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Introduction

The current high rates of global energy consumption causes serious concerns with needs for awareness; where a large chunk of the world’s energy is produced by a small group of nations. Energy forecasts have shown that these mineral resources are not unlimited (European Commission, 2013).  Another issue that the current global energy consumption poses is its flipside; environmental pollution from fossil fuel generation and consumption, raising concerns regarding global warming and global health deterioration (Goldemberg, 2000).

 In order for the aforementioned issues to be addressed, renewable and sustainable energy sources are to be exploited, improved, modified, and championed. Biomass is an excellent choice due to its “worldwide” availability, abundance, variability, versatility, high yield and also its ability to act as a near-perfect substitute for fossil fuel (Faaij, 2000). Current research has depicted that some parts of Latin America and Europe do possess high potential for generating bio-energy compared to other parts of the world, owing to factors like vast vegetation agglomeration, optimum population densities and a cultural adoption of agriculture. This explains why some countries are basically exporters of bio-energy while others find themselves at the other end of a fine spectrum; translating to inflated costs and energy losses due to bio-energy transport (Hoogwijk et al., 2003; Damen and Faaij, 2003; Agterberg and Faaij, 1998). The world has undergone massive changes over time mainly as a result of global energy and its implied costs from its demand, strict doctrines with respect to the environment, and the global energy tussle; notably in renewability, hegemony, energy economics and quality. Optimization has been depicted, and demonstrated to be an effective tool for solving these issues (Han et al., 2021). 

Process and plant design operations have been modified to minimize cost, maximize efficiency and improve economic effects by increasing profitability. In the global industry, efforts have been made to define and implement optimal operating conditions and process variables, in a bid to improve efficiency and reduce cost.  These efforts define and describe the term “Optimization”; obtaining the most efficient and effective solution to a problem among the feasible solutions (Geng et al., 2017).

Optimization problems are pervasive industrially, most notably in the global energy industry. There are various concepts to be treated like “Loss reduction to the barest minimum”, “cost reduction to the barest minimum”, “profit increment to the maximum”, “optimal use of available resources”, and “the use of the least possible efforts” in a bid to maximize profitability (Chen et al., 2020). A basic industrial problem may be described as follows: representing the whole process with certain mathematical equations and/or some statistical data. There would be an objective either to minimize cost or to maximize a certain dependent process variable. The aim would be to obtain the minimum/maximum independent variable(s) at which you would achieve the said optimum cost/dependent process variable . This describes an optimization problem with an objective function; where there is usually a trade-off between certain process variables (Zhiqiang et al., 2018).

The UK government has implemented systems to abate these costs and arising issues with examples demonstrated with the development of agencies like Renewable Transport Fuel Organization (RTFO) with the aim of meeting goals set out in the European Commission’s renewable energy directives; delivering a distinctive percentage of fuels supplied in the country’s trading system as biofuels. It also has the objective of ensuring the country’s energy suppliers hit biofuel targets set as directives; and also provide technical reports and data to back them up (European Commission, 2003; Renewable Fuels Agency, 2011).

However, an  operations optimization of the total bioenergy costs in the UK which satisfies the country’s varying industrial and municipal demands for the sole purpose of achieving accountability and rationality in the use of bio-energy resources, considering transport, energy losses, and also inflated energy costs should be presented (Krause et al., 2010).

Large scale municipal, industrial and government energy systems, as well as systems derived from community-supplied electricity  from bio-energy sources should be considered. Various primary systems in the UK with varying energy quantity and quality levels should be modeled to meet the totality of user demands which varies with respect to time (ECBCS).

The aforementioned results in the formulation of a multi-objective linear programming problem whose objective is depicted to be the total bio-energy cost to be optimized (minimized). An overall bio-energy efficiency could also be optimized (maximized) as an objective (Di Somma et al., 2014; Krause et al., 2010).

Problem Statement

The global drive for renewable energy has come with both its pros and its cons; with even first-world countries finding it quite difficult to effectively and efficiently minimize bio-energy costs while also maximizing energy efficiency (BNEF, 2013).

This work seeks to model and formulate a multi-objective linear programming problem with its objective function being the UK bio-energy cost to be optimized(minimized) considering its various constraints, and optimize the function with a suitable software/method.

Aim and Objectives

The aim of this study is to efficiently optimize the total bio-energy costs in the UK, fully considering the various constraints involved.  It has the following objectives;

• Objective 1: Development of a feasible and comprehensive multi-objective linear programming problem (total bio-energy costs in the UK) as a function of the appropriate variables.
• Objective 2:  Development of the appropriate constraints involved.
• Objective 3: Obtaining solutions of the developed problem using a suitable software/method(s).
• Objective 4:  Testing the objective functions to reveal the accuracy and efficiency of the developed model.
• Objective 5:  Carrying out sensitivity analysis on the developed models.

Research Questions

The identified research questions for this project are provided below:

• What variables are considered while developing the objective function(s)?
• What constraints are considered while developing the objective function(s)?
• Are there government policies that cannot be accounted for in the development of the objective function(s) (IEA, 2013)?
• If political constraints are considered, how would they affect the accuracy of the obtained results?
• How sensitive are the considered variables?

Deliverables

The deliverables of this project are; a project report, mathematical models and simulated results. The models should be able to consistently represent the relationship between the  objective function(s) and the proposed variables. Also, the report should contain a complete documentation of how the mathematical models were arrived at.

Relevance

This project mainly focuses on consistently representing the bio-energy cost situation in the UK as a function of various variables, and obtaining significantly accurate results to determine the optimum variable points at which an efficient bio-energy cost situation can be attained.

Methodology

This project focuses on secondary research, development of an optimization problem and obtaining results, and they are discussed below:

Secondary research

The secondary research in this project will utilize a systematic approach (Johnson et al., 2016) to review the works of literature. The steps involved in the systematic review of the literature are provided below:

• Step 1: Identify the research questions that can be used for the project.
• Step 2: Identify the keywords that should be used to research the works of literature.
• Step 3: Extract the journals and books that are appropriate for this project.
• Step 4: Write the literature review chapter.

Development of an optimization problem

 The development of the optimization problem are in stages:

• Stage 1:  Development of the needed variables.
• Stage 2: Development of a multi-linear objective function.
• Stage 3:  Developing the appropriate constraints.
• Stage 4: Testing the objective function

Obtaining results

The developed optimization problem would be solved using an appropriate software/method(s); and the results would be evaluated.

Evaluation

The risk assessment conducted for this project is provided in the table below:

Table 1:  Risk assessment