A MULTICRITERIA OPTIMISATION APPROACH FOR INVESTMENT PROJECT FUNDING

Abstract

This research focuses on the allocation of limited financial resources among competing investment projects using multicriteria methods, with a particular emphasis on funding procedures in which projects are evaluated according to economic, social, environmental and other policy-relevant criteria. In many practical contexts, funding agencies must decide which projects deserve support and how much of the requested budget to allocate to each one when the available budget is insufficient to finance all eligible proposals. The study aims to develop and demonstrate a transparent decision-support model that improves the flexibility and efficiency of financing investment projects by enabling funding decisions to be made on a partial rather than an all-or-nothing basis. The proposed methodology builds on an earlier multicriteria integer linear programming formulation by introducing continuous variables representing the proportion of funding granted to each project, as well as auxiliary binary variables indicating whether a project is approved. The logical relationship between approval and allocation is modelled using Big-M constraints, resulting in a mixed-integer linear programming (MILP) formulation. This model simultaneously maximises the cumulative evaluation scores under each criterion and the number of supported projects while ensuring that the total budget constraint is satisfied. As these objectives may be in conflict with one another, the weighted-sum method is employed to generate Pareto-optimal funding plans. Two procedures for generating weights are considered: systematic iterative stepping over the unit simplex, and quasi-random Sobol-sequence-based generation. To inform the final decision, the global criterion method is used to select the Pareto solution that is closest to the utopian point. The model was implemented in MATLAB using the intlinprog solver and tested on an illustrative dataset comprising eleven investment projects evaluated under three criteria, subject to a fixed total budget. The results show that the partial-funding formulation increases the practical flexibility of the allocation process, offering more options than the original integer-only model. In the binary case, the selected solution may leave part of the budget unused because no additional project can be fully financed. However, the proposed MILP formulation allows the remaining budget to be allocated in fractions, ensuring full utilisation of the budget and enabling support for additional or higher-ranked projects. Computational experiments indicate that this added flexibility does not substantially increase solution time, and may even improve average runtime in the examined setting. The main conclusion is that partial funding provides a more realistic and efficient framework for selecting investment projects under multiple criteria. Nevertheless, the study also shows that unrestricted fractional allocations may result in funding shares that are too small to be meaningful in practice. Therefore, future refinements should include minimum funding thresholds and other policy constraints to ensure that mathematically efficient solutions can be implemented in real financing programmes.