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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.20 No.2 pp.289-296

A Novel Mathematical Model to Optimize Sustainable Supply Chain in the Lighting Products Industry

Gulmira Baybalinova*, Andrey Goncharov, Igor Zavalishin, Igor Sokolov, Inna Trofimova, Denis Yashin, Alla Aleinova, Dmitry Piotrovsky, Rustem Zalilov
Shakarim University of Semey, Semey city, Kazakhstan
K.G. Razumovsky Moscow State University of technologies and management (The First Cossack University), 73, Zemlyanoy Val St., Moscow, 109004, Russian Federation
Nosov Magnitogorsk State Technical University, 38 Lenin Street, Magnitogorsk City, Chelyabinsk Region, 455000 Russian Federation
*Corresponding Author, E-mail:,
February 27, 2021 March 22, 2021 April 11, 2021


Nowadays, due to changing conditions in global markets and competition, the issue of sustainability is a priority for the work of world leaders and business managers and is of great importance. Many supply chain issues are affecting greenhouse gas emissions and supply chain sustainability, such as facility location design, transportation routes, inventory policies, and so on. Lighting products due to the nature of consumption and its very high waste, is one of the most important products in terms of environment and society. In this research, an attempt has been made to design logistics optimization model at the strategic and tactical level in a sustainable supply chain for lighting products, taking into account the economic dimension. In this regard, a nonlinear mathematical model for a sustainable supply chain has been developed with the aim of reducing carbon emissions and reducing total costs. In order to optimize this mathematical model, genetic algorithm has been used. The results of this study show that the design of a sustainable supply chain network in the lighting products industry can significantly reduce the adverse environmental impact of this supply chain.



    In the modern era and by the development of communications and reduction of the geographical borders, organizations have found themselves in a more competitive situation and due to disturbance in the competition status and the importance of creation and maintenance of the competitive advantages has increased potentially. The advantage of sustainable advantage is that it cannot be copied and used by others and can assist the organization in the competitive environment (Krysovatyy et al., 2020). On the other hand, regarding the discussion of sustainability and sustainable development, new discussions have emerged in the supply chain. Even though today several definitions and dimensions have been proposed for a sustainable supply chain. Sustainable supply chain management can be defined as the management of the flow of materials, information, and coordination all around the supply chain, which is carried out upon considering the economic, social, and environmental dimensions. Even though there is no definite consensus regarding the definition of the sustainable supply chain, it has been supported as a new pattern. Since the activity of the agency corresponds to the needs of the stakeholders and increases profitability and competitiveness, besides it should enhance environmental efficiency and social accountability (Sokil et al., 2020; Ahi et al., 2016; Zhu et al., 2013). In recent years, climate change and environmental concerns regarding global warming have been the most crucial issue of society. For instance, the emission of greenhouse gases, especially Carbon dioxide, which is one of the main causes of global warming and the reason for the change of the environmental conditions. Various contracts have been confirmed around the world in this regard. For instance, agreements such as the Kyoto Protocol and the various laws of different countries. These new instructions can lead to increasing the pressure on the companies to reduce the emission of greenhouse gases (Paksoy et al., 2010;Bagheri Sadr and Bozorgian, 2021;Samimi, 2021). The developed countries and several developing countries set up goals that will result in the reduction of emission of greenhouse gases. For instance, the European Union energy policy set the target of a 20% reduction of the emission of greenhouse gases up to 2020. It appears that there is a consensus regarding the social costs and global costs of emission of carbon.

    In the second chapter of the article, the theoretical basis and the literature review are studied and in the third chapter, the mathematical statement of the problem is provided. In the fourth chapter, a case study in the lighting industry is stated and in the final chapter, the results are discussed.

    The supply chain includes all activities pertinent to the flow and transformation of goods from the stage of providing raw materials up until delivering the product to the final consumer and the information flows in that regard. The supply chain and the related information flows through the improvement of the relationships in the chain, strive to achieve a reliable and stable competitive advantage. Therefore, they seek to obtain management of sustainable supply chain, management of capital, information, and material flow plus cooperation between companies. Together with integrating the objective includes all Triads of Sustainability (economic, environmental, and social), which arises from the needs of the consumers and stakeholders (Seuring and Müller, 2008;Egilmez and Stewart, 2019). In the literature regarding the subject, the operation of sustainable supply chain management comprises two separate groups:

    • 1. Sustainable Process Management: Sustainable process management is one of the fundamental activities in the environmental and social fields, which is carried out without the direct participation of the suppliers. For example, economic design, health and safety, social campaigns (Gavronski et al., 2011).

    • 2. Sustainable Supply Management: Activities including transactions with suppliers (e.g. assessment and sustainable cooperation of suppliers) are considered as the activities of sustainable supply management (Klassen and Vereecke, 2012).

    Chaban proposed a mathematical programming model for designing the logistic networks with the environment and the environmental impacts in this regard will be measured together with carbon emission costs pertinent to transportation in the supply chain (Chaabane et al., 2008a). The problem is resolved through single-objective optimization taking into account these costs and other costs considered in this regard. Chaban and other researchers used Mixed Linear Programming for solving various strategic problems such as selecting suppliers and contractors, product allocation, using capacity and allocating transportation links required for corresponding the market demand.

    In the past, the managers of the supply chain emphasized the assessment of the level of services and economic performance in order to evaluate the effectiveness and efficiency of a supply chain network (Chaabane et al., 2008b;Nor and Zawawi, 2020;Gaikwad et al., 2021). However, the increasing concerns regarding environmental sustainability propound a concept that the performance of a chain should cover not only its profit but also the impact of its activities on the environment and social issues (Gladwin et al., 1995;Gutsalenko et al., 2020).

    Taking into account the viewpoint of sustainability the traditional supply chain management approach is limited and in sustainable supply chain management, the environmental dimensions are considered in the assessments. BL3 is a new concept that close to and pertinent to the performance of a company (Kleindorfer et al., 2005). A BL3 concept is a theoretical approach for assessment of the performance that simultaneously considers the objective pertinent to economic prosperity, social responsibility, and environmental sustainability.

    When studying the texts by some authors it might seem that there is a goal conflict, however this does not necessarily mean that there are conflicts regarding these three objectives. There are activities that the companies can create to have a positive impact on the environment and society, besides, leading to long-term and competitive economic advantages (Kleindorfer et al., 2005: Chapnevis et al., 2020;Kazemi and Yang, 2021).

    For instance, replacing incandescent light bulbs and fluorescent lights with LED light bulbs and the modern lighting industry. In this technology, less energy is used to produce more light and heat. In fact, earning more profit by paying less cost.

    Srivastava defined green supply chain management as a combination of the environmental and supply chain management concepts (Srivastava, 2007). The practical application of green supply chain management is considered by identifying the most suitable environmental impacts. For example, carbon emission and using nonrenewable natural resources, which must be minimized in the production and distribution activities (Butner et al., 2008).The most popular and beneficial method for the assessment of whether a supply chain is green is the life cycle (Dekker et al., 2013). The life cycle of a product includes the environmental effects of activities from designing to the final product through selecting the materials, process of production, transportation, distribution, delivery to the consumers, consumers’ consumption, and the final destination of a product after expiration of its shelf life (Wanke et al., 2015). Some authors conducted research on inventory and routing. The model was designed in the network of the economic supply chain and in a hybrid production system. Furthermore, the model of routing and network design was implemented in a Brazilian model (Wanke and Saliby, 2009;Wanke et al., 2015;Taleizadeh et al., 2019: Fallahtafti et al., 2019).

    In their most recent research, Sarkar et al. (2021) investigated the environmental effects of using the sustainable supply chain network. In this research, quality improvement was proposed as an efficient approach in designing a sustainable supply chain network with the least unpleasant impact in the environment through studying the life span of the product.


    In this chapter, the problem is described mathematically and the parameters are specified. In the previous problems, inventory, storage, and distance were considered limitless. In the model suggested in the present article, an approach was employed to make the problem more real. One of the problems of most of the articles and the proposed solutions in the industry is the failure to notice the limitations and the real conditions in a model. At first, the indices, input and output parameters, and the variables of the problem are explained, these parameters are pertinent to the inventory routing of carbon emission and other problems. A mathematical programming model was used.

    The objectives of this model included the total cost of the chain including the costs of distribution, transportation, storage, maintenance, and the costs of greenhouse gas emission. This model aimed at minimizing the model for the purpose of optimization. The costs of storage such as transportation from the factory to the warehouse, cost of distribution such as transportation from the warehouse to the consumption market, cost of maintenance such as saving and storage, costs pertinent to the emission of the greenhouse gases are considered as transportation-related costs. In the following Figure, a general view is displayed from the objective function.

    The hypotheses of the research are described as follows. Several hypotheses are considered for this model:

    • - The location of the factory should be fixed and specified.

    • - The location of the consumer market should be fixed and specified.

    • - This network has one product.

    • - Filling the warehouse using the cross methods is authorized.

    • - Only carbon factor is considered among the emitted gases.

    • - The foundation of the optimal order placement is based on Wilson’s formula.

    Indices and variables of the model are as follows: i Market index i = {1, …, n}

    • j : potential warehouse index j = {1, …, m}

    • Lj : Mean supply time for warehouse j

    • Lij : Mean supply time from warehouse to market i to j

    • σDi : Standard deviation of demand for market i

    • σLj : Standard deviation of supply time for warehouse j

    • kj : Storage in warehouse index j

    • Tij : Cost of transportation unit between market and warehouse i and j

    • dj : Distance between factory and warehouse j

    • dij : Distance between warehouse and market i and j

    • S : Cost of daily supply from factory to warehouse

    • CE : Cost for emission of carbon in kg

    • α : Carbon emission index in distance and weight

    • δ : Product weight

    • N : maximum number of consumers

    • m : Collection of potential warehouses

    • M : maximum number of warehouses

    • Aj : Cost of order placement in warehouse j

    • Cj : Cost of commodity storage in warehouse j

    • Di : Mean demand in the market i

    • MaxDi : Maximum total mean demand in the market i

    • ρil : Correlation between demand and market i and l

    • Wij : Variable of decision and the percentage of mean market demand which is corresponded by the warehouse

    The objective function of the programming model is as follows:

    M i n   C = j = 1 m i = 1 n S L j W i j D i + j = 1 m i = 1 n T i j W i j D i + j = 1 m 2 C j A j i = 1 n W i j D i + j = 1 m k j C j L j i = 1 n W i j 2 σ D i 2 + 2 i = 1 n i = 1 i 1 W i j W i j ρ i j σ D i σ D i + σ L j 2 ( i = 1 n W i j D i ) 2 + j = 1 m i = 1 n C j L j W i j D i + j = 1 m i = 1 n C j L i j W i j D i + C E δ α ( j = 1 m i = 1 n d j W i j D i + j = 1 m i = 1 n T i j W i j D i )

    Subject to:

    j = 1 m W i j = 1 i i = 1 n n i N j j = 1 m W j M i

    i = 1 n D i M a x D i   j

    The descriptions of the objective function are provided hereinbelow:

    This section indicated the cost of supply for the warehouse:

    j = 1 m i = 1 n S L j W i j D i

    This section indicated the cost of supply for the market:

    j = 1 m i = 1 n T i j W i j D i

    This section indicated the cost of order placement:

    j = 1 m 2 C j A j i = 1 n W i j D i j = 1 m k j C j L j i = 1 n W i j 2 σ D i 2 + 2 i = 1 n i = 1 i 1 W i j W i j ρ i l σ D i σ D i + σ L i 2 ( i = 1 n W i j D i ) 2

    The above relation is used to show the cost of storage:

    This section indicated the cost of transportation:

    j = 1 m i = 1 n C j L j W i j D i + j = 1 m i = 1 n C j L i j W i j D i

    The cost of carbon emission during transportation is provided as follows:

    C E δ α ( j = 1 m i = 1 n d j W i j D i + j = 1 m i = 1 n T i j W i j D i )

    In the limitations section, the first limitation signifies that the market demand has corresponded. The second limitation signifies the maximum number of consumers. The third limitation is an indication of the maximum number of warehouses and the final limitation covers the maximum demand.

    In this problem, limitations resulted in the creation of new conditions for the model, and the costs of transportation and storage are among the important costs included in this programming model. The factor of carbon emission is one of the main indices for the separation and creation of a sustainable supply chain in the system. The chain that despite the storage and its costs and transportation and logistics lead to examining two levels in chain programming.

    In the network of Figure No. 1, a schematic view from the sustainable supply chain problem-solving method is provided.

    The model was optimized after imposing restrictions through optimal simulation. The objective of using simulation optimization is to obtain a logical solution for the best answer. The sensitivity analysis was carried out easily using the simulation method and it could be investigated in different states. Without simulation optimization, there could be no certainty regarding the optimization of the simulation. In Figure 2, a schematic view from the SA algorithm is displayed.

    There is a variety of methods for simulation optimization. The Scheduling model was assessed using Arena simulation software or a simulated annealing optimization technique.

    Model output determines the methods of storage such as cross-docking, centralized warehouse, or other storage methods. Moreover, this model determines the general policies of a chain.


    The proposed model in the non-linear programming of the sustainable supply chain was implemented in the lighting industry. The lighting industry underwent many changes due to the impact of new technologies. This industry used to activate in the field of fluorescent lamps or lamps with magnetic core. However, in recent years due to the development of technology, they changed their products to LED lights and created less heat, and increased the efficiency of the lights; In fact, it has resulted in both economic and environmental improvements. In the present article, the model of programming was studied in one of the great lighting and bulb manufacturing industries of the country.

    This study included 20 consumers and a factory, which is described in the problem. The cost of carbon emission was considered as one million tomans per ton of emission. The safety stock percentage was considered 95% in this study. Meaning that there is 95% certainty of the coverage regarding prevention of deficit by the determined storage.

    In the following table, the total information regarding the sustainable supply chain of the study are included:

    In the proposed problem, 20 agencies from different cities in the country who sold the light, which was the subject of this article, were selected and the information regarding the cost of order placement for the warehouse, cost of storage in the warehouse, mean demand in the warehouse, the time for supplying the market, time for supplying from the warehouse, cost of transportation from the warehouse, cost of transportation from the consumer, and the weight of the product were specified and the information is provided in Table 1. The industry of lighting is among the greatest industries in the country that few studies were conducted in that regard. After preparation, the information was simulated in Arena simulation software and optimized. The results indicated the amount of the corresponded demands for each market by each warehouse.

    The results of the models demonstrated that the agencies could correspond to the demands by using seven warehouses. In this model, choosing different storage methods was authorized. Therefore, the results revealed that in some cases the cross docking and in some cases centralized warehouse methods were used.

    To analyze the sensitivity with respect to the different input values, the safety stock percentage was increased. The results indicated that by increasing the safety stock percentage from 95% to 98%, the storage value was increased and the number of warehouses was increased from 7 to 9.

    In this problem, there were several conditions for sensitivity analysis. One of the factors that could be analyzed and mentioned in the present research was using railroad transportation and road transportation together for carrying out the sensitivity analysis. The cost of railroad transportation amounted to 50% of the land transportation and the mean speed of railroad transportation was examined to be 40 km per hour, while the mean transportation speed for land transportation was 60 km per hour. The model indicated that land transportation costs less in the total sustainable supply chain. The status of gas emission was studied before and after the execution of the model for the purpose of validation. The numbers indicated that the amount of greenhouse gas emission was decreased. Figure 2 displays the status before and after the execution of the model.


    Reduction of the pollution and increase of the life quality and health are numbered among the most crucial global concerns. In the present research, a model was proposed to optimize and reduce the emission of greenhouse gases. Most of the studies conducted in the field of sustainability are concerned with qualitative problems and few studies are carried out regarding optimization issues. By optimizing the amount of the demand corresponded by each warehouse and by the approach of considering the emission of the greenhouse gases in the supply chain, this model transformed this chain into a sustainable supply chain. The proposed model is a non-linear model and it was optimized using simulation optimization. The suggested optimization in the simulation follows the SA algorithm. The proposed model was implemented for investigating the lighting industry of the country and the results indicated improvement of the conditions. Furthermore, a sensitivity analysis was carried out for a more precise examination of the subject on the certainty of the safety stock percentage and the type of transportation (railroad or land). It is suggested to design a periodic model for future studies. Besides, it is recommended to use multi-product models for the development of the present model.



    Diagram of total costs of chain and the constituent components.


    View of SA algorithm


    Primary information of the problem

    Results of the Model


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