**1. Introduction**

Nowadays, natural gas (NG) is the main source of energy in many countries. Being more efficient and having less carbon, NG is increasingly used in different sectors rather than other fossil fuels and non-renewable energy sources [1]. While the global portion of oil consumption in the energy sector fell from 45% in 1970 to 43.6% in 2020, NG experienced an increase from 17.2% to 33.7% in a similar period [2]. Iran is known to be among the main suppliers of NG in the world and its own region. Having been explored and found to have more than 33.5 trillion cubic meters of NG reserves in 2015, Iran is the second-biggest owner of NG reserves globally, and it is estimated to own almost 18% of all explored NG on the Earth (Figure 1).

Importantly, explorations by Iran over the past two decades increased its global proportion by 2% [2]. Energy use and consequent NG consumption in Iran has dramatically increased over the past 10 years. Despite all mentioned facts, and its increased extraction, Iran is currently an importer of NG from Turkmenistan, and in search of new NG exporters [3]. It is worth mentioning that there is a reliable planning and allocation sector which is associated with population and consumption, and that forecasting is crucial.

**Citation:** Meidute-Kavaliauskiene, I.; Davidaviciene, V.; Ghorbani, S.; Sahebi, I.G. Optimal Allocation of Gas Resources to Different Consumption Sectors Using Multi-Objective Goal Programming. *Sustainability* **2021**, *13*, 5663. https://doi.org/10.3390/su13105663

Academic Editors: Farhad Taghizadeh–Hesary and Han Phoumin

Received: 23 February 2021 Accepted: 12 May 2021 Published: 18 May 2021

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**Figure 1.** Country natural gas reserves (Data from eoearth.org, 2020, access on 3 October 2020).

Because of its operational features, NG can be distributed to different sectors of energy consumers. NG is the main fuel used by petrochemical and refinery industries to gain added value. However, a significant proportion of NG is consumed in transportation, domestic heating and cooking, and industry.

NG allocation should be associated with the expansion of social welfare over time, and this measure must be considered as the opportunity cost of gas distribution to various sectors. Consequently, the cost of allocation between the NG exploitation time and various sectors' uses should be minimized. Hence, a function of the profit and costs of gas allocation to the different sectors should be considered [4]. In fact, optimally allocating limited sources of NG to different consumers is a crucial political and economic challenge. Hence, this paper aims to study the optimal allocation of NG to distinct sectors in Iran by developing an optimization model.

One of the major factors playing a key role in optimally allocating resources is predicting future consumptions in order to make it applicable. There are several approaches to forecast energy demand, e.g., artificial neural network, data-driven model, time-series analysis such as ARIMA, etc. [5–7]. However, in this paper, forecasts of future energy consumptions in Iran are extracted from energy balance sheets by simple statistical methods. As well, different approaches and optimization algorithms, such as fuzzy goal programming [8], weighted goal programming [9], and mixed integer programming [10], are employed by operations research scholars to optimize energy resource allocation.

In this paper, a multi-objective goal programming method is employed to optimally allocate NG to the different Iranian consumers for the horizon of 2025. The rest of the paper is organized as follows: in Section 2 the literature is reviewed, in Section 3 the methodology and the mathematical model are presented, in Section 4 the results are demonstrated and discussed, and, finally, there is a conclusion on the research and the results.
