1. INTRODUCTION
In greening the supply chain, there must be proper minimization of costs due to the facilities, transportation and also the environmental impacts of these facilities and transportation. When an environmental constraint is added into a normal supply chain, the costs are impacted. An environmental constraint can be included by considering nitrogen emissions. Nitrogen oxides can affect both the environment and human health. These gases can be harmful to vegetation which in turn reduce crop yields. These gases also impact the environment by reducing visibility due to smog.
The greenness of supply chains can also be studied through green operations. These green operations cover topics such as reverse logistics and network designs. Liu et al. (2019) conducted an exploratory case study that found out that different green operations strategies require the support of different supply chain flexibility dimensions. Each flexibility dimension’s role varies depending on the degree of innovativeness in the green design initiatives and the types of green purchasing initiatives. Chawla et al. (2020) evaluated green operations management practices and also highlighted the benefits of green operations management over conventional management. They used fuzzy analytical hierarchy process to justify the adoption of green operations management practices. Saha et al. (2017) examined the impact of dynamic retailer investments in green operations. Their findings suggested that continuous investments in green operations can significantly improve retailer’s financial performance. Kuo and Lin (2020) examined the relationships among lean management green operations and green behavior with respect to green performance. The findings pointed to lean management positively influencing green operations and green behavior. MesjaszLech (2016) identified green logistics tasks in the area of reducing the negative environmental impacts of households in the cities. They determined changes in relation to the effect of economic entities.
Decisionmaking is critical in supply chains whereby precautions are being taken against environmental decay. Meng et al. (2020) examined the demanddependent products recovery decisionmaking problem for a couple of products that undergo remanufacturing. Flexible recovery decisions on product recovery strategies are critical in enabling a successful and sustainable operations. Baller et al. (2019) stated that suppliers manage the inventory of its customers and arrange for the transportation of the replenishments. So, the supplier bears both the inventory holding and transportation costs. They strive to minimize the costs by optimizing inventory and shipping decisions. Baller et al. (2019) stated that the supplier ends up facing an optimization problem known as Joint Replenishment problem. Alzaman et al. (2018) stated that normally production costs are lumped as just one cost. The authors believe that this prevents one from seeing the hidden opportunities in shortening the production duration. Shortening is well known for increasing the direct production costs. Jeon et al. (2019) stated that sustainable manufacturing is one of important areas in smart production strategies and operations, this is because more production energy data can be collected from the smart manufacturing environment. Reduction of greenhouse gases and excessive energy consumption is a necessary condition. Sun et al. (2019) stated that most literature are about procurement of transportation services for a single transportation mode. Few studies have looked at problems with more than one transportation mode such as shipping and trucking. Alzaman et al. (2018) stated that papers that deal with binary functions are scarce. They decided to look at the lack of papers that investigated both the direct and indirect cost.
Brunaud et al. (2018) compared alternatives for addressing discrete transportation costs. They found out that the most efficient formulation was obtained by using integer variables to account for the number of units used for each transportation mode. Hanbazazah et al. (2019) states that a key challenge in management is to minimize costs while meeting customer satisfaction levels. This challenge is greater in transportation where costs tend to increase with reduced delivery lead times. De Laporte and Ripplinger (2019) model incorporated spatial considerations of yields and production costs including opportunity costs. A lot of previous studies have shown that companies and governments should implement efficient environmental policies for better supply chains. Matsumoto (2020) found out that the demand for better environmental conditions tends to influence waste management ability. Huang et al. (2020) investigated the effects of carbon policies on integrated inventory of a twoechelon supply chain. They found out that firms adopting this policy prefer to invest in a relatively efficient green technology. Scavarda et al. (2019) proposed a recycling activity implementation policy which aimed at emphasizing the corporate social responsibility and the philosophy of the healthcare institution. It was found that the healthcare supply chain management is capable of improving the population’s quality of life. It is also advisable for the implementation of the educational program and the development the corporate social responsibility through the Triple Bottom Line. Fernado et al. (2018) tested the effects of energy management practices on renewable energy supply chains initiatives in manufacturing firms. Their results showed three dimensions of energy management practices, they also found out that insufficient knowledge of energy efficiency leads to struggles with energy management. They also suggested on how to farther develop energy efficiency policy in emerging economies. De Laporte and Ripplinger (2019) stated that policy initiatives in agricultural prices have led farmers to consider alternatives to current cropping practices. In the context of land quality and feedstock supply, the authors assessed the impacts of site selection, transportation and opportunity costs on a bioethanol production plant and other models of biomass production and transport.
It is important for products to be delivered to the customer while also considering that the products are environmentally compliant. This can be achieved when companies invest in optimizing their networks while also taking into account the tradeoffs between the costs of those products and the environmental effects. Garcia Freites et al. (2020) investigated the environmental effects of putting in practice modern bioenergy applications in the coffee sector. The results of their study allowed them to identify environmental tradeoffs. Liao et al. (2018) investigated the tradeoff relationship between the environmental effects and quality condition of a remanufacturing system. The model developed can be useful for the implementation of environmental regulations by the government. Huang et al. (2020) provided practical implications for the government to make appropriate policies in balancing the tradeoffs between economic growth and environmental protection. A lot of studies have been done to reduce the amount of emissions due to produce. GarciaFreites et al. (2020) showed that greenhouse gases can be significantly reduced due to modern methods such as modern bioenergy. Liao et al. (2018) studied a remanufacturing system whereby the emission reduction increases with rising complex quality while its marginal increase rate decreases rapidly.
A lot of models for total cost of the supply chain minimization have been derived in recent years. Brunaud et al. (2018) used a mixed integer linear program to determine the optimal number, location and capacity of warehouses required to support a long term forecast with seasonal demand. Transportation costs, warehouse contracting and safety stock handling were the main features of the problem. Brunaud et al. (2018) used an MILP that includes discrete transportation costs while contracting warehouse. The model is also a multiperiod model as a way of addressing demand seasonality. Tshivhase (2018) studied the airport industry which is a wellknown contributor of emissions. Tshivhase and Vilakazi (2018) focused on the mining industry which is also a strong contributor of emissions. Companies are working on cutting costs, as they reduce their emissions. Brunaud et al. (2018) considered a piecewise linear formulation that implicitly considered demand variability. Larger problems require additional modelling schemes. Hanbazazah et al. (2019) studied freight consolidation for a logistics provider that transships products from multiple suppliers to a single business customer once over a multiperiod horizon. Sun et al. (2019) stated that in the context of global slow down, most studies do not consider transaction costs. Once transportation service is traded auctioneer requires these costs to be covered in case the cargo is damaged. Miranda et al. (2018) stated that the number and location of visited docks at the islands have a relevant effect on maritime transportation costs. They additionally impact transportation costs incurred for moving the household waste or freight from within the islands to the selected docks. Brunaud et al. (2018) found out that the warehouses can either remain closed or opened during the planning horizon. The gap that has been identified in these distribution type of work has to do with the comparison of the transportation costs and the fixed costs at the plant. Tshivhase and Kainuma (2019c) solved a mathematical model with the help of a software package to optimize the costs. The problem was solved using a mixed integer linear program (MILP) which required a binary which was applied between the customer bases and the warehouses to capture economies of scale that are common in transportation. The methods were also investigated for sensitivity to key factors such as demand structure. Miranda et al. (2018) agree that the effect on ground transportation costs and also the specific problem and formulation are strongly dependent on the transportation strategy.
Many models considering environmental effects have been proposed in recent years. Liao et al. (2018) proposed an environmental benefits and costs assessment model for remanufacturing process and evaluated the environmental benefits of remanufacturing. They analyzed the carbon emissions between machine manufacturing and cannibalization. Tseng et al. (2019) studied different scenarios and their greenhouse gas emissions and environmental costs using a system dynamics model. They managed to reach maximum greenhouse gas mitigation. Meng et al. (2020) also proposed a multiobjective decisionmaking model that identified demanddependent optimal solutions that balance different sustainable performance constraints. Zhang et al. (2013) optimized terminal networks taking into consideration the costs of carbon dioxide emissions. They optimized the problem through bilevel programming with upper level searches for the optimal terminal network. They found out that a reduction in total system costs appears feasible when carbon dioxide emission prices are raised. Tshivhase (2018) studied the airport industry which is a wellknown contributor to carbon emissions. Tshivhase and Vilakazi (2018) focused on the mining industry which is also a strong contributor of carbon emissions. Tshivhase and Kainuma (2019b) addressed the emissions of carbon into the atmosphere by proposing a single period, multisupplier lowcarbon mixed integer model. This model was proven to reduce carbon emissions in the supply chain and also find the optimum distribution levels among different facilities including factories. Tshivhase and Kainuma (2018) identified the existing literature gaps and possible future research focus with respect to carbon emission reduction by looking at literature done between 1995 1nd 2018. In the 1990s due to improved computer models a consensus was formed that stated that greenhouses gases were deeply involved in most climate changes and emissions were bringing discernable global warming. During the same decade, scientific research in emissions has included multiple disciplines. Tshivhase and Kainuma (2019a) reviewed the literature of what has been studied with respect to carbon emissions and also identify the gaps in the literature using a systematic literature review approach. Content analysis was used to categorize existing literature on the various topics and methods over time in the area of carbon emissions in the supply chain. Hanbazazah et al. (2019) developed a mixed integer programming model employing cost functions.
This paper attempts to study the impact of nitrogen emissions in the supply chain. A lot of studies about optimization while also taking into account overall emissions have been done. It is also beneficial for the full impact of nitrogen emissions to be studied as this can be useful for smaller firms that are interested in focusing in reducing one type of emission at a time. In recent months the study of the full impact of nitrogen oxides has been gaining momentum. Åström et al. (2018) analyzed the socioeconomic justification of implementing nitrogen emission control area. They also analyzed the potential for emission reduction, emission control costs and monetary benefits. They found out that calculated benefits surpass costs for most scenarios. Ozgen et al. (2021) reviewed the literature regarding nitrogen oxides from the emission source while also discussing the main formation mechanisms techniques. The review managed to crosslink several aspects that are usually treated separately in scientific papers such as laboratory tests with basic theory or only field tests. Most nitrogen emission studies normally deal with pure chemistry without employing other areas of engineering and sciences. Zaborowska et al. (2019) determined through experiments, nitrogen oxides production and emissions in a large scale plant which employs combined nitrogen and phosphorus removal. Different operational strategies were evaluated following the proposed modelbased procedure.
In this paper we study a supply chain that delivers products from the suppliers to the customers. All the facilities and transportations have capacity constraints. There is an objective that minimizes the total cost of the supply chain which includes transportation, raw material, holding, fixed and variable costs. The second objective is to minimize the amount of nitrogen oxides produced by the facilities. The supply chain is initially modelled mathematically and then algorithms are used to produce a feasible solution.
The rest of the paper is organized as follows. Section 2 is the model development which basically shows the mathematical formulation. Section3 describes the computational approach. Section 4 describes the results with some example problems. Section 5 is the conclusion.
2. MODEL DEVELOPMENT
2.1 Description of the Model
The description of the mathematical model is explained in this chapter. This is followed by the mathematical model. The model deals with the allocation of facilities while also considering the transportation options. A simple supply chain is considered and it consists of the plant, warehouses and the customer outlets. Only one type of transportation option is considered. In this study we are looking at the environmental impacts of nitrogen oxides produced by the transportation option. We will only consider two objective functions. The first one will minimize the total costs of this supply chain and the second objective function will minimize the environmental impact of nitrogen oxides (NO_{x}).
The diagram of the flow of products shows the flow of the products being produced at the plant, these products are then transported to the warehouses and then to the customer outlets. Products are produced at the plant. There is also a certain amount of demand at the at the customer centres. The objective is to minimize the total costs of this supply chain and the environmental impact of nitrogen oxides. The plan is to optimize the model such that the total costs including transportation costs are minimized.
Some assumptions of this mathematical problem:

• All the facilities have capacity constraints

• Only one warehouse can fulfill the demands of each customer outlet

•The transportation options used between the facilities is identical

• These transportation options emit nitrogen oxides

• The facilities also do emit nitrogen oxides

• Demand is met

•Only one type of product is produced
2.2 Environmental Impact of Nitrogen Oxides (NO_{x})
Emission of nitrogen oxides contribute to environmental decay. Industrial operations are also high emitters of these dangerous gases. Hence the reason that researches on minimization of carbon emissions including nitrogen oxides are really important. The amount of nitrogen oxides depends on the number of products being transported and the distance between the facilities.
2.3 Mathematical Model
The two objectives are each divided into several components. Table 1 shows the components of these objective functions.
The objective model is formulated in the next steps:
Objective function 1 (1) minimizes the total costs that we are looking at in a typical supply chain. The plant costs (2) comprises of the variable and fixed costs. Objective function 2 (3) minimizes the nitrogen oxides. Equation (4) determines the fixed costs of this supply chain when the facilities are in operation. Equation (5) calculates the amount of variable costs according to the facilities’ demands. Equation (6) Computes the transportation cost according to the distance and amount of transported product Equation (7) Determines the inventory holding cost at the warehouses. Equation (8) calculates the amount of produced nitrogen oxides taking into account that the released amount by the facilities is calculated based on the release rate and the demand. Equation (9) and (10) determines the demand at each facility. Equation (11) calculates the inventory level at the warehouse and ensures that demand is always lower than the facility’s capacity. The standard deviation of demand (12) is defined as the weighted average of the standard deviation of other facilities’ demand. The capacity of a facility is always higher (13) and (14) than the demand in the next facility Equation (15) and (16) ensures that the amount of products from facility A to facility B must be equal to facility B’s demand Equation (17) and (18) ensures that transportation is not overloaded. The population standard deviation (19) depends on the mean of the data.
3. COMPUTATIONAL APPROACH
The two different objectives calculate the total cost of the supply chain and the other one determines the amount of nitrogen oxides produced in the supply chain. The random weighting method is a weighting methods for fitness evaluation.
The dimensions of these two objective functions are obviously different and hence the value of each objective is normalized by Eq (20). The solutions with the best fitness function value are passed on to the next population.
The weighted objective function is then shown in Eq. (21)
The random weight, w_{j} for the objective function j is calculated by Eq.(22), where rn_{j} is the random number for the jth objective function.
The solution is modified by an improvement function for a better fitness. This function always starts with a new solution which has been generated at random. It goes on to iterate into a new solution. The solution with the better fitness value between the second and first solution becomes the solution for the next step.
4. RESULTS AND DISCUSSIONS
4.1 Genetic Algorithm
The algorithms were coded in MATLAB. It is a requirement for repeated simulations to find suitable parameter values. Eleven test instances of different sizes were evaluated to examine the proposed algorithm method. The parameters for these instances are generated randomly using uniform distribution.
In Figure 2a and 2b, the objective functions are plotted for various warehouses. The objective functions are for all the facilities i.e. plants, warehouses and customer outlets. However, the concentration of this study is on warehouses. Initially, the values of these facilities is chosen with the condition that these facilities in the above mentioned areas are located in separate locations and that means when the densities of these facilities i.e. factories, warehouses and customer outlets are summed, the answer should be less or equal to one. This process applies to all the facilities i.e. plants, warehouses and customer outlets. The objective function is plotted for all of the 11 numerical examples, two of these examples are shown in Figure 2 i.e. for 24 and 28 warehouses.
Initially, genetic algorithm (GA) is used for the total costs of the supply chain. The standard deviation in Figure 3 is just the square root of the variance. This is basically a standard way of knowing what is considered normal. The standard deviation for the costs were calculated at 2.6226 e7 (1.1647 e7and 1.4579e7) for transportation, 1.5745 for raw material purchasing and 0.667 e7 for the fixed and variable costs at the factory.
The standard deviation is very useful. It shows what is standard basically normal and also what is outside the normal range. This is the measure of how numbers are spread. The symbol is σ (the Greek letter sigma) is used to indicate the standard deviation. Having calculated the variance, the standard deviation is the square of the answer to the variance. The difference from the mean is then calculated. For the variance, each difference is squared and the result is then averaged. The standard deviation will just be the squared root of the variance.
4.2 Particle Swarm Optimization
From Table 4, random weighted results are shown. The final results are obtained by the implementation of the particle swarm optimization (PSO). For all the 11 cases, both the GA and the PSO techniques are used to calculate average objective values. The PSO average values are found to be lower than the GA results. PSO results are used because the average values obtained through this method are lower. The test results of the PSO are shown in the table below.
Increasing the number of customers has a cost impact on the supply chain. The impact of increasing the number of customers on the total cost of the supply chain is also shown in Table 4. Figure 4 shows the percentage contribution of each cost. From these data, it can be seen that the transportation costs are the major contributors to the total costs. The costs of purchasing raw material are the next highest contributor. The fixed costs and the variable costs are the lowest contributors. As the number of customers increases, this leads to an increase in the average costs values.
There is a capacity constraint at the factory which makes sure that the produced products at the factory can be within factory limits. There is also a limit at the warehouse which translate to the warehouse capacity.
The PSO results have lower average costs than the GA as shown in Figure 5. And hence, the final results are implemented with the help of the PSO.
The final average value was taken as the optimization result. The average value and standard deviation were used to reflect on the accuracy and stability of optimization respectively.
4.3 Managerial Implications
One of the most strategic decisions in a logistics system is to determine the structure and costs in terms of the number of facilities and the transportation strategy as these have significant influence on long term profitability. This is a complicated decision making problem due to economic benefits. The solutions here emphasize profit expectations due to lower costs and also reliability. The model was tested with several test instances. The results also showed that the number of facilities can affect the configuration costs and hence profitability. Due to economic scales, from the higher number of facilities, the economic performance can be improved if the increase of investment for facility expansion and transportation is maintained at a proper level.
5. CONCLUSION
The supply chain problem looked at a situation whereby the facilities and the transportation option had capacity constraints. The problem also looked at the environmental impact of nitrogen oxides from both the facilities and the transportation moving the products between the facilities. Genetic algorithm was initially used for cost evaluation. It caused a decrease in the average costs. However, particle swarm optimization had lower cost values. There were 11 random data that were tested with this model. The model took into account the various constraints of a typical optimization problem and these constraints included the factory and the warehouses constraints. The various numerical examples were helpful in showing the application of the model and the algorithm and some managerial implications are shared from these results. This research helped in developing a model for various facilities’ numbers under some requirements. The deviation calculations were also really helpful and useful. The obtained results proved that the proposed methods are effective for a wide set of problem definitions. The model will be extended in future work to a multiobjective model.