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Dynamical System Modeling and Stability Investigation�DSMSI-2025

May 08-10, 2025, Kyiv, Ukraine

Enhancement of a Mathematical Model for a Method of Calculating the Reputation Index of Contractors in Public Procurement

Oleksandr Korniichuk, Maryna Graf

Zhytomyr Polytechnic State University

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Introduction

Why Reputation Matters in Public Procurement

Promote fair competition;�
Encourage new market entrants;�
Prevent monopolization by dominant players;�
Improve quality and accountability in contract execution.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

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Problem

Limitations of Current Reputation Models

Existing models often favor established contractors, creating barriers for new or small companies.�
High-performing contractors may dominate tenders, reducing competition and innovation.�
Lack of objective, multidimensional assessment increases risks of contractor failure and poor delivery.�

Need for a refined system that:

Encourages fair access,�
Measures performance accurately,�
Aligns with strategic procurement objectives.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

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Proposed Solution

Building Reputation System

The reputation system is a structured mechanism for evaluating contractors based on past performance, reliability, and compliance. It serves as a quantitative decision-support tool in public procurement.

Key features:

Score-based system: Each contractor is assigned a numeric reputation index.�
Historical performance tracking: Reputation evolves based on actual results, not just claims.�
Dynamic updates: Scores are updated after each completed project.�
Transparent and consistent: All contractors are assessed using the same algorithm and criteria.�

This approach ensures that procurement decisions are not solely based on price but also on quality, responsibility, and trustworthiness.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

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Formula

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Contractor reputation is a complex integrated indicator that takes into account their ability to perform contracts on time, within the established budget, and with the required level of quality. In this regard, the main goal of improving reputation assessment methods is to ensure transparency and encourage contractors to increase their efficiency. In the article, the authors propose a new method that considers financial stability, a differentiated approach to reputation growth depending on the company's current rating, as well as past order fulfillment history. The improved formula for calculating reputation, which is the basis of the method proposed by the authors, is as follows

The described enhancement allows for a level-sensitive reputation evaluation, promoting a balanced growth dynamic. It facilitates rapid reputation accrual for emerging companies to enhance their competitiveness while simultaneously ensuring a stable and controlled development trajectory for companies already possessing a strong reputation, all informed by their historical success in contract execution.

The proposed formula considers the specifics of both new and established companies in the public procurement market. It allows for:

Rapidly increasing the reputation of new participants, encouraging their active participation.
Ensuring stable and fair market development, where leaders cannot excessively dominate due to logarithmic reputation growth.
Updating the reputation of companies, giving more weight to the latest results of their activities.
Considering the financial responsibility of the contractor through the mechanism of insurance payments, creating equal conditions for all market participants.

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Growth Function – Dual Approach

Dynamical System Modeling and Stability Investigation, DSMSI-2025

The approach proposed by the authors ensures a balance between the need for the relevance of reputation assessments and the necessity to maintain fair competition among all market participants. In the new formula, it was proposed to divide the reputation growth process into two stages:

A linear function is used for new companies. This allows them to reach a competitive level faster, despite the lack of a long history of executed contracts. The linear function provides stable and predictable growth for new companies, which is important for the development of competition in the market.
For companies with a reputation above 70%, logarithmic growth is applied. This is important to avoid excessive market dominance by companies with a high reputation, as logarithmic growth is gradual and slows down with increasing reputation. This encourages market leaders to maintain their reputation at a high level while preventing their monopolization of the market.

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Insurance Payment Limit

Dynamical System Modeling and Stability Investigation, DSMSI-2025

The insurance payment allows for transferring a significant portion of financial risks to insurance companies or banks, which perform a professional assessment of the contractor's solvency. This solution helps to reduce the administrative workload on public authorities, as financial verification is delegated to specialized institutions that possess the necessary resources and expertise to perform such tasks.

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Differentiated Reputation Growth.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

The proposed method is expected to have the following several important advantages:

Limiting rapid reputation growth: Logarithmic growth prevents a situation where established companies accumulate rating points too quickly, creating barriers for new market entrants.
Minimizing the impact of minor errors: For companies with a high rating, minor errors have less impact on the overall result, which encourages them to maintain high standards of work.
Maintaining market stability: The logarithmic approach promotes a more even distribution of reputation among participants, preventing monopolization.

The approach proposed by the authors ensures a balance between the need for the relevance of reputation assessments and the necessity to maintain fair competition among all market participants. In the new formula, it was proposed to divide the reputation growth process into two stages:

A linear function is used for new companies. This allows them to reach a competitive level faster, despite the lack of a long history of executed contracts. The linear function provides stable and predictable growth for new companies, which is important for the development of competition in the market.
For companies with a reputation above 70%, logarithmic growth is applied. This is important to avoid excessive market dominance by companies with a high reputation, as logarithmic growth is gradual and slows down with increasing reputation. This encourages market leaders to maintain their reputation at a high level while preventing their monopolization of the market.

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Rating Formation Based on Historical Data.

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Using past reputation to calculate the current one establishes a data minimization principle, which reduces the amount of memory required for data storage by unifying it into a general assessment. By reusing past reputation, we can guarantee a predictable change in contractor reputations and exclude any anomalous behavior.

The formula is based on the idea from the research "Public Procurement and Reputation: An Agent-Based Model" [18] of considering previous reputation to evaluate the current one. The proposed approach ensures an adaptive change in weighting coefficients for new and old results, which allows for adjusting the contractor's reputation based on recent contracts, taking into account previous performance history.
Using past reputation to calculate the current one establishes a data minimization principle, which reduces the amount of memory required for data storage by unifying it into a general assessment. By reusing past reputation, we can guarantee a predictable change in contractor reputations and exclude any anomalous behavior. Using past reputation helps to accurately define the evaluation criterion for companies - the quality of previous contract execution, as reputation reflects the level of trust in a particular participant and the quality of work they provide.

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Experiments

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Assumption 1 - Calculation of the current company reputation assessment.
Assumption 2 - Reputation Calculation for Companies with Different Insurance Coverage.

Figure 1: Graph of company reputation growth over time with (orange) and without (blue) the logarithmic component of the function.

During the experiment, the impact of varying insurance coverage on a company's reputation was demonstrated, validating the formula's sensitivity to financial responsibility. As shown with Company 1 and Company 2, even a relatively small difference in insurance percentage resulted in a noticeable divergence in reputation scores, emphasizing the insurance factor's role in differentiating contractor reliability. Furthermore, simulations effectively illustrated the differentiated reputation growth mechanism, confirming the intended behavior of the proposed formula. The graph visually corroborated the rapid initial reputation gain for new companies using a linear function, while also highlighting the controlled, logarithmic growth for established companies with higher initial reputations. This experiment and simulation data together support the effectiveness of the refined reputation index in providing a more nuanced, responsive, and equitable assessment framework for public procurement, aligning with the research assumptions and objectives.

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Final results

Dynamical System Modeling and Stability Investigation, DSMSI-2025

Problem Identified: Existing public procurement reputation formulas are inadequate; they fail to consider contractor financial capacity, past performance history, and differentiate between new and established companies, hindering fair competition.
Proposed Solution: Developed an improved reputation formula using distinct mathematical functions:

Linear function: For new companies, enabling faster initial reputation growth and market entry.
Logarithmic function: For established companies, promoting sustained quality performance while preventing market stagnation.

Key Criteria Incorporated: The new formula integrates crucial factors:

Insurance Payment Availability: Leverages bank risk assessment as a proxy for financial stability.
Successful Past Order Completion: Rewards reliability and track record.
Differentiated Growth Logic: Balances encouragement for newcomers with standards for experienced firms.

Overall Impact: The proposed approach creates a more adaptive, comprehensive, and equitable contractor assessment, promoting fairer competition and allowing for greater flexibility and future optimization in public procurement.

Okay, here are several key points summarizing the research results, suitable for a presentation slide:

Problem Identified: Existing public procurement reputation formulas are inadequate; they fail to consider contractor financial capacity, past performance history, and differentiate between new and established companies, hindering fair competition.
Proposed Solution: Developed an improved reputation formula using distinct mathematical functions:

Linear function: For new companies, enabling faster initial reputation growth and market entry.
Logarithmic function: For established companies, promoting sustained quality performance while preventing market stagnation.

Key Criteria Incorporated: The new formula integrates crucial factors:

Insurance Payment Availability: Leverages bank risk assessment as a proxy for financial stability.
Successful Past Order Completion: Rewards reliability and track record.
Differentiated Growth Logic: Balances encouragement for newcomers with standards for experienced firms.

Validation & Findings: Experiments and simulations demonstrated:

The formula's sensitivity to financial indicators (e.g., insurance coverage).
Successful implementation of the intended differentiated reputation growth curves.

Overall Impact: The proposed approach creates a more adaptive, comprehensive, and equitable contractor assessment, promoting fairer competition and allowing for greater flexibility and future optimization in public procurement.

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Thank you for your attention