A Novel Robust Mixed Integer Linear Programming Model for Index Tracking Problem Under No Rebalancing

Jul 16, 2026

Passive management has become popular due to lower management fees and transaction costs. Index tracking aims to replicate the performance of a target index using smaller asset sets. This paper introduces a novel mixed-integer linear programming formulation with enhanced robustness, improved out-of-sample behavior, and long-horizon tracking without substantial deviation or the need for rebalancing. Because index tracking is NP-hard, a metaheuristic with local branching is developed. OR-library data validates performance against commercial solvers, showing convergence to optimal solutions on smaller instances and superior in-sample and out-of-sample results.

LanguageEnglish

CategoryResearch & Report

FormatPDF

Pages23

Reading Time58 min

Introduction

Literature review

arXiv :2607 .09556v 1 [ cs .CE] 10 Jul 2026 A novel robust mixed integer linear programming model for index tracking problem under no rebalancing: heuristic optimization approach Danial Ramezani 1 , Mostafa Abouei Ardakan2 , and Mohamadreza Dehghani Ahmadabad3 1 MSc. Student, Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran. [danialramezani@khu.ac.ir](danialramezani@khu.ac.ir) 2 Associate Prof. , Department of Industrial Engineering, Faculty of Engineering, Kharazmi University, Tehran, Iran [abouei@khu.ac.ir](abouei@khu.ac.ir) 3 Assistant Prof. , Department of Financial Management, Faculty of Financial Sciences, Kharazmi University, Tehran, Iran [mr.dehghani@khu.ac.ir](mr.dehghani@khu.ac.ir) Abstract. Passive management has increasingly won popularity over the past few years because of its advantages, such as lower management fees and transaction costs. Index tracking endeavors to reproduce the performance of an index with smaller sets of assets. In this paper, a novel formulation is proposed that is not only more robust than the existing ones but also performs better on out-of-sample data and tracks indices over long periods without any considerable deviation or the need for rebalancing. Solving index tracking problems in a polynomial time is a challenging task due to their NP-hard nature. To address this issue, a novel heuristic based on metaheuristic algorithms and local branching is also developed to solve the proposed model. The heuristic enjoys not only the exploration capabilities of a genetic algorithm but the characteristics of local search algorithms as well. The data from the OR library is used to verify the capabilities of the proposed heuristic in comparison with commercial solvers. Results indicate that not only is the heuristic able to converge to optimal solutions for not-solarge problem sizes, but the portfolios it generates also outperform those yielded by commercial solversin terms of both in-sample and out-of-sample data. Keywords: Index tracking · Heuristics · Passive fund management · Mixed-integer linear programming · GALB · Portfolio management. 1 Introduction Fund management, alternatively called ‘asset management,’ involves making decisions on behalf of clients to manage their capital toward profits based on their desired risk level. The management styles commonly employed in the relevant financial institutions may be clustered under the two general groups of active and passive management. Active fund managers proactively make decisions on changing the composition of the portfolio and buying or selling assets to gain profits. Indeed, it is the objective of these funds to outperform the market. To achieve this goal, the managers draw upon their expertise, knowledge, and experience in selection of securities, overview of the economy, and market timing, among others. Compared to passive funds, this management style, however, suffers from such drawbacks as higher management fees, regardless of the profitability of the manager, and higher portfolio turnovers and transaction costs. Obviously, the cumulative costs may, at times, ruin the marginal profits made. Passive fund management, also known as passive investment or indexing, is based on the belief that it is not possible to outperform the market in the long run. This belief is crystalized in the celebrated saying that ‘time in the market is more important than market timing’. Indeed, it is the goal of this investment style to create portfolios of constituent assets that replicate the return of the benchmark (market index) . In this situation, a simple solution that comes to mind is full replication. However, buying or selling some of the companies, especially small ones, in the market might run the risk of liquidity since the costs associated with transactions, monitoring, and rebalancing can be huge enough to make this strategy impractical in real-life applications. The stra

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How are the proposed solutions computed and validated?

The work develops a heuristic combining metaheuristic ideas with local branching. It validates results using OR-library data and compares outcomes with commercial solvers on both in-sample and out-of-sample performance.

Jul 16, 2026

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