarding the environmental issues.

With the advent of covid-19 restrictions, people began shopping online for groceries and groceries. Statistics show that before the start of the corona, 11% of purchases were made online, while with the corona, this amount has increased to 47% (Loni et al., 2018). This is a great opportunity for online businesses that can improve the environmental conditions in addition to high profits by launching a digital sales and supply chain management platform. This online shopping has gradually become a shopping habit of customers due to convenience, cost reduction and pollution as the three main factors of shopping.

Since the green supply chain management related to the multiobjective optimization by considering time, efficiency and cost (Papen and Amin, 2019;Fadeeva et al., 2018;Dong and Wu, 2020), the medium and large-scale numerical examples of this problem need to be solved with meta-heuristic algorithms. One of the most important issues in using meta-heuristic methods is the proper selection of the algorithm according to the nature and structure of the problem. Considering the good performance of population-based swarm intelligence metaheuristic algorithms, they are a perfect choice for solving the modeled problem. Among these algorithms, the gray wolf optimizer, antlion optimizer, and dragonfly algorithm have shown excellent performance and found to be more or less superior over other algorithms in solving almost all problems. The multi-objective versions of these algorithms are also highly efficient and can swiftly shift from exploitation to exploration to produce high-quality solutions. In this study, the Multi-Objective constrained optimization is used to solve the problem. Given the generally good performance of genetic algorithms in solving all optimization problems, they can serve as good benchmarks for performance evaluation. The second version of the nondominated sorting genetic algorithm (NSGAII) is the most prominent multi-objective algorithm of this family in all areas of optimization. Therefore, in this study, the results of the proposed algorithms are compared with those of NSGAII.

## 2. METHOD

This section describe the mathematical model of closed supply chain for the optimization. The production centers are connected to directly consumer market. In addition returned goods sent to the collecting and checking centers, which should evaluate the status of the returned products, re-send them to production center and regulate the rules for returning them.

### 2.1 The Proposed Mathematical Model

The total cost of supply network design includes fixed costs of construction and variable costs of process and transportation between networks; therefore, the objective function is expressed as Equations 1-3, and Equations 4-17 represent the constraints.

Indexes:

• (∀iI ) , where I indicates collection / primary centers

• (∀jJ) , where J indicates potential locations of disassembling and dismantling plants

• (∀kK) , where K indicates potential locations of processing plants

• (∀lL) , where L indicates recovery centers

• (∀mM) , where M indicates centers of conversion to waste

• (∀nN) , where N indicates locations of intermediate market

• (∀t T) , where T indicates periods

• (∀pP) , where P indicates spare parts of vehicles

Parameter

• $( c ˜ j )$ : Fuzzy cost of establishing the disassembling and dismantling plant J

• $( c ˜ k )$ : Fuzzy cost of establishing the processing plant K

• $( c a p ˜ j )$ : the Fuzzy capacity of disassembling and dismantling plant J

• $( c a p ˜ k )$ : Fuzzy capacity of processing plant K

• $( c a p ˜ l )$ : Fuzzy capacity of the recovery center l

• $( c a p ˜ m )$ : Fuzzy capacity of conversion to waste center m

• (ctij) : transportation cost of each unit from collection / primary center to disassembling and dismantling plant J

• (ctjk) : transportation cost of each unit from disassembling and dismantling plant J to processing plant K

• (ctjn) : transportation cost of each unit from disassembling and dismantling plant J to the location of intermediate market n

• (ctkl) : transportation cost of each unit from processing plant K to the recovery center l

• (ctkm) : transportation cost of each unit from processing plant K to the center of conversion to waste m

• (ctjm) : transportation cost of each unit from disassembling and dismantling plant J to the center of conversion to waste m

• (cd) : the cost of turning into waste for each unit

• (cv) : the cost of incentives to return each vehicle to collection centers

• (ocjt) : the cost of operating each unit for disassembling and dismantling plant J in the period t

• (ockt) : the cost of operating each unit for processing plant K in the period t

• (rp) : the profit of each unit from reusable spare parts

• (rr) : the profit of each unit from recovered products

• (eit) : the number of vehicles admitted by the collection/ primary centers in the period t

• (k1) : the amount of material transported from disassembling and dismantling plant to the center of conversion to waste

• (k2) : the amount of material transported from processing plant to the center of conversion to waste

• (aw1) : the average weight of the vehicle

• (aw2) : the average weight of the disassembled vehicle

• (qp) : the number of spare parts in each vehicle

• (vp) : the number of reusable spare parts in each vehicle

• (EIj) : Environmental effects of performed operations for each EOL vehicle in disassembling and dismantling plant J

• (EIk) : Environmental effects of performed operations for each EOL vehicle in processing plant k

• (EIT) : Environmental effects of transporting EOL car units per kilometer

• (dij) : the distance between collection/primary center i and disassembling and dismantling plant J

• (djk) : the distance between disassembling and dismantling plant J and processing plant k

• (djn) : the distance between disassembling and dismantling plant J and the location of intermediate market n

• (dkl) : the distance between processing plant k and recovery center l

• (djm) : the distance between disassembling and dismantling plant J and the center of conversion to waste m

• (dkm) : the distance between processing plant k and the center of conversion to waste m

• (Wem) : the normalized weight of employment

• (Wid) : the normalized weight of local development

• (Wdm) : the normalized weight of high-risk work situation

• (Wpr) : the normalized weight of product risk

• (EMj) : the score for the employment of disassembling and dismantling plant J

• (Ldj) : the score for local development of disassembling and dismantling plant J

• (DMj) : the score for worker's damage in the disassembling and dismantling plant J

• (PRj) : the product risk of disassembling and dismantling plant J

• (EMk) : the score for the employment of processing plant k

• (ldk) : the score for local development of processing plant k

• (DMk) : the score for worker's damage in the processing plant k

• (PRk) : the product risk of processing plant k

F has been considered as the set of sub-sets j for all sections.

• (0∈ F,SD(o)) determines the maximum number of disassembling and dismantling plant J for sub-set o

### 2.2 Decision-Making Variables

• (xijt) : the number of vehicles transported from collection / primary center I to the disassembling and dismantling plant J during period t

• (Yjkt) : the number of vehicles transported from disassembling and dismantling plant J to the processing plant k during period t

• (Zjnpt) : the number of spare parts p transported from disassembling and dismantling plant J to the location of intermediate market n during period t

• (wklt) : the amount of materials transported from processing plant k to the recovery center l during period t

• (ujmt) : the amount of materials transported from disassembling and dismantling plant J to the center of conversion to waste m during period t

• (ukmt) : the amount of materials transported from processing plant k to the center of conversion to waste m during period t

(1)

$M i n z 2 = ∑ j ∑ k ∑ t Y j k t E I k + ∑ i ∑ j ∑ t X i j t E I j + E I C T [ ∑ i ∑ j ∑ t X i j t d i j + ∑ j ∑ k ∑ t Y j k t d j k + ∑ j ∑ n ∑ t Z j n p t d j n + ∑ k ∑ l ∑ t W k l t d k l + ∑ j ∑ m ∑ t U j m t d j m + ∑ k ∑ m ∑ t U k m t d k m ]$
(2)

(3)

(4)

(5)

$∑ i = 1 I x i j t ≤ c a p ˜ j a j ∀ j , t$
(6)

$∑ j ∈ O a j ≤ S D ( O ) − ∀ O ∈ F$
(7)

$∑ j = 1 J y j k t ≤ c a p ˜ k b k ∀ k , t$
(8)

$∑ k = 1 K w k l t ≤ c a p ˜ l ∀ l , t$
(9)

$∑ j = 1 J u j m t + ∑ k = 1 K u k m t ≤ c a p ˜ m ∀ m , t$
(10)

$∑ i = 1 I x i j t = ∑ k = 1 K y j k t ∀ j , t$
(11)

$∑ i = 1 I x i j t a w 1 k 1 = ∑ m = 1 M u j m t ∀ j , t$
(12)

$∑ i = 1 I x i j t q p υ p = ∑ n = 1 N z j n p t ∀ j , p , t$
(13)

$∑ j = 1 J y j k t a w 2 ( 1 − k 2 ) = ∑ l = 1 L w k l t ∀ k , t$
(14)

$∑ j = 1 J y j k t a w 2 k 2 = ∑ m = 1 M u k m t ∀ k , t$
(15)

$x i j t , y j k t , z j n p t , w k l t , u j m t , u k m t ≥ 0 ∀ i , j , k , m , l , n , t$
(16)

$a j , b k , α i j ∈ { 0 , 1 } ∀ j , k$
(17)

The objective function (1) indicates the final profit of the network. The objective function (2) indicates the environmental effects of network and objective function (3) indicate social benefit. Constraint (4) requires that all vehicles admitted by the collection / primary centers must be processed during the period of admission. Constraint (5) ensures the uniqueness of the flow from a collection/ primary center to a disassembling and dismantling plant. Constraint (6) ensures that the final number of vehicles transported to disassembling and dismantling plant does not exceed their capacity at any time. Constraint (7) limits the number of disassembling and dismantling plants that have been established in each section. Constraint (8) ensures that the final number of vehicles transported to plants does not exceed the capacity of their capacity at any time. Constraints (9) and (10) ensure that the final amount of material transported to recycling centers does not exceed their capacity at any time. Constraints (9) and (10) ensure the compatibility of the amount of disassembled vehicles implemented and materials transported to processing plants and the centers of conversion to waste capacity at any time, respectively. Constraint (13) ensures the compatibility of the number of spare parts transported to the intermediate market at any time. Constraint (14) ensures the amount of material transported from processing plants to recovery centers at any time. Constraint (15) ensures the compatibility of the amount of material transported from processing plants to centers of conversion to waste during period t. Constraint (16) ensures that the value of decision variables $X i j t , Y j k t , Z j n p t , u k m t , u j m t and W k l t$ is higher than zero and Constraint (17) determines that the value of decision variables aj, bk and αijt is zero or one.

## 3. RESULTS

In this research, the problem of multi-objective optimization with evolutionary algorithms in MATLAB environment has been solved. All calculations are performed on a 32-bit computer with a 1.67 GHz microprocessor and 2 GHz internal memory. Therefore, it was decided to use a response variable comprised of 5 criteria and with the formula given in equations 1-3 for the objectives the comparing multi-objective algorithms. Are presented in Table 1.

There are different pricing strategies under different decision-making models in the supply chain. Both higher and lower cross-channel recovery rates and channel preference influence the pricing strategies choices. These measures will create favorable conditions for the formation of small and medium-sized businesses, contribute to the acquisition of confidence in the future of a novice entrepreneur, and also reduce risks to existing enterprises. In the new economic conditions at the state level, it is necessary to recognize the special role and value of entrepreneurship and private initiative as an active creative force of society, an internal resource for long-term economic growth, increasing welfare, quality of life and ensuring national security.

One of the factors that influence the objectives and can play an active role in the analysis is customer demand. Thus, this section examines the sensitivity of outputs to changes in this parameter.

Having studied some articles of the Tax Code of the Russian Federation that regulate the simplified taxation system, we can conclude that they create a kind of problem that does not allow the simplified use of the simplified tax system. Let’s highlight three main difficulties: 1. The problem is that the taxpayer is denied by the tax authorities in the division of business in order to apply the simplified tax system. As of October 1, 2018, 71 entrepreneurs carried out economic activities in the Republic of Mordovia. 2. On December 25, 2018, Federal Law No. 408 came into force, which stipulates the extension of the moratorium on routine inspections of small businesses from January 1, 2019 to December 31, 2020. 3. The analysis of sensitivity to increased demand showed that the higher the demand, the higher the company’s profit. However, a 24% increase in demand caused the profit to increase by only 4%, which indicates that the impact of increased demand on the company’s distribution costs almost matches the impact on the profit. Meanwhile, the increased demand also led to extreme prolongation of transport makespan. This is due to the multitude of trips needed to cover the extra demand, which causes the transport makespan to increase by 28%.

The multi objective optimization performance by regarding the constraints are presented in the Figures 2, as shown in Figure 2, by the optimization the cost function reduces whilst the time increases. By proposed model the constraints criteria are considered in the optimization process and the third objective as the green supply chain are kept in the specified area.

## 4. CONCLUSIONS AND RECOMMENDATIONS

The multi-objective constrained model proposed for closed green supply chain in the enterprise development. Given the prominent role of distribution processes in manufacturing businesses, transportation planning, routing, and inventory and warehousing optimization are extremely important subjects of discussion in this field. Considering the influence of environmental protection investment on the coordination of the whole green closed-loop supply chain, this work constructed a green closed-loop supply chain to recycle waste products by the third party. Aiming at the decision-making of each node enterprise in the closed-loop supply chain, we developed the centralized decision-making model and the decentralized decision- making model, respectively. By comparing the advantages and disadvantages between the two models, we further proposed the optimized cooperative mechanism decision-making model to integrate the advantages of the previous two. The cooperative mechanism decisionmaking model can not only maximize the benefit of centralized decision-making, but also avoid the negative influence of the “double marginal effect” on profit under decentralized decision-making, thus making each node enterprise in the supply chain get more profit than decentralized decision-making. Organization of tax accounting at an enterprise is an important stage, which is the basis for accounting, management and personnel accounting. As a result, the correct organization of supply chain strategy at the enterprise makes it possible to prevent inaccuracies in the company's reporting, avoid environmental concerns and receive prompt and accurate information from the accounting department. To bring the developed model closer to the real world, parameters such as customer demand in each period, transportation costs of raw materials and products, purchase price of raw materials and the rate of return of consumed products are considered uncertain. For future studies, the proposed model can be considered by considering more definite parameters and using fuzzy or probabilistic programming, because at a higher size the problem will not be solved in an acceptable time, and should use approximation methods or metaheuristic algorithms.

## Figure

Comparison of pricing in a models with optimized supply chain.

Objective and constrain function variation.

## Table

Optimal levels of algorithm parameters

Analysis of sensitivity to demand

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