The traditional energy resources allocation problem is concerned with the allocation of limited resources among the end-uses such that the overall return is maximized. In the past, several techniques have been used to deal with such a problem. Ramanathan and Ganesh used integrated goal programming to optimally match seven energy resources usable for lighting in households against 12 objectives representing the energy-economy-environmental system. Hoog and Hobbs discussed an integrated resource planning model, which considered several objectives such as cost, emissions, regional economic impact and net value to customers. More recently, fuzzy dynamic programming has been applied to the resource allocation problem, adding more flexibility to the selection procedure used by decision makers. It can be concluded that the energy sector is an essential part of the whole economic system and that modern energy planning must incorporate social and environmental objectives, leading to a multi-objective optimization problem.

The economic objectives in this paper consider costs, efficiency, energy conservation, and employment generation. The environmental objectives account for environmental-friendliness factors. The objectives are first quantified, then transformed into mathematical language to obtain a multi-objective allocation model which will be solved using pre-emptive goal programming techniques.

Lebanon is a country on the East Mediterranean Sea with an area of 10,452 km². It has approximately four million people in 800,000 households (five persons per household). Since the end of the Lebanese war, the need for energy has increased creating a gap between supply and demand. To bridge this gap, there is a need to develop a strategy that can help to allocate optimally the various energy resources to energy needs. Table 1 presents the total annual demand of household end-uses.

The objective of this paper is to allocate optimally to each end-use a certain amount of power, ?_i, to be supplied by a given resource. The energy resources were selected based on either their present use or potential availability in Lebanon. On the other hand, the end uses such as cooking, water pumping, lighting, space heating, hot water and home appliances reflect the existing major applications in the household sector. Altogether, 11 energy resources and six end uses were identified, of which 49 resource-end-use combinations have been selected for the formulation of the current problem.

Six objective functions are considered in this work. What follows is a description of these objectives, together with the corresponding mathematical formulation.

The main factor affecting the choice of technology is generally cost-effectiveness. The term ‘cost’ refers to the actual cost of bringing the energy resource to the end-use point. Table 3 provides details on the unit cost of energy in $/kWh for the different combinations.

We need to maximize the system efficiency of a particular resource-end-use combination which is the total efficiency of energy utilization, including the efficiencies of production, distribution, and end-use utilization. The energy of production and distribution is referred to as the external efficiency and it is the system efficiency just before the end-use point.

This objective function is represented as:
max??_i×?_i

where ?_i represents the efficiency coefficient for cooking, water pumping, lighting, heating, hot water and home appliances, respectively.

Lebanon is a fuel-importing country. Therefore, it is desirable that the use of petroleum products and natural gas be minimized.

This objective function is represented as:
min??_i

where i=1, 6, 7, 10, 14, 15, 21, 22, 25, 30, 31, 34, 40, 41, 46 and 47.

The use of locally available resources must be addressed to reduce the vulnerability of the country’s supply-system to some uncertainties (transport strikes, breakdowns in power supply, etc.).

This objective function is represented as:
max??_i

where i=2, 3, 9, 11, 17, 18, 24, 26, 27, 33, 35, 36, 43 and 49.

One important criterion for selecting an energy resource is its ability to make available as many jobs as possible. Table 5 provides details of the number of people employed in sectors related to various energy resources, along with the total consumption of energy resources for the year 1995.

The objective function is represented as:
max?e_i×?_i

where e_i denotes the number of persons employed per kWh of energy allocated for a combination ‘i’.

Three major pollutants are considered to describe the impact of human activities on the air quality. These are carbon oxides (CO and CO₂), sulfur oxides, and nitrogen oxides. The emissions due to the combustion of any energy resource depend on its composition. In this paper, three types of fuels are adopted: solids (fuelwood) and liquids (diesel, fuel oil), and gaseous fuels (natural gas, biogas). The emissions per kWh of carbon, sulfur and nitrogen calculated for the diesel energy resource, natural gas, biogas, fuelwood and fuel oil, are shown in Table 6. The same approach is used to calculate the emissions of each energy resource allocated for an end-use sector. Table 7 shows the calculated emissions in kg/kWh for cooking, water pumping, lighting, heating, hot water and home appliances, respectively. The objective function is represented as:

min?E_i×?_i

The constraints in this project have been determined based on field surveys done by the authors on household energy consumption in Lebanon. Ten constraints are considered in this problem. These are:

1. Total cooking-energy demand 7.9962 × 10⁹ MJ/year.

i.e. ??_i7.9962×10⁹,where i=1,2,3…9.

2. Total pumping-energy demand 6.3072 × 10⁸ MJ/year.

i.e. ??_i6.3072×10⁸,where i=10,11,12,…17.

3. Total lighting energy demand 1.26 × 10⁹ MJ/year.

i.e. ??_i1.26×10⁹,where i=18,19,20,…24.

4. Total heating energy demand 3.2382 × 10⁹ MJ/year.

i.e. ??_i3.2382×10⁹,where i=25,26,27,…33.

5. Total hot-water energy demand 3.007 × 10⁹ MJ/year.

i.e. ??_i3.007×10⁹,where i=34,35,36,…43.

6. Total home-appliances energy demand 6.6078 × 10⁹ MJ/year.

i.e. ??_i6.6078×10⁹,where i=44,45,46,…49.

7. Limit on solar thermal cooking. The thermal stoves cannot cook all varieties of food and therefore they cannot meet the total cooking requirement. As such, they can be used for low-temperature cooking purposes only, which accounts for about 40% of the total cooking requirement, which is equal to 3.19848 × 10⁹ MJ/year.This constraint is represented as: ?₄3.19848×10⁹.

8. In Lebanon, the cattle population is 90,000. Assuming each animal provides 12.5 kg of waste per day (10.07 MJ/day of energy), the availability of power from biogas is 906,300 MJ/year.This constraint is represented as: ?_i/?_i906,300where i=2, 11, 18, 26 and 35 and ?_i is the end-use device efficiency: ?₂=50%, ?₁₁=45%, and ?₁₈=?₂₆=?₃₅=1%.

9. Availability of hydro-electric power. The average kWh produced averaged over 19 years from 1974 until 1992 is 790.45 × 10⁶ kWh/year (2.84562 × 10⁹ MJ/year).This constraint is represented as: ?₉+?₁₇+?₂₄+?₃₃+?₃₄+?₄₉2.84562×10⁹.

10. An upper-bound constraint must be imposed on some variables to secure a solution when solving a maximization problem. Otherwise, the solution will be unbounded. The variables in constraints 8 and 9 are bounded from the upper side, so all the other variables need to be bounded.

This constraint is represented as: ??_i 22.73912×10⁹ where i=1, 3, 5, 6, 7, 8, 10, 12, 13, 14, 15, 16, 19, 20, 21, 22, 23, 25, 27, 28, 29, 30, 31, 32, 34, 36, 37, 38, 39, 40, 41, 42, 44, 45, 46, 47 and 48; the right-hand side being the total energy demand for the six end-use sectors.