© S.M. Rafie & H. Sahebi, published by IFP Energies nouvelles, 2021

1 Introduction

Current global energy consumption shows a significant upward trend by 2030. Rising pollution, declining fossil fuels, environmental concerns, economic development, climate change, the food crisis, and fuel price fluctuations have posed serious challenges for energy planning and management [1]. In recent years, on the one hand, issues such as energy security and countries’ dependence on fossil fuels that end one day, and on the other hand, crises caused by environmental pollution have shifted countries to alternative sources that address the above two challenges [2]. Experts have examined alternative sources that are both renewable and cleaner. Considering that the transportation sector has a great impact on environmental pollution, finding alternative sources in this sector can greatly help reduce environmental pollution [3].

Experts believe that using clean energy such as solar energy, wind, biomass, etc., instead of fossil fuels, will prevent environmental pollution and its dangers [4]. Expert research shows that biofuels, which can be supplied from various sources, can be economically and environmentally suitable alternatives to fossil fuels [5]. Biofuels can be produced from biomass, including agricultural, household, commercial and industrial waste, crops and natural biomass. Bioethanol and biodiesel can be used as liquid biofuels as fuel for vehicles or additives to petroleum-based fuels [6]. Biodiesel is a type of biofuel that can be successfully combined with diesel earned from fossil fuels at different percentages for transportation [7]. Jatropha is a promising source of biodiesel production that has received much attention due to its high oil content for biodiesel production, drought tolerance and water scarcity, soil reclamation, desert reduction, rural development, and environmental benefits [8].

Despite much attention to the biofuel supply chain in recent years, few papers have addressed the drop-in property of advanced hydrocarbon biofuel. The US Department of Energy in a study has addressed the issue of integrating a hydrocarbon biofuel supply chain with existing oil supply chain production and distribution infrastructure. They show three connection points for these two chains. First, after pre-processing the biomass and liquefying it, they combine it with the crude oil and lead it to the distillation towers. The second is for the semi-finished material to go to upgrade units for further processing, and the third is for the finished fuel to come to a warehouse or distribution point for petroleum products to use the existing distribution capacity. This eliminates the need of building many facilities in the biofuel supply chain and reduces many costs [9]. Therefore, some papers have studied how to integrate these two supply chains. Huber and Corma [10] studied biomass conversion techniques for biofuels through existing oil refineries. They concluded that there are three techniques for this: catalytic cracking, hydro-treating, and hydrocracking. In order to lower the cost of advanced hydrocarbon biofuels to a level comparable to conventional fuels, a sophisticated supply chain model, which considers designing, logistics, and planning decisions, is urgently needed to take the advantage of the existing petroleum refinery infrastructures.

This paper proposes a multi-objective Mixed Integer Linear Programming (MILP) model to design an integrated biodiesel and gas-oil supply chain. The proposed model considers all parts of both chains from harvesting sites of the biodiesel supply chain and oil fields of the gas-oil supply chain to the final customers. Besides maximizing profits as an economic goal, the proposed model also minimizes the emission of carbon dioxide as an environmental goal. Jatropha is considered a feedstock in the biodiesel supply chain due to its proper biodiesel production characteristics, which has already been pointed out. According to [11] and its case study that was done for Iran, Jatropha is more viable than bio-wastes. Also, due to the model’s reduced complexity and its solution time, only Jatropha is considered feedstock. This model can be used in many strategic and tactical decisions such as location, allocation, capacity expansion, production planning, and inventory management. This paper has been used for a genuine case in Iran for the 20-year planning horizon.

The rest of this article is as follows. The literature review is presented in Section 2. The concerned problem is described in Section 3. The symbols used in the model and the developed model are presented in Section 4. The solution method used is described in Section 5. The case study and its relevant results are described in Section 6. Finally, the results and some directions for future research are presented in Section 7.

2 Literature review

The issue of designing a network of oil supply chains and biofuels has been the focus of many researchers due to the inclusion of various strategic, tactical, and operational decisions. Responses to all decisions such as location, allocation, capacity determination, capacity expansion, technology selection, production planning, inventory management, and so forth can be obtained as a chain network design model. Numerous papers have examined the supply chain of crude oil and petroleum products and biofuels to provide energy with maximum profit and minimum environmental pollution. In papers related to the oil supply chain and petroleum products, part or all of the supply chain is optimized. Papers optimizing the supply chain by considering biomass generation as raw material are also discussed in papers on the biofuel supply chain.

To better understand the studies conducted on the oil supply chain and its derivatives and the biofuel supply chain, we would separately investigate the papers and studies conducted on these two issues. Table 1 shows the papers’ classification on the oil supply chain and its derivatives and on the biofuel supply chain. The upper half of the table shows the papers on oil, and the lower half shows the ones on biofuels.

2.1 Literature review of oil and petroleum products supply chain

The oil supply chain and its derivatives have always attracted researchers’ attention due to their breadth, importance and attractiveness. The studies carried out in this field are very extensive. Therefore, in this paper, only the studies conducted on designing the oil supply chain network and its derivatives are discussed.

As shown in Table 1, the papers’ structure on the oil supply chain and its derivatives can include upstream parts such as oil fields and crude oil storage centers and intermediate parts such as refineries and product storage centers and downstream parts such as distribution centers and customer types. Much research has been done on the downstream and midstream of the oil supply chain. Fernandes et al. [12] consider a multi-level, multi-product and multi-transportation downstream Petroleum Supply Chain (PSC) network. In another paper, they [13] developed their work with a dynamic MILP model for collaborative design and tactical planning. Guajardo et al. [14] presented a model for a company’s downstream oil supply chain and determined the optimal plan for it. Fiorencio et al. [15] presented a MILP-based Decision Support System (DSS) that enables strategic planning of the oil supply chain. This model is used for studies evaluating investment options for a logistics infrastructure. Kazemi and Szmerekovsky [16] presented a MILP model for a multi-product, multi-level downstream oil supply chain network that minimizes costs. Their model addresses multi-modal transportation planning in strategic supply chain design. Ghezavati et al. [17] designed the downstream part of the PSC. They demonstrated a hierarchical structure including a mathematical optimization model for determining strategic decisions in the leader problem and a simulation model for determining tactical and operational decisions in a follower problem. Öztürkoğlu and Lawal [18] developed a single-period and single-product deterministic mathematical model and analyzed scenarios such as breakdowns in pipeline connections. Ghaithan et al. [19] have presented an integrated multi-objective model for mid-term tactical decision-making for the downstream part of the oil and gas supply chain. Lima et al. [20] presented a multi-stage stochastic programming to solve the refined product distribution problem optimally. Wang et al. [21] have presented a MILP model for optimizing the downstream segment of the oil supply chain to plan new pipelines.

Many researchers have studied the upstream oil supply chain, and some by considering it as integrated. Leiras et al. [22] address integration and coordination under uncertainty the tactical and operational levels. Spatial integration is examined the tactical level, while temporal integration is examined by the interaction between tactical and operational levels. Gamari and Sahebi [23] presented a multi-objective mathematical model for stochastic lot-sizing in the petrochemical supply chain, considering uncertainty. In a study, Nasab and Amin-Naseri [24] investigated a multi-level, multi-modal transportation and multi-period integrated oil supply chain to obtain a global optimal solution. They simultaneously considered both the construction and capacity expansion of the facilities and the pipeline route. Jabbarzadeh et al. [25] presented a multi-period MILP mathematical model for designing the oil supply chain network. Farahani and Rahmani [26] introduced a MILP model to maximize the net present value of a crude oil network. The effect of gas injection and swap simultaneously is considered in the proposed model. Azadeh et al. [27] presented a multi-objective mathematical model for integrating the upstream and middle sectors of the crude oil supply chain of environmental indicators. In this paper, an algorithm based on the Multi-Objective Evolutionary Algorithm Based on Decomposition (MOEA-D) approach is used to solve the proposed nonlinear Mixed Integer Programming (MINLP) model. Azadeh et al. [28] also presented another paper that year that simultaneously focuses on the upstream and downstream sectors of the crude oil supply chain. This paper also puts into consideration the simultaneous development of the oil field and the planning of the transformation.

As shown in Table 1, decision levels can vary from paper to paper. Among the most important decisions are location, capacity determination or expansion, technology selection, allocation, production planning, inventory planning, and transportation-related decisions. Fernandes et al. [12], through developing MILP, strategically designed and planned the PSC downstream network and determine the optimal locations of depots, optimal capacities, modes of transport and long-term planning. MILP maximizes profit of petroleum companies and is tested with a real PSC network in Portugal. Guajardo et al. [14] addressed tactical issues related to decision making in production, distribution to customers, and inventory. The decision levels of other papers are also listed in Table 1.

To model, papers can be classified into different categories. The major problems are actually MINLP, but the mathematical models are in the LP, MILP, NLP, and MINLP types. Papers can also be classified into single-objective and multi-objective in terms of the type of objective function. Most multi-objective models in this area have used economic and environmental functions. Zhou et al. [29] presented a multi-objective MILP model for minimizing total economic costs and CO₂ gas emissions simultaneously. They identified the Pareto boundary for solving the multi-objective model and examined it in a real-world example. Also Ghaithan et al. [19] have presented an integrated multi-objective model. The objectives of this paper are: minimize total costs, maximize total revenue, and maximize service level. Uncertainty in parameters is another important factor that should be considered in the classification of papers. In a general division, the approach to dealing with uncertainty in papers can be divided into three categories: fuzzy, robust, and stochastic. For example, Oliveira et al. [30] presented a two-stage stochastic programming model for the petroleum products supply chain. They also used the development of stochastic Benders decomposition method to solve. Gupta and Grossmann [31] presented a multi-stage stochastic programming model for planning the offshore oil and gas fields’ infrastructure. They considered endogenous uncertainties and complex fiscal rules into their planning model. Jabbarzadeh et al. [25] investigated uncertain parameters via fuzzy theory. Lima et al. [20] presented a multi-stage stochastic programming model. To investigate the uncertainty in oil price and demand, they used time series as well as scenario tree analyses. They also used Auto-Regressive Integrated Moving Average (ARIMA) method for time series analysis and a scenario reduction method to compress the problem dimensions. Beiranvand et al. [32] proposed a robust optimization model to consider demand and price uncertainties.

2.2 Literature review of biofuel supply chain

Although biofuel supply chain studies are not as old as oil supply chain studies, they have attracted the attention of many researchers in recent years. Crises caused by countries’ dependence on oil have drawn the attention of researchers to alternative sources, the most important of which are biofuels. Features of biofuel supply chain papers can also be included in Table 1. The structures of the supply chain network, considered in most papers in this field, are similar, and in some cases, there is a slight difference. The feedstock considered in the biofuel supply chain papers can vary. Most papers consider the second generation of feedstock. Some papers also consider a combination of generations. Babazadeh [33] presented a multi-period and multi-product biodiesel supply chain network design model. He is considering Jatropha seeds and waste cooking oil to produce second-generation biodiesel. Babazadeh et al. [34] presented a possible multi-objective programming model for the design of the second generation biodiesel supply chain network under risk conditions. This paper presents a planning method for risk reduction based on uncertainty. Ezzati et al. [35] designed the biodiesel supply chain network with Jatropha, waste cooking oil, and microalgae as feed stocks. They offered a multi-period, multi-product, multi-mode MILP model that integrates all levels of the chain. Mahjoub et al. [11] developed a multi-period multi-objective MILP model that designs the second/third generation biofuel supply chain. They studied three types of biomass simultaneously as a feedstock for production and used an augmented ε-constraint approach to solve it. Kheybari et al. [36] focused on identifying the best location for the production of bioethanol. They proposed an evaluation framework that based on the three dimensions of sustainability. They applied the Best-Worst Method (BWM) in their paper. Kang et al. [37] proposed a three-step model for designing a biofuel supply chain from microalgae. The first stage is the design of economic decisions and analyses. The second stage is selecting candidate locations based on GIS, and the third stage is the mathematical optimization.

Biofuel papers, as shown in Table 1, can help make various decisions at different levels. Lin et al. [38] presented a MILP model for optimizing strategic and tactical decisions. This model covers all activities from harvesting to distribution. In some papers, issues such as seasonal feedstock are considered in the design of biofuel supply chain networks. Xie et al. [39] proposed a multi-stage MILP model for the cellulosic biofuel supply chain. This paper deals with the feedstock’s seasonality. Santibañez-Aguilar et al. [40] presented a dynamic optimization model for optimal supply chain planning. They considered the seasonality of biomass cultivation in their study.

Papers on biofuels can also single-objective or multi-objective. The objectives of these papers are mainly economic, environmental, and social. Mousavi Ahranjani et al. [41] presented a model that simultaneously considers economic, environmental, and social objectives. Also, Fattahi and Govindan [42] considered environmental and social aspects. Ghani et al. [43] examined the impact of incentives on one side and the greenhouse gas emissions penalty. On the other, it made farmers refrain from burning biomass residues and provide opportunities to convert these materials into biofuels. As a result, the costs and emissions of greenhouse gases are reduced.

Another feature of papers in this field is the certainty or uncertainty in network design. Papers that consider uncertainty in parameters are generally classified into three categories: fuzzy, robust, and stochastic. Azadeh et al. [44] presented a multi-period stochastic linear programming model that maximizes profits and then analyzed the results. Zhang and Jiang [45] designed biofuel supply chain based on waste cooking oil at strategic and tactical levels. They introduced a multi-objective MILP model with a robust approach. Mohseni et al. [46] presented a two-stage model for designing and planning a biodiesel supply chain from microalgae. They used GIS and AHP to determine potential locations. They used a robust MILP model to optimize in uncertainty. Gilani et al. [47] proposed a three-phase robust optimization model for network design of supply chain to produce bioethanol from sugarcane. They employed fuzzy integrated data envelopment analysis method to select suitable cultivation lands as supply potential points. Their model performance has been illustrated through a case study in Iran. Bairamzadeh et al. [48] presented a MILP model for determining the strategic and tactical decisions of the bioethanol lignocellulosic supply chain. A hybrid robust optimization model has been used to consider the uncertainties. Ghelichi et al. [1] presented a two-stage stochastic programming model for designing an integrated green biodiesel supply chain from Jatropha seeds. In their multi-product, multi-period MILP model, they developed a two-stage scenario-based stochastic programming approach. Shavazipour et al. [49] presented a two-stage scenario-based multi-objective optimization methodology. They considered three objectives in their problem under uncertainty of six parameters. A case study of South African sugarcane industry utilized to examine the proposed model. Mousavi Ahranjani et al. [41] presented a hybrid multi-objective robust possibilistic programming model for designing and planning a multi-period biofuel supply chain network under uncertainty. Fattahi and Govindan [42] presented a multi-stage stochastic programming model for biofuel supply chain design and planning. Ghaderi et al. [50] presented a multi-objective robust possibilistic programming model for designing a sustainable bioethanol supply chain network. Babazadeh et al. [51] presented a possibilistic programming model for designing the second-generation biodiesel supply chain network under uncertainty, in which case Jatropha seeds and waste cooking oil are considered the raw material of biodiesel. They also used a benders-local branching algorithm to solve their model. Razm et al. [52] made a redesign of the biomass supply network by considering price changes as a decision variable. They examined demand and exchange rates in three different scenarios.

None of the above papers have considered the use of oil network infrastructure to produce biofuels. Tong et al. [53] optimized and strategically planned the integrated hydrocarbon biofuel system and oil supply chain under uncertainty. This paper proposes a two-stage stochastic MILP model for optimal design and strategic planning of hydrocarbon and petroleum fuels using uncertainty. Tong et al. [54] designed the optimal design of an advanced integrated hydrocarbon biofuel supply chain with existing oil refineries and analyzed the three points of connection of the biofuel supply chain with oil refineries. They also provided a multi-period fuzzy MILP model to consider uncertainties. In another paper in the same year, Tong et al. [55] designed an optimal biofuel supply chain for advanced integrated hydrocarbons with existing oil refineries and identified an integration strategy using the robust optimization approach.

Therefore, the contributions of this, are briefly as follows:

• Elaborating a novel sustainable planning model to design a fuel and biofuel supply chain network to mitigate CO₂ emissions and improve economic performance.

• Addressing a comprehensive diesel supply chain including upstream, midstream, and downstream entities.

• Developing a bi-objective model to integrate gas-oil and biodiesel supply chain network design.

• Simultaneous consideration of environmental pollution caused by transportation within the supply chain and reduction of pollution due to the use of biodiesel instead of diesel.

• Applying the developed bi-objective mathematical model to a real case study.

3 Problem definition

The issue under discussion in this study is the design of an integrated gas-oil and biodiesel supply chain network that considers all parts of both chains, from harvesting sites in the biodiesel supply chain and oil fields in the gas-oil supply chain to final products for the customers. The issue discussed in this study is examined through a deterministic multi-objective MILP model so that in addition to maximizing profits as an economic goal, it also minimizes the emission of carbon dioxide as an environmental goal.

According to [56], the harvested biomass feed stocks can either be sent to integrated bio-refineries for direct production, or undergo a two-stage conversion process, namely pre-conversion and upgrading. Pre-conversion stage converts biomass into bio-intermediates (e.g., bio-oil and bio-slurry) that is economical and efficient for transportation, whereas upgrading stage upgrades the bio-intermediates into final products [57]. Crude oil flows from oil fields to crude oil storage facilities, some of which are exported. In the biodiesel supply chain, Jatropha can be transferred from harvesting sites to collection centers and pre-processing centers and biodiesel refineries. On the one hand, after pre-processing in the biomass supply chain, the bio-slurry enters the crude oil storage. The inflows to the crude oil storage centers enter the distillation towers. After separation, diesel is obtained in distillation towers, which the consumer cannot use according to the standards, and the final processing must be done in the production units. Bio-slurry and bio-oil were obtained in pre-processing units, where bio-oils directly enter the upgrading units in oil refineries. On the other hand, the materials that come out of the pre-processing units can be turned into the final product in the upgrading units that are in the biofuel chain. Also, from biomass collection centers, they can be transferred directly to biodiesel refineries where all processes can be done and the final product can be obtained. The final product obtained from the upgrade units in the oil supply chain as well as the production units enters the product storage centers. There are two ways to get the final products from biodiesel refineries and upgrade centers in the biofuel supply chain: either entering the products’ storage centers and sending them to the distribution centers after mixing or sending them directly to the distribution centers where they can be mixed. Finally, the final product is sent from distribution centers to customer centers, industry and export centers. Figure 1 shows the schematic of the network examined in this paper: Oil fields, crude oil storage centers, distillation towers, upgrading units in the diesel supply chain, refinery production units, product storage centers, export terminals, distribution centers, Jatropha farms, Jatropha collection centers, pre-processing units, upgrading units in the biodiesel supply chain, and bio-refineries, each has a certain level of capacity. Except for the refinery production units, other cases have a fixed capacity. Refinery production units can increase capacity to a certain extent. There is infinite capacity for the means of transport and only one mode of transport is considered. The model will determine the construction of upgrading units in the diesel supply chain, Jatropha harvesting sites, Jatropha collection centers, pre-processing units, upgrading units in the biodiesel supply chain, bio-refineries and distribution centers.

For crude oil storage centers, product storage centers and Jatropha storage centers, inventory costs are considered. In the upgrading units in the diesel supply chain, refinery production units, pre-processing units, upgrading units in the biodiesel supply chain and bio-refineries production yield. The environmental goal function considers two issues. The first is to minimize the emissions of carbon dioxide from transportation in the supply chain network, and the second is to maximize future savings from using biodiesel instead of diesel. These two issues are simultaneously considered in the environmental objective function. The problem is considered for a 7-year planning horizon. However, to reduce the computational complexity of the problem, a time is considered each year. The main decisions made by the model: location, allocation, capacity expansion, inventory management, and production planning.

4 Model formulation

The indices, parameters, and variables of the proposed model are defined in the Table A.1 (Appendix).

In the current study, a MILP model with two objective functions is proposed. The first objective function is presented in equation (1) which maximizes the profit using net present value method. The second objective function is presented in equation (9) which minimizes the adverse environmental effects in a certain way that will be explained.

4.1 Economic objective function

The net present value of profit is equal to the net present value of incomes, minus the net present value of costs,

$$\max \mathrm{profit}=\mathrm{income}-\mathrm{cost}.$$(1)

The net present value of the income is obtained by converting the income of each period to the present value in accordance with equation (2),

$$\mathrm{income}=\sum _{t=1}^T\mathrm{}(1+\mathrm{dr}{)}^{-\left(t-1\right)}\bullet {\mathrm{inc}}_t.$$(2)

The income of each period in accordance with equation (3) is obtained from the total income from the sale of the product to local customers, industries and export centers, as well as the sale of crude oil to export centers,

$$\mathrm{in}{\mathrm{c}}_t=\sum _{\mathrm{ex}}\mathrm{}\sum _{\mathrm{so}}\mathrm{}{q}_t^{\mathrm{so},\mathrm{ex}}·{\mathrm{oex}}_t+\sum _{\mathrm{ex}}\mathrm{}\sum _{\mathrm{dc}}\mathrm{}{q}_t^{\mathrm{dc},\mathrm{ex}}·{\mathrm{prex}}_t+\sum _{\mathrm{in}}\mathrm{}\sum _{\mathrm{dc}}\mathrm{}{q}_t^{\mathrm{dc},\mathrm{in}}·{\mathrm{prin}}_t+\sum _{\mathrm{cu}}\mathrm{}\sum _{\mathrm{dc}}\mathrm{}{q}_t^{\mathrm{dc},\mathrm{cu}}·{\mathrm{prcu}}_t\hspace{1em}\forall t.$$(3)

Similar to the present value of incomes, to obtain the present value of the costs, we convert the sum of the costs of each period to the present value in accordance with equation (4),

$$\cos t=\sum _{t=1}^T\mathrm{}(1+\mathrm{dr}{)}^{-\left(t-1\right)} · \left({\mathrm{cinv}}_t +{\mathrm{cop}}_t+{\mathrm{ctr}}_t+{\mathrm{ch}}_t\right).$$(4)

According to equation (4), costs comprise several elements: investment costs, operating costs, transportation costs, and inventory holding costs. Investment costs in accordance with equation (5) are obtained from the costs of building potential centers and the costs of increasing the capacity of refinery production units,

$${\mathrm{cinv}}_t= \sum _{\mathrm{uu}}\mathrm{}{\mathrm{cc}}_t^{\mathrm{uu}}· x_{\mathrm{uu},t} +\sum _h\mathrm{}\mathrm{c}{\mathrm{c}}_t^h· x_{h,t} · \mathrm{c}{\mathrm{a}}_h+\sum _c\mathrm{}\mathrm{c}{\mathrm{c}}_t^c· x_{c,t} +\sum _p\mathrm{}\mathrm{c}{\mathrm{c}}_t^p· x_{p,t} +\sum _u\mathrm{}\mathrm{c}{\mathrm{c}}_t^u· x_{u,t} +\sum _{\mathrm{dc}}\mathrm{}\mathrm{c}{\mathrm{c}}_t^{\mathrm{dc}}· x_{\mathrm{dc},t}+\sum _{\mathrm{br}}\mathrm{}\mathrm{c}{\mathrm{c}}_t^{\mathrm{br}}· x_{\mathrm{br},t} +\sum _{\mathrm{pu}}\mathrm{}\mathrm{c}{\mathrm{c}}_t^{\mathrm{pu}}·l_t^{\mathrm{pu}}\hspace{1em}\forall t.$$(5)

The second cost element is operating costs, which are obtained in accordance with equation (6). In units where processing is performed, we have operating costs,

$${\mathrm{cop}}_t=\sum _{\mathrm{du}}\mathrm{}\sum _{\mathrm{so}}\mathrm{}{\mathrm{cprdu}}_t · q_t^{\mathrm{so},\mathrm{du}} +\sum _{\mathrm{uu}}\mathrm{}\sum _{\mathrm{du}}\mathrm{}{\mathrm{cpruu}}_t · q_t^{\mathrm{du},\mathrm{uu}}+\sum _{\mathrm{pu}}\mathrm{}\sum _{\mathrm{du}}\mathrm{}{\mathrm{cprpu}}_t · q_t^{\mathrm{pu},\mathrm{du}}+\sum _p\mathrm{}\sum _c\mathrm{}{\mathrm{cpr}p}_t · q_t^{c,p}+\sum _u\mathrm{}\sum _p\mathrm{}{\mathrm{cpru}}_t · q_t^{p,u}+\sum _{\mathrm{br}}\mathrm{}\sum _c\mathrm{}\mathrm{cprb}{\mathrm{r}}_t · q_t^{c,\mathrm{br}}.$$(6)

The third cost element is transportation costs, which are obtained in accordance with equation (7). Transportation costs are considered between all network units where raw materials, intermediate products and final products are transported.

$$\mathrm{ct}{\mathrm{r}}_t= \mathrm{chan} ·\left(\sum _{\mathrm{so}}\mathrm{}\sum _{\mathrm{of}}\mathrm{}\mathrm{ct}{\mathrm{r}}_{\mathrm{of},\mathrm{so}} · q_t^{\mathrm{of},\mathrm{so}}+\sum _{\mathrm{ex}}\mathrm{}\sum _{\mathrm{so}}\mathrm{}\mathrm{ct}{\mathrm{r}}_{\mathrm{so},\mathrm{ex}}· q_t^{\mathrm{so},\mathrm{ex}} +\sum _{\mathrm{du}}\mathrm{}\sum _{\mathrm{so}}\mathrm{}\mathrm{ct}{\mathrm{r}}_{\mathrm{so},\mathrm{du}} · q_t^{\mathrm{so},\mathrm{du}}+\sum _{\mathrm{pu}}\mathrm{}\sum _{\mathrm{du}}\mathrm{}\mathrm{ct}{\mathrm{r}}_{\mathrm{du},\mathrm{pu}}· q_t^{\mathrm{du},\mathrm{pu}} +\sum _{\mathrm{uu}}\mathrm{}\sum _{\mathrm{du}}\mathrm{}\mathrm{ct}{\mathrm{r}}_{\mathrm{du},\mathrm{uu}} · q_t^{\mathrm{du},\mathrm{uu}}+\sum _s\mathrm{}\sum _{\mathrm{pu}}\mathrm{}\mathrm{ct}{\mathrm{r}}_{\mathrm{pu},s} · q_t^{\mathrm{pu},s}+\sum _s\mathrm{}\sum _{\mathrm{uu}}\mathrm{}\mathrm{ct}{\mathrm{r}}_{\mathrm{uu},s} · q_t^{\mathrm{uu},s}+\sum _{\mathrm{dc}}\mathrm{}\sum _s\mathrm{}\mathrm{ct}{\mathrm{r}}_{s,\mathrm{dc}} · q_t^{s,\mathrm{dc}} +\sum _{\mathrm{ex}}\mathrm{}\sum _{\mathrm{dc}}\mathrm{}\mathrm{ct}{\mathrm{r}}_{\mathrm{dc},\mathrm{ex}} · q_t^{\mathrm{dc},\mathrm{ex}}+\sum _{\mathrm{cu}}\mathrm{}\sum _{\mathrm{dc}}\mathrm{}\mathrm{ct}{\mathrm{r}}_{\mathrm{dc},\mathrm{cu}} · q_t^{\mathrm{dc},\mathrm{cu}}+\sum _{\mathrm{in}}\mathrm{}\sum _{\mathrm{dc}}\mathrm{}\mathrm{ct}{\mathrm{r}}_{\mathrm{dc},\mathrm{in}}· q_t^{\mathrm{dc},\mathrm{in}}+\sum _c\mathrm{}\sum _h\mathrm{}\mathrm{ct}{\mathrm{r}}_{h,c} · q_t^{h,c}+\sum _p\mathrm{}\sum _c\mathrm{}\mathrm{ct}{\mathrm{r}}_{c,p} · q_t^{c,p}+\sum _{\mathrm{br}}\mathrm{}\sum _c\mathrm{}\mathrm{ct}{\mathrm{r}}_{c,b\mathrm{r}}· q_t^{c,b\mathrm{r}}+\sum _u\mathrm{}\sum _p\mathrm{}\mathrm{ct}{\mathrm{r}}_{p,u} · q_t^{p,u} +\sum _{\mathrm{uu}}\mathrm{}\sum _p\mathrm{}\mathrm{ct}{\mathrm{r}}_{p,\mathrm{uu}} · q_t^{p,\mathrm{uu}}+\sum _{\mathrm{so}}\mathrm{}\sum _p\mathrm{}\mathrm{ct}{\mathrm{r}}_{p,\mathrm{so}} · q_t^{p,\mathrm{so}}+\sum _s\mathrm{}\sum _{b\mathrm{r}}\mathrm{}\mathrm{ct}{\mathrm{r}}_{\mathrm{br},s} · q_t^{\mathrm{br},s}+\sum _{\mathrm{dc}}\mathrm{}\sum _{\mathrm{br}}\mathrm{}\mathrm{ct}{\mathrm{r}}_{\mathrm{br},\mathrm{dc}} · q_t^{\mathrm{br},\mathrm{dc}}+\sum _s\mathrm{}\sum _u\mathrm{}\mathrm{ct}{\mathrm{r}}_{u,s} · q_t^{u,s}+\sum _{\mathrm{dc}}\mathrm{}\sum _u\mathrm{}\mathrm{ct}{\mathrm{r}}_{u,\mathrm{dc}} · q_t^{u,\mathrm{dc}}\right)\forall t.$$(7)

The fourth cost element is inventory holding costs, which are obtained in accordance with equation (8). This cost is calculated for Jatropha storage units, crude oil storage units, and final product storage units,

$${\mathrm{ch}}_t= \sum _{\mathrm{so}}\mathrm{}{\mathrm{inv}}_t^{\mathrm{so}}· {\mathrm{ho}}_t^{\mathrm{so}} +\sum _s\mathrm{}{\mathrm{inv}}_t^s· {\mathrm{ho}}_t^s\hspace{0.5em}+\sum _c\mathrm{}{\mathrm{inv}}_t^c· {\mathrm{ho}}_t^c\hspace{1em}\hspace{1em}\forall t.$$(8)

4.2 Environmental objective function

In this paper, the environmental objective function is obtained from the difference between the two equations. Using the first equation, the goal is to reduce the amount of carbon dioxide emissions caused by transportation on the network. With the help of the second equation, the goal is to increase the savings in carbon dioxide emissions by using biodiesel instead of gas-oil. This is shown in equations (9)–(11),

$$\sum _{t=1}^T\mathrm{}\left({\mathrm{envt}}_t- {\mathrm{envi}}_t\right).$$(9)

In equation (10), according to the amount of carbon dioxide emissions per unit distance due to network transport, the amount of carbon dioxide produced by transportation throughout the network is obtained,

$${\mathrm{envt}}_t=\mathrm{enchan} ·\left(\sum _{\mathrm{of}}\mathrm{}\sum _{\mathrm{so}}\mathrm{}\mathrm{entr} · q_t^{\mathrm{of},\mathrm{so}} · d^{\mathrm{of},\mathrm{so}} +\sum _{\mathrm{so}}\mathrm{}\sum _{\mathrm{ex}}\mathrm{}\mathrm{entr} · q_t^{\mathrm{so},\mathrm{ex}} · d^{\mathrm{so},\mathrm{ex}}\hspace{0.5em}+\sum _{\mathrm{so}}\mathrm{}\sum _{\mathrm{du}}\mathrm{}\mathrm{entr} · q_t^{\mathrm{so},\mathrm{du}} · d^{\mathrm{so},\mathrm{du}}+\sum _{\mathrm{du}}\mathrm{}\sum _{\mathrm{pu}}\mathrm{}\mathrm{entr} · q_t^{\mathrm{du},\mathrm{pu}} · d^{\mathrm{du},\mathrm{pu}}\hspace{1em}+\sum _{\mathrm{pu}}\mathrm{}\sum _s\mathrm{}\mathrm{entr} · q_t^{\mathrm{pu},s} · d^{\mathrm{pu},s}+\sum _{\mathrm{uu}}\mathrm{}\sum _s\mathrm{}\mathrm{entr} · q_t^{\mathrm{uu},s} · d^{\mathrm{uu},s}+\sum _s\mathrm{}\sum _{\mathrm{dc}}\mathrm{}\mathrm{entr} · q_t^{s,\mathrm{dc}} · d^{s,\mathrm{dc}}+\sum _{\mathrm{dc}}\mathrm{}\sum _{\mathrm{ex}}\mathrm{}\mathrm{entr} · q_t^{\mathrm{dc},\mathrm{ex}} · d^{\mathrm{dc},\mathrm{ex}}+\sum _{\mathrm{dc}}\mathrm{}\sum _{\mathrm{cu}}\mathrm{}\mathrm{entr} · q_t^{\mathrm{dc},\mathrm{cu}} · d^{\mathrm{dc},\mathrm{cu}} +\sum _{\mathrm{dc}}\mathrm{}\sum _{\mathrm{in}}\mathrm{}\mathrm{entr} · q_t^{\mathrm{dc},\mathrm{in}} · d^{\mathrm{dc},\mathrm{in}} +\sum _h\mathrm{}\sum _c\mathrm{}\mathrm{entr} · q_t^{h,c} · d^{h,c}+\sum _c\mathrm{}\sum _p\mathrm{}\mathrm{entr} · q_t^{c,p} · d^{c,p} +\sum _c\mathrm{}\sum _{\mathrm{br}}\mathrm{}\mathrm{entr} · q_t^{c,\mathrm{br}} · d^{c,\mathrm{br}}+\sum _p\mathrm{}\sum _u\mathrm{}\mathrm{entr} · q_t^{p,u} · d^{p,u}+\sum _p\mathrm{}\sum _{\mathrm{uu}}\mathrm{}\mathrm{entr} · q_t^{p,\mathrm{uu}} · d^{p,\mathrm{uu}}+\sum _p\mathrm{}\sum _{\mathrm{so}}\mathrm{}\mathrm{entr} · q_t^{p,\mathrm{so}} · d^{p,\mathrm{so}}+\sum _{\mathrm{br}}\mathrm{}\sum _s\mathrm{}\mathrm{entr} · q_t^{\mathrm{br},s} · d^{\mathrm{br},s}+\sum _{\mathrm{br}}\mathrm{}\sum _{\mathrm{dc}}\mathrm{}\mathrm{entr} · q_t^{\mathrm{br},\mathrm{dc}} · d^{\mathrm{br},\mathrm{dc}} +\sum _u\mathrm{}\sum _s\mathrm{}\mathrm{entr} · q_t^{u,s} · d^{u,s}+\sum _u\mathrm{}\sum _{\mathrm{dc}}\mathrm{}\mathrm{entr} · q_t^{u,\mathrm{dc}} · d^{u,\mathrm{dc}}\right)\forall t.$$(10)

In equation (11), according to the amount of biodiesel produced from different units of the supply chain network and the coefficient indicating a decrease in carbon dioxide emissions due to biodiesel instead of gas-oil, the amount of carbon dioxide emission reduction is obtained,

$$\mathrm{env}{\mathrm{i}}_t=\mathrm{echan} · \left( \sum _{\mathrm{uu}}\mathrm{}\sum _s\mathrm{}{q}_t^{\mathrm{uu},s}+\sum _{\mathrm{br}}\mathrm{}\sum _s\mathrm{}{q}_t^{\mathrm{br},s}+\sum _{\mathrm{br}}\mathrm{}\sum _{\mathrm{dc}}\mathrm{}{q}_t^{\mathrm{br},\mathrm{dc}}+\sum _u\mathrm{}\sum _s\mathrm{}{q}_t^{u,s}+\sum _u\mathrm{}\sum _{\mathrm{dc}}\mathrm{}{q}_t^{u,\mathrm{dc}}\right)\hspace{1em}\forall t.$$(11)

4.3 Model constraints

Material balance constraint: equations (12)–(21) show the balance between inputs and outputs to network elements. In some elements, due to the loss of inputs, the output value is less than the input, which is formulated by considering the element’s efficiency factor,

$$\sum _{\mathrm{of}}\mathrm{}{q}_t^{\mathrm{of},\mathrm{so}}+\sum _p\mathrm{}{q}_t^{p,\mathrm{so}}=\sum _{\mathrm{du}}\mathrm{}{q}_t^{\mathrm{so},\mathrm{du}}+\sum _{\mathrm{ex}}\mathrm{}{q}_t^{\mathrm{so},\mathrm{ex}}+\mathrm{plu}{s}_t^{\mathrm{so}}\hspace{1em}\forall \mathrm{so}, t,$$(12)

$$\sum _{\mathrm{so}}\mathrm{}{q}_t^{\mathrm{so},\mathrm{du}}= \sum _{\mathrm{pu}}\mathrm{}{q}_t^{\mathrm{du},\mathrm{pu}}\hspace{1em}\forall \mathrm{du}, t,$$(13)

$$\left(1-\mathrm{alpha}1\right)· \sum _p\mathrm{}{q}_t^{p,\mathrm{uu}}= \sum _s\mathrm{}{q}_t^{\mathrm{uu},s}\hspace{1em}\forall \mathrm{uu}, t,$$(14)

$$\left(1-\mathrm{alpha}2\right)· \sum _{\mathrm{du}}\mathrm{}{q}_t^{\mathrm{du},\mathrm{pu}}= \sum _s\mathrm{}{q}_t^{\mathrm{pu},s}\hspace{1em}\forall \mathrm{pu},t,$$(15)

$$\sum _{\mathrm{uu}}\mathrm{}{q}_t^{\mathrm{uu},s}+\sum _{\mathrm{br}}\mathrm{}{q}_t^{\mathrm{br},s}+\sum _u\mathrm{}{q}_t^{u,s}+\sum _{\mathrm{pu}}\mathrm{}{q}_t^{\mathrm{pu},s}= \sum _{\mathrm{dc}}\mathrm{}{q}_t^{s,\mathrm{dc}}+\mathrm{plu}{s}_t^s\hspace{1em}\forall s,t,$$(16)

$$\sum _h\mathrm{}{q}_t^{h,c}= \sum _p\mathrm{}{q}_t^{c,p}+\sum _{\mathrm{br}}\mathrm{}{q}_t^{c,\mathrm{br}}+{\mathrm{plus}}_t^c\hspace{1em}\forall c, t,$$(17)

$$\left(1-\mathrm{alpha}3\right)· \sum _c\mathrm{}{q}_t^{c,p}= \sum _{\mathrm{so}}\mathrm{}{q}_t^{p,\mathrm{so}}+\sum _u\mathrm{}{q}_t^{p,u}+\sum _{\mathrm{uu}}\mathrm{}{q}_t^{p,\mathrm{uu}}\hspace{1em}\forall p, t,$$(18)

$$\left(1-\mathrm{alpha}4\right)· \sum _c\mathrm{}{q}_t^{c,\mathrm{br}}= \sum _s\mathrm{}{q}_t^{\mathrm{br},s}+\sum _{\mathrm{dc}}\mathrm{}{q}_t^{\mathrm{br},\mathrm{dc}}\mathrm{v}\forall \mathrm{br}, t,$$(19)

$$\left(1-\mathrm{alpha}5\right)· \sum _p\mathrm{}{q}_t^{p,u}= \sum _s\mathrm{}{q}_t^{u,s}+\sum _{\mathrm{dc}}\mathrm{}{q}_t^{u,\mathrm{dc}}\hspace{1em}\forall u, t.$$(20)

Demand constraint: equations (22)–(25) indicate demand satisfaction. Equation (22) shows the satisfaction of crude oil demand for export terminals, equation (23) shows satisfaction of product demand for export terminals, equation (24) shows satisfaction of product demand for local customers and equation (25) shows satisfaction of product demand for industries,

$$\sum _u\mathrm{}{q}_t^{u,\mathrm{dc}}+\sum _{\mathrm{br}}\mathrm{}{q}_t^{\mathrm{br},\mathrm{dc}}+ \sum _s\mathrm{}{q}_t^{s,\mathrm{dc}}= \sum _{\mathrm{ex}}\mathrm{}{q}_t^{\mathrm{dc},\mathrm{ex}}+\sum _{\mathrm{in}}\mathrm{}{q}_t^{\mathrm{dc},\mathrm{in}}+\sum _{\mathrm{cu}}\mathrm{}{q}_t^{\mathrm{dc},\mathrm{cu}}\hspace{1em}\hspace{1em}\forall \mathrm{dc}, t,$$(21)

$$\sum _{\mathrm{so}}\mathrm{}{q}_t^{\mathrm{so},\mathrm{ex}}\ge \mathrm{de}{x}_t^{\mathrm{ex}}\hspace{1em}\hspace{1em}\forall \mathrm{ex}, t,$$(22)

$$\sum _{\mathrm{dc}}\mathrm{}{q}_t^{\mathrm{dc},\mathrm{ex}}\ge \mathrm{dp}{r}_t^{\mathrm{ex}}\hspace{1em}\hspace{1em}\forall \mathrm{ex}, t,$$(23)

$$\sum _{\mathrm{dc}}\mathrm{}{q}_t^{\mathrm{dc},\mathrm{cu}}\ge \mathrm{dp}{r}_t^{\mathrm{cu}}\hspace{1em}\hspace{1em}\forall \mathrm{cu}, t,$$(24)

$$\sum _{\mathrm{dc}}\mathrm{}{q}_t^{\mathrm{dc},\mathrm{in}}\ge \mathrm{dp}{r}_t^{\mathrm{in}}\hspace{1em}\hspace{1em}\forall \mathrm{in}, t.$$(25)

Capacity constraint: equations (26)–(39) are related to considering network elements’ capacity for inputs and outputs. For potential points, the availability of that location is to be first checked, and if available, the capacity of that location to enter and exit the stream would be considered. In the case of refinery production units, the capacity varies according to the possibility of increasing production capacity, which is shown in equations (30) and (31),

$$\sum _{\mathrm{so}}\mathrm{}{q}_t^{\mathrm{of},\mathrm{so}}\le \hspace{0.5em}c{a}_{\mathrm{of}}\hspace{1em}\hspace{1em}\forall \mathrm{of}, t,$$(26)

$$\sum _{\mathrm{of}}\mathrm{}{q}_t^{\mathrm{of},\mathrm{so}}+\sum _p\mathrm{}{q}_t^{p,\mathrm{so}}\le \hspace{0.5em}c{a}_{\mathrm{so}}\hspace{1em}\hspace{1em}\forall \mathrm{so}, t,$$(27)

$$\sum _{\mathrm{so}}\mathrm{}{q}_t^{\mathrm{so},\mathrm{du}}\le \hspace{0.5em}c{a}_{\mathrm{du}}\hspace{1em}\hspace{1em}\forall \mathrm{du}, t,$$(28)

$$\sum _p\mathrm{}{q}_t^{p,\mathrm{uu}}\le \hspace{0.5em}c{a}_{\mathrm{uu}} · y_{\mathrm{uu},t}\hspace{1em}\hspace{1em}\forall \mathrm{uu}, t,$$(29)

$$\sum _{\mathrm{du}}\mathrm{}{q}_t^{\mathrm{du},\mathrm{pu}}\le \hspace{0.5em}c{a}_t^{\mathrm{pu}}\hspace{1em}\hspace{1em}\forall \mathrm{pu}, t,$$(30)

$${\mathrm{ca}}_{t+1}^{\mathrm{pu}}\le {\mathrm{ca}}_t^{\mathrm{pu}}+l_{t+1}^{\mathrm{pu}}\hspace{1em}\hspace{1em}\forall \mathrm{pu}, t,$$(31)

$$\sum _{\mathrm{uu}}\mathrm{}{q}_t^{\mathrm{uu},s}+\sum _{\mathrm{br}}\mathrm{}{q}_t^{\mathrm{br},s}+\sum _{\mathrm{pu}}\mathrm{}{q}_t^{\mathrm{pu},s}+\sum _u\mathrm{}{q}_t^{u,s}\le {\mathrm{ca}}_s\hspace{1em}\hspace{1em}\forall s, t,$$(32)

$$\sum _{\mathrm{so}}\mathrm{}{q}_t^{\mathrm{so},\mathrm{ex}}+\sum _{\mathrm{dc}}\mathrm{}{q}_t^{\mathrm{dc},\mathrm{ex}}\le {\mathrm{ca}}_{\mathrm{ex}}\hspace{1em}\hspace{1em}\forall \mathrm{ex}, t,$$(33)

$$\sum _c\mathrm{}{q}_t^{h,c}\le {\mathrm{ca}}_h · y_{h,t}\hspace{1em}\hspace{1em}\forall h, t,$$(34)

$$\sum _h\mathrm{}{q}_t^{h,c}\le {\mathrm{ca}}_c · y_{c,t}\hspace{1em}\hspace{1em}\forall c, t,$$(35)

$$\sum _c\mathrm{}{q}_t^{c,p}\le {\mathrm{ca}}_p · y_{p,t}\hspace{1em}\hspace{1em}\forall p, t,$$(36)

$$\sum _c\mathrm{}{q}_t^{c,\mathrm{br}}\le {\mathrm{ca}}_{\mathrm{br}} · y_{\mathrm{br},t}\hspace{1em}\hspace{1em}\forall \mathrm{br}, t,$$(37)

$$\sum _p\mathrm{}{q}_t^{p,u}\le \hspace{0.5em}{\mathrm{ca}}_u · y_{u,t}\hspace{1em}\hspace{1em}\forall u, t,$$(38)

$$\sum _{\mathrm{br}}\mathrm{}{q}_t^{\mathrm{br},\mathrm{dc}}+\sum _u\mathrm{}{q}_t^{u,\mathrm{dc}}+\sum _s\mathrm{}{q}_t^{s,\mathrm{dc}}\le \hspace{0.5em}{\mathrm{ca}}_{\mathrm{dc}} · y_{\mathrm{dc},t}\hspace{1em}\hspace{1em}\forall \mathrm{dc}, t.$$(39)

Logical constraint: In this model, we have two types of binary variables: construction variables and availability variables. If a facility is built in one course, it can be used (available) from later courses. So if y (t − 1) is one, it means it is available from the previous period and no longer needs to be constructed in this period (x(t) = 0). In fact, it must have been built once from the first period to before the t period, and there is no need to rebuild it as shown in equations (40)–(46),

$$y_{\mathrm{uu},t}=y_{\mathrm{uu},t-1}+x_{\mathrm{uu},t}\hspace{1em}\hspace{1em}\forall \mathrm{uu}, t>1,$$(40)

$$y_{h,t}=y_{h,t-1}+x_{h,t}\hspace{1em}\hspace{1em}\forall h, t>1,$$(41)

$$y_{c,t}=y_{c,t-1}+x_{c,t}\hspace{1em}\forall c, t>1,$$(42)

$$y_{p,t}=y_{p,t-1}+x_{p,t}\hspace{1em}\hspace{1em}\forall p, t>1,$$(43)

$$y_{u,t}=y_{u,t-1}+x_{u,t}\hspace{1em}\hspace{1em}\forall u, t>1,$$(44)

$$y_{\mathrm{br},t}=y_{\mathrm{br},t-1}+x_{\mathrm{br},t}\hspace{1em}\hspace{1em}\forall \mathrm{br}, t>1,$$(45)

$$y_{\mathrm{dc},t}=y_{\mathrm{dc},t-1}+x_{\mathrm{dc},t}\hspace{1em}\hspace{1em}\forall \mathrm{dc}, t>1.$$(46)

Also, for the first period, availability means construction. This is shown in equations (47)–(53),

$$y_{\mathrm{uu},t}=x_{\mathrm{uu},t}\hspace{1em}\hspace{1em}\forall \mathrm{uu},t=1,$$(47)

$$y_{h,t}=x_{h,t}\hspace{1em}\hspace{1em}\forall h,t=1,$$(48)

$$y_{c,t}=x_{c,t}\hspace{1em}\hspace{1em}\forall c,t=1,$$(49)

$$y_{p,t}=x_{p,t}\hspace{1em}\hspace{1em}\forall p,t=1,$$(50)

$$y_{\mathrm{br},t}=x_{\mathrm{br},t}\hspace{1em}\hspace{1em}\forall \mathrm{br},t=1,$$(51)

$$y_{u,t}=x_{u,t}\hspace{1em}\hspace{1em}\forall u,t=1,$$(52)

$$y_{\mathrm{dc},t}=x_{\mathrm{dc},t}\hspace{1em}\hspace{1em}\forall \mathrm{dc},t=1.$$(53)

The increase in refinery’s capacity production units cannot exceed a certain level. It is also possible to increase the capacity from the second period. The increases, as mentioned earlier, can be seen in equations (54) and (55),

$$l_t^{\mathrm{pu}}=0\hspace{1em}\hspace{1em}\forall \mathrm{pu}, t=1,$$(54)

$$\sum _t\mathrm{}{l}_t^{\mathrm{pu}}\le \mathrm{ca}‐\mathrm{peak}\hspace{1em}\hspace{1em}\forall \mathrm{pu}.$$(55)

Inventory constraint: The inventory in each period is equal to the sum of the inventory of the previous period, and is also equal to the difference between the outputs and inputs to each storage centre in the same period, all of which are shown in equations (56)–(58),

$${\mathrm{inv}}_{t+1}^{\mathrm{so}}={\mathrm{inv}}_t^{\mathrm{so}}+{\mathrm{plus}}_{t+1}^{\mathrm{so}}\hspace{1em}\hspace{1em}\forall \mathrm{so},t,$$(56)

$${\mathrm{inv}}_{t+1}^s={\mathrm{inv}}_t^s+{\mathrm{plus}}_{t+1}^s\hspace{1em}\hspace{1em}\forall s,t,$$(57)

$${\mathrm{inv}}_{t+1}^c={\mathrm{inv}}_t^c+{\mathrm{plus}}_{t+1}^c\hspace{1em}\hspace{1em}\forall c,t.$$(58)

The inventory of each storage centre’s first period is equal to the difference between the outputs and inputs of the first period in the same storage centre,

$${\mathrm{inv}}_t^{\mathrm{so}}={\mathrm{plus}}_t^{\mathrm{so}}\hspace{1em}\hspace{1em}\forall \mathrm{so}, t=1,$$(59)

$${\mathrm{in}v}_t^s={\mathrm{plus}}_t^s\hspace{1em}\hspace{1em}\forall s, t=1,$$(60)

$${\mathrm{inv}}_t^c={\mathrm{plus}}_t^c\hspace{1em}\hspace{1em}\forall c, t=1.$$(61)

5 Solution approach

Several methods have been proposed to solve multi-objective problems. These methods are classified into three categories: priori, interactive, and posteriori, depending on the type of decision-maker’s role in decision-making. In priori methods, the decision maker is involved before the problem is solved. In interactive methods, communication with the decision maker is continuous and according to the received feedback, the calculations continue to converge to the desired result. In posteriori methods such as the ε-constraint method, a set of optimal Pareto points is first obtained, which the decision makers can choose according to their own priorities. In this paper, the ε-constraint method is used to solve the two-objective model. First, each of the goals is optimized separately, the results of which can be seen in Table 2. Then, one goal is considered as a constraint and the other is optimized to get the Pareto border according to Figure 2.

6 Case study

In order to show the performance of the proposed model, the gas-oil and biodiesel supply network in Iran has been studied. The network includes 44 oil fields, 16 crude oil storage centers, 11 export terminals, 9 distillation units, 9 refinery production units, 9 potential locations for upgrading gas-oil supply chain units, 9 gas-oil and biodiesel storage centers, 10 potential locations for harvesting Jatropha, 10 potential locations for collecting Jatropha, 10 potential locations for pre-processing sites, 6 potential locations for upgrading units in the biodiesel supply chain, 6 potential locations for bio-refinery sites, 37 potential locations for distribution centers, 31 local customer centers, and finally 43 locations for Industry centers. The time horizon is 20 years. The provided information is summarized in the Table 3 (for more information please see Tables A.2, A.3 and A.4 from the Appendix).

Figure 3 shows the points in the network of case study. As can be seen in the figure, in the center of Iran the density of points is low. Conversely, in the southwestern border cities, the density is very high. The highest density rates of oil fields and other network elements exist in Khuzestan and Bushehr provinces.

Figure 3 shows all potential and actual points. After the equations in the model are solved and the answers are obtained, the set of network points will be as Figure 4. Crude oil is transported from 44 oil fields to crude oil storage centers. Crude oil is transferred directly to 11 export terminals or enters the country’s refinery network through 16 crude oil storage centers to produce its derivatives. After being transferred to 9 refineries, the crude oil first enters the distillation tower and then enters the refinery’s production units. The produced gas oil is transferred to 9 product storage centers. All of these elements are typically present in the diesel supply chain and are actual. Data related to the elements have been extracted from the hydrocarbon balance sheet of Iran [58]. In the biodiesel supply chain, the 10 potential Jatropha planting centers transfer Jatropha to its collection centers. These collection centers have been selected from 10 potential centers. Jatropha is either moved directly from collection centers to bio-refineries or transferred to pre-processing units. Bio-refineries are selected from 6 potential centers and pre-processing units from 10 potential centers. After pre-processing, the bio-slurry enters the crude oil storage and bio-oils directly enter the upgrading units at oil refineries. These upgrading units are selected from 9 potential units. The materials coming out of the pre-processing units can be turned into the final product in the upgrading units that are in the biodiesel supply chain. Upgrading units in the biodiesel supply chain have been selected from 6 potential units. Data on potential locations of biodiesel supply chain elements are given in papers [11] and [59]. Biodiesel produced in bio-refineries and upgrading units in the biodiesel supply chain can be transported directly to distribution centers or first to product storage centers and then to distribution centers. Distribution centers are selected from 37 potential centers. Finally, fuel is transported from distribution centers to local customers in 31 provinces and industries that are the 43 major diesel power plants.

6.1 Results and discussion

The proposed model is coded in GAMS 24.1 optimization software and solved by CPLEX solver. The model characteristics are illustrated in Table 4.

In the Table 5, three models of gas-oil supply chain, non-integrated gas oil and biodiesel supply chain, and integrated gas oil and biodiesel supply chain (study done in this article) have compared. As can be seen, although the costs of the biodiesel supply chain increase compared to the gas oil supply chain due to the construction of some facilities, the amount of the environmental objective function improves. Also, as mentioned in this article, if we use the supply chain integration approach, we have economic savings compared to the non-integrated state.

Given that the model has been formulated and solved for a 20-year time horizon, it is necessary to analyze the effects of changes in demand over the years. In this regard, we analyze the effect of demand changes up to 5% more or less on model elements. Given that the importance of economic and environmental goals in different years varies according to the policies adopted, the analysis is performed for both objective functions.

Figure 5 shows the changes in total profit relative to the change in demand. In both objective functions, as the demand increases or decreases, the amount of total profit decreases. To analyze this issue, it is necessary to identify the elements that make up the total profit and have them studied. In general, it can be said that with the increase in demand, although revenues increase, the rate of increase in expenditures to meet the specific demand is higher than the increase in revenues. Moreover, the decrease in demand, as the costs also decrease, the rate of decrease in revenues is higher than the rate of decrease in costs.

Total income is generated through sales as much as demand, so the amount of income is equal for each economic and environmental goal. Figure 6 shows the rate of change in total income per change in demand. With increasing demand, total income will also increase.

The total cost increases with increasing demand. As shown in Table 6, costs vary between 5% and 10% when they depend on an economic or environmental objective. These percentages vary by several hundred milliards dollars. As shown in Figure 7, the graph’s slope is less in the former parts of the graph. Given that the cost ratio is inversely related to total profit, Figure 5 shows that the first part of the diagram is sloping more.

The total amount of costs is derived from the sum of investment, transportation, operating, and holding costs. Due to the fact that the value of t is one year, in response to the model, the inventory has not been kept for 1 year. Therefore, investment, transportation, and operating costs must be investigated.

As shown in Figure 8, when the objective function is to maximize profits, investment costs, operating costs and transportation costs all increase with increasing demand. Also, in higher demand rates, the slope of changes in these costs increases with the change in demand. As can be seen in Figure 9, investment costs in both economic and environmental functions do not change in the same way. In the environmental objective function, because the cost is not considered important, the amount of investment costs does not coincide with demand change. With the change in demand in order to minimize the environmental impact, construction sites will also change and may decrease or increase the investment costs. In the case of operating costs and transportation costs, they increase as demand increases.

Changing environmental impacts by changing demand is another critical issue, which is shown in Figure 10 for both economic and environmental objectives. As expected, as the demand increases, the amount of environmental impact increases, which is less when the objective is to minimize the environmental impact.

Interest rate changes are one of the essential factors in the profitability of the entire supply chain in its time horizon. Figure 11 shows the total profit changes per change in interest rates. In two ways, the chart is upward; Firstly, income is higher than cost, therefore with the increase in interest rates, the difference in current value of income and cost will increase. Secondly, a large part of the investment costs are incurred in the first period and therefore are not affected by the interest rate changes.

Changes in total profit relative to price changes can be seen in Figure 12. As it is known, due to the higher price and high volume of exports, the most significant impact is due to the increase in export prices. The least impact is on changes in selling prices to industries because industries seem to have less demand. Figure 13 shows the amount of income generated by selling the product in different ways. In Figure 12, price changes for exports have a much more significant impact on overall profits. Figure 13 also shows that most of the income comes from exports and a very tiny percentage from the industry.

7 Conclusion and future research direction

In recent years, finding alternative energy sources to fossil fuels has become an important issue in the world. In addition to reducing environmental pollution and being renewable, these resources must be economical. Biofuels are considered to be a good source of energy due to their credible properties.

This paper examines the composition of the oil-gas supply chain and the biodiesel supply chain and provides a model for using the oil gas network infrastructure to produce biodiesel to make biofuel production more economical. In this paper, for the first time, all the two supply chains’ elements are considered and optimized with integration. All location decisions, selection of the connection point of two supply chains, allocation, production planning, inventory management, and capacity expansion are all done by solving the MILP model. In order to consider environmental aspects, the function of the second objective is also used. In addition to considering the amount of carbon dioxide emissions due to transportation in the network, the environmental objective function also considers the reduction of carbon dioxide emissions due to the use of biodiesel instead of gas oil. In order to better evaluate the model, a real-world case study was performed in Iran and according to the data gathered, the model was solved and sensitivity analysis was performed. The multi-objective model was solved using the ε-constraint method and the Pareto boundary was obtained.

The model results show that with increasing demand, total profit does not necessarily increase because as demand increases, increasing costs is more considerable than increasing incomes. As demand declines, incomes decline more than costs do, and total profit declines as well. Therefore, at a certain point in demand, the total profit is the highest. Also, in order to make the whole supply chain more profitable, the effect of increasing export prices is more than increasing sales prices to local customers or industries. By reducing the production costs of biodiesel, the proposed model on the one hand, makes it more economical to use instead of gas oil, and one the other hand, it is very effective in reducing the environmental pollution.

The above model can be expanded by considering social issues in order to achieve sustainable development. Also, considering uncertainty in important parameters such as demand, selling price and so forth can help make better decisions. Future researchers can consider second-generation biomass such as livestock waste and municipal wastewater that have the reliable potentiality in energy production.

References

Appendix

All Tables

All Figures