Town Planning and the Power of Linear Programming

This report details the application of Integer Linear Programming (ILP) to optimise the design of a 500-unit inner-city housing development. The project faces multiple constraints, including minimum numbers of flats for various demographics (senior citizens, single persons, small and large families), a maximum average building height, a minimum percentage of low-rise buildings, a land area limit, and a cost minimisation objective. The problem is formulated as an ILP, where decision variables represent the number of each of five pre-designed building block types to be constructed. The objective function minimises the total construction cost, subject to constraints reflecting the project's requirements. The ILP model is solved using both Excel Solver and Python's PuLP library, yielding nearly identical optimal solutions specifying the number of each block type to construct, resulting in a minimum total cost. A sensitivity analysis of the solution reveals that while most constraints have significant slack or surplus, the constraint regarding single-person flats is relatively tight, highlighting this as a key area for monitoring. The report concludes by presenting a management report summarising the findings for decision-makers, emphasising the cost-effectiveness and compliance of the optimal plan, identifying potential opportunities for resource reallocation based on surpluses, and considering the broader ethical implications of equitable urban planning. The report advocates for a holistic approach that integrates data-driven optimisation with ethical considerations to ensure a just and sustainable urban development.