In examining budget allocation dilemmas within organisations in the public domain, there are various techniques and strategies. Here are some of the key methods and techniques used:

• Descriptive Statistics (for Trend)
• Regression Analysis
• ANOVA and F-Test
• Correlations Analysis
• Case Studies and Interviews

Here's some study and journal about budget allocation problems:

[The Basic Budgeting Problem : Approaches to Resource Allocation in the Public Sector and their Implications for Pro-Poor Budgeting]

https://cdn-odi-production.s3.amazonaws.com/media/documents/2069.pdf

[The Basic Budgeting Problem Approaches to Resource Allocation in the Public Sector and their Implications for Pro-Poor Budgeting]

http://erepository.uonbi.ac.ke/bitstream/handle/11295/108069/Osore_Determinants%20Of%20Budgetary%20Allocation%20In%20The%20Public%20Sector%20A%20Case%20Of%20Government%20Ministries.pdf?isAllowed=y&sequence=1

Hi

Studying budget allocation problems in public sector organizations requires a blend of quantitative, qualitative, and theoretical approaches. Here are some common methods I have worked as an economist and public policy researcher:

1. Cost-Benefit Analysis (CBA)

• Purpose: This method evaluates the benefits and costs of different allocation choices.
• Application: CBA is useful in determining which public projects or services provide the most value for the least cost, helping policymakers allocate resources effectively.
• Example: Evaluating the allocation of funds for public health programs by comparing expected health outcomes to the costs involved.

2. Linear Programming (LP) and Optimization Models

• Purpose: Optimization models help identify the most efficient allocation of limited resources to achieve specific objectives.
• Application: Linear programming can be used to solve allocation problems, such as minimizing costs while achieving a specific service level across different public sector units.
• Example: Allocating funds across various government departments to maximize overall utility without exceeding the budget.

3. Participatory Budgeting

• Purpose: This method involves the public in the decision-making process for budget allocations.
• Application: It allows community input to help prioritize public spending based on societal needs and preferences.
• Example: Citizens voting on how to allocate a portion of the municipal budget to various projects, such as education, infrastructure, or healthcare.

4. Game Theory

• Purpose: Game theory models the strategic interactions between different stakeholders (e.g., government agencies) who compete for limited resources.
• Application: It helps in understanding the negotiation dynamics between departments and predicting the outcomes of different budgetary strategies.
• Example: Modeling how different ministries might negotiate for a larger share of the budget based on their strategic interests.

5. Regression Analysis

• Purpose: Regression analysis helps study the relationship between budget allocations and outcomes (e.g., service delivery performance).
• Application: It is used to evaluate how changes in budget allocations impact various performance metrics, helping to identify effective spending areas.
• Example: Analyzing the impact of increased education funding on student performance in public schools.

6. Case Study Analysis

• Purpose: This qualitative method examines specific instances of budget allocation within public sector organizations to identify challenges, strategies, and outcomes.
• Application: It helps build an in-depth understanding of how budget allocation decisions are made in practice and their real-world implications.
• Example: Studying how a city allocates its budget for disaster preparedness and the effectiveness of the allocation during an actual emergency.

7. Dynamic Simulation Models

• Purpose: Dynamic simulations model complex systems over time, allowing policymakers to test different budgetary scenarios and observe potential outcomes.
• Application: Useful for long-term planning, where changes in one part of the system affect the whole.
• Example: Simulating the long-term effects of budget cuts on healthcare systems and public health outcomes.

Application to Public Sector Institutions:

When studying budget allocation in public sector institutions, these methods allow for a comprehensive analysis that considers both efficiency (achieving maximum output with given resources) and equity (fair distribution of resources across different groups or sectors). Research often integrates these methods to assess how budget allocations align with policy objectives and public needs, while ensuring transparency and accountability.

For more detailed academic studies, the use of regression analysis or optimization techniques is common, particularly in economics and public administration literature.

I hope my response will be helpful to you.