*3.3. Objective Function Model Optimizing Energy Security Cost*

Energy security is a factor that is associated with national security and the availability of natural resources. In this context, the security of the energy supply is of the utmost importance. It is worth mentioning that energy security plays the most important role for decision-makers, that is to say, this factor is highly influential on the price of energy resources, and political power and relation among exporter and importer counties.

The cost of energy security should be quantized and have a measurement. All applications to secure energy should be taken into account, e.g., increasing fuel costs from a source to reduce consumption from an unsafe and insecure source, costs of infrastructure construction to create new and safe systems, and the political costs of securing and storing energy resources. Accordingly, in a country which holds energy policy as its priority, circumstances are different to those where cheaper energy is the objective.

Threats endangering the transmission and consumption of fuel in any of the subsectors can be categorized into seven general groups:

Investment threats: This threat is considered as a physical threat that affects the external or physical nature of fuel transmission. Delay or lack of investment due to the administrative bureaucracy and the complexity of the country's structure in absorbing domestic and foreign capital, legal restrictions, international sanctions, and taxes, uncertainty about the fate of investment, the high risk of investing in the particular project, and the lack of return on investment are among the investment threats.

Technical threats: This threat can disrupt the supply. Technical problems in the process of the production can result in waste or no fuel extraction, however, those problems related to gas transmission pipelines are likely to be solved by storing it or bypassing to injection fields.

The threats of demand management and consumption growth: Mismanagement in demand and supply can lead to a threat. If a supplier is unable to provide storage facilities, consumption fluctuations can become problematic. In cases where a supplier has not considered urgent matters of sudden cold or gradual growing demand, the distribution could face difficulties due to lack of proper infrastructure.

Other physical threats: Earthquakes, pipeline failure, and terrorist attacks on facilities are among these threats. Some of these threats are taken seriously and some less seriously in Iran.

Pricing and marketing threats: These threaten the security of fuel exports. Pricing could threaten supply security by conflicts before and after contract. Energy security imposes costs on the supplier and the importer. Due to security issues and administrative allocation strategy, competitive pricing is a conflict between the authority and the private sector, making the market impossible.

Internal management threats: In addition to geopolitical issues which are compromised with the nature of the energy sector, national problems, such as economic crises and mass strikes, influence the security of supply.

Foreign and international political threats: Foreign countries which are stakeholders in energy trade in the region could be counted as threats by implication. In addition, actions implemented by other countries or unions, such as sanctions, could highly threaten safe and secure supply.

The objective function and constraints are as follows:

$$\text{Min } P\_1 d\_1^+ \text{ } \text{ } P\_2 d\_2^+ \text{ } \text{ } P\_3 d\_3^+ \text{ } \text{ } P\_3 d\_4^+ \text{ } \text{ } P\_5 d\_5^+ \text{ } \text{ } P\_6 d\_6^+ \text{ } \text{ } P\_7 d\_7^+ \tag{9}$$

Subject to:

$$\sum\_{i} \sum\_{j} \mathbb{C}\_{ij} \cdot X\_{ij} = Z\_i \tag{10}$$

$$\sum\_{k=1}^{i} \sum\_{l=1}^{j} X\_{kl} = \sum PR\_k \tag{11}$$

$$d\_{k}^{+}, d\_{k}^{-} = 0; \quad \forall \ k \in i \tag{12}$$

$$X\_{ij\prime} \; d\_k^+ \; d\_k^- \; \geq 0 \; ; \quad \forall \; k \in i \tag{13}$$

In this paper, the developed model is a seven-objective and linear model. Therefore, goal programming and lexicographer methods have been used to solve the MODM models. It is worth noting that Lingo software is used to solve this problem.
