BUST10134 Mathematical Programming in Advanced Analytics
Project Assignment
January 2024
General background: Optimal Sustainable Development Goals
The Sustainable Development Goals (SDGs) are a set of 17 global goals adopted by all United Nations Member States in 2015 as part of the 2030 Agenda for Sustainable Development. These goals represent an urgent call for action by all countries in a global partnership to address several interconnected challenges facing the world, including poverty & hunger, inequality, climate change, environmental and ecosystems’ protection, world’s peace & and justice for all. The SDGs provide a structured framework for countries, organisations, and individuals to work toward a more sustainable and equitable future. See more in https://sdgs.un.org/2030agenda. The 17 SDGs are as follows:
• Goal 1. End poverty in all its forms everywhere.
• Goal 2. End hunger, achieve food security and improved nutrition and promote sustainable agriculture.
• Goal 3. Ensure healthy lives and promote well-being for all at all ages.
• Goal 4. Ensure inclusive and equitable quality education and promote lifelong learning opportunities for all.
• Goal 5. Achieve gender equality and empower all women and girls.
• Goal 6. Ensure availability and sustainable management of water and sanitation for all.
• Goal 7. Ensure access to affordable, reliable, sustainable and modern energy for all.
• Goal 8. Promote sustained, inclusive and sustainable economic growth, full and productive employment and decent work for all.
• Goal 9. Build resilient infrastructure, promote inclusive and sustainable industriali- sation and foster innovation.
• Goal 10. Reduce inequality within and among countries.
• Goal 11. Make cities and human settlements inclusive, safe, resilient and sustainable.
• Goal 12. Ensure sustainable consumption and production patterns.
• Goal 13. Take urgent action to combat climate change and its impacts.
• Goal 14. Conserve and sustainably use the oceans, seas and marine resources for sustainable development.
• Goal 15. Protect, restore and promote sustainable use of terrestrial ecosystems, sustainably manage forests, combat desertification, and halt and reverse land degradation and halt biodiversity loss.
• Goal 16. Promote peaceful and inclusive societies for sustainable development, provide access to justice for all and build effective, accountable and inclusive institutions at all levels.
• Goal 17. Strengthen the means of implementation and revitalise the global part- nership for sustainable development.
The goals are followed by a set of specific targets and indicators that measure the progress of achieving (some of) the objectives. The SDGs are designed to be intertwined and mutually reinforcing, recognising the interconnections between social, economic, and environmental dimensions of the sustainable development. The target date for achieving the SDGs is 2030. For this reason, Governments, businesses, civil society, and individuals must act now to be possible to promote & achieve these goals, thus helping the overall planet. In this context, Mathematical Programming & Optimisation arises as powerful tools for addressing and achieving the Sustainable Development Goals by making better (optimal) decisions regarding overall resource allocation, and planning & implementing processes optimally. Here are some examples of how mathematical optimisation can be applied to support the SDGs:
• Resource Allocation: Optimisation models can be used to allocate scarce resources, such as money, manpower, materials, and technology in the most efficient, effective, and equitable manner. This can ensure that resources are directed towards projects or initiatives that contribute most significantly to achieving specific SDGs.
• Supply Chain Optimisation: For goals related to sustainable production and con- sumption (e.g., SDG 12 - Responsible Consumption and Production), optimisation techniques can be applied to supply chain management. This includes optimising production processes, minimising waste generation, and reducing the environmental impact of logistics.
• Renewable Energy Planning: Optimisation models can help identify the optimal locations for renewable energy installations (such as wind or solar farms) as well as energy deployment, taking into account factors like environmental impact, energy production potential, and cost. This contributes to goals like SDG 7 - Affordable and Clean Energy.
• Transportation Planning: Optimisation can be applied to transportation systems to minimise fuel consumption, reduce emissions, enhance the efficiency of transporta- tion networks, as well as maximising transportation accessibility. This supports goals related to sustainable cities and communities (e.g., SDG 11).
• Climate Change Mitigation: Mathematical optimisation models are very useful to support the design and evaluation of strategies for reducing greenhouse gas emissions, optimising land use, developing policies that align with climate action goals (SDG 13), and support preparedness & response operations of disasters and conflicts.
• Healthcare Resource Optimisation: In the context of SDG 3 - Good Health and Well- being, optimisation models can be used to allocate healthcare resources efficiently, effectively, and equitably, optimise the distribution of medical supplies, and design vaccination campaigns.
• Water Resource Management: Optimisation techniques can be applied to manage water resources effectively, addressing goals such as clean water and sanitation (SDG 6). This includes optimising water distribution systems, managing water quality, and minimising water wastage.
• Land Use Planning: Optimisation models can assist in optimising land use for agricultural purposes, urban development, and conservation efforts, contributing to goals related to life on land (SDG 15).
• Disaster Response and Recovery: Mathematical optimisation are very convenient to support an optimised allocation of resources during and after disasters, helping in rapid response and recovery efforts, which is aligned with goals related to resilient infrastructure and sustainable cities (SDG 9 and SDG 11).
To implement mathematical optimisation for the SDGs, interdisciplinary collaboration is crucial. Experts in business analytics & management science, as well as other relevant fields need to work together to identify problems, develop models, gather data, and interpret results in the context of sustainable development. Additionally, it is essential to involve stakeholders and policymakers to ensure that the optimised solutions are implementable and somehow aligned with broader societal goals and values of the SDGs.
Your Task
Given this brief context and general background, your group is required to develop and solve mathematical optimisation models that can address at least one SDG, with the understanding that SDGs eventually overlap. Your specific tasks (parts I and II) are as follows:
1. Identify/select a relevant decision-making problem within one of the 17 SDGs; justify the importance of the chosen SDG and to what extent solving this problem will help achieve this SDG; try to be as specific as you can by including the corresponding target as well.
2. Review relevant literature on your decision-making problem and the methodologies you intend to implement in your work. Ideally, you should look at related literature that proposes modelling/solving a similar problem to your chosen one.
3. Develop the (linear or mixed-integer) deterministic mathematical programming model that reflect your decision-making problem. Make sure the parameters and decision variables are well explained/justified. There are many academic papers that can help you in this regard. It is totally fine to use existing mathematical structures, as long as you cite the original study. Important: Keep in mind that your proposed mathematical programming model is only an abstraction of the real-world problem. Therefore, you are supposed to provide and justify the assumptions needed to build your model(s), as well as discuss the limitations of the mathematical programming formulations.
4. Develop the scenario-based two-stage stochastic programming model that reflect your decision-making problem. Make sure the parameters and decision variables are well explained/justified. There are many academic papers that can help you in this regard. It is totally fine to use existing mathematical structures, as long as you cite the original study.
5. You need to computationally solve the proposed models, thus having accurate data is fundamental. Ideally, you should try to find real data to feed your optimisation models. However, in the absence of real data, you can generate (part of) your data set parameters using simulation techniques, and/or making assumptions (with justification). A lot of existing academic papers and web- sites also provide data sets that can be used in your own work (do not for- get to cite the original studies!). Examples: https://unstats.un.org/sdgs/, https://unstats.un.org/sdgs/dataportal, etc.
6. Code your mathematical programming models in GAMS2 or another optimisation package. Solve the proposed mathematical programming models in GAMS or another optimisation package. For this purpose, select the most suitable method and justify your choices.
7. Report the results of your implementations and draw useful overarching, as well as specific, conclusions and interpretations from them based on the problem ans specific SDG/target. Make use of relevant tables and visuals to underpin your findings and conclusions. Conducting sensitivity analysis on key parameters of the model can be useful to provide managerial insights. To this end, formulated specific research questions and answer them through your sensitivity analysis. Discuss the overall limitations of your work and what can be done to improve your results.
The project is subdivided into Part I and Part II. Part I report is related to items 1-3, while Part II is concerned to items 1-7. Notice that the overall project is the same, i.e., it refers to the same problem. However, the idea of having Part I and Part II is to help students to improve their final reports. I will provide comprehensive feedback of Part I so as students can improve their problem understanding, writing & maths for Part II. I expect that major concerns I identify in Part I be properly revised in Part II.