A risk-constrained time-dependent cash-in-transit routing problem in multigraph under uncertainty

Abstract The Cash-in-Transit (CIT) deals with the transportation of banknotes, coins, and other valuable items. Due to the high-value density of these products, incorporating security strategies in the carrier operations is crucial. This paper proposes new CIT models involving deterministic and stochastic time-varying traffic congestion. Since risk exposure of a vehicle is proportional to the time-dependent travel time, a new formula is introduced to measure the risk of traveling. Moreover, this study covers one of the important weaknesses of previous CIT routing models by investigating the problem in multigraph networks. Multigraph representation maintains a set of non-dominated parallel arcs, which are differentiated by two attributes including travel time and robbery risk. Considering maximum allowable time duration together with a risk threshold yields to design a more balanced routing scheme. Multi-attribute parallel arcs in a stochastic time-dependent network bring high computational challenges. Herein, we introduce efficient algorithms including a novel flexible restricted Dynamic Programming and a self-adaptive caching Genetic Algorithm. The proposed algorithms are tested on both a real case study in Isfahan metropolis and generated instances. Ultimately, sensitivity analyses are conducted to assess the importance of the use of multigraph networks in the CIT and to provide significant managerial insights for administrators and practitioners.