A multi-objective mathematical model for addressing human factors in the risk of cash-in-transit problem using hybrid multi-objectives metaheuristic algorithm


Akefi H., Jolai F., AGHSAMI A.

Neural Computing and Applications, vol.38, no.5, 2026 (Scopus) identifier

  • Publication Type: Article / Article
  • Volume: 38 Issue: 5
  • Publication Date: 2026
  • Doi Number: 10.1007/s00521-025-11742-0
  • Journal Name: Neural Computing and Applications
  • Journal Indexes: Scopus, Compendex, Index Islamicus, INSPEC, zbMATH
  • Keywords: Cash-in-transit, Dissimilar vehicle routing problem, Human factors, Human resource risk, Risk management
  • Ankara Yıldırım Beyazıt University Affiliated: Yes

Abstract

One of the major challenges in the banking sector is cash-in-transit (CIT), which involves moving cash and valuables securely from one location to another. Banks and other financial institutions rely on CIT services to protect their cash operations. These operations require the transportation of banknotes, coins, and other items of value. The main risks associated with CIT are routing plans and human factors, such as the possibility of collusion between staff and robbers or the formation of habits that make transfers predictable. In order to address these risks, we propose a multi-objective mathematical model that designs random schedules. The first objective function seeks to minimize the similarity of schedules among the staff, to avoid creating regular patterns. The second objective function tries to reduce travel time and the time spent by the staff inside the vehicle, to lower the chances of fatigue or distraction. The third objective function intends to minimize exposure to theft by considering the amount of money transferred and the travel duration. The proposed CIT problem is very complex and hard to solve, as it belongs to the NP-hard class of problems. Therefore, we develop a hybrid algorithm, called MOPGA, that combines NSGA II and MOPSO algorithms. We compare the proposed algorithm with NSGA-II, PESA, MOEA/D, and SPEA on several test instances. The results show that it delivers superior solution quality with competitive computational time, confirming its effectiveness for solving the CIT problem.