ATM cash replenishment under varying population coverage requirements

Inspired by an automated teller machine (ATM) cash replenishment problem involving population coverage requirements (PCRs) in the Netherlands, we propose vehicle tour with minimum requirements. In this problem, a set of minimum-cost routes is constructed subject to constraints on duration each route and replenished ATMs. A compact formulation incorporating family valid inequalities efficient tour-splitting metaheuristic are proposed tested 77 instances derived from real-life data up 98 ATMs 237,604 citizens 144 newly generated synthetic instances. Our results for indicate significant cost differences replenishing seven major Dutch cities when PCRs vary. Additionally, illustrate impact different ATM costs Netherlands presenting aggregated evaluation 11 1,003,519 citizens, 338 ATMs, 19 distribution vehicles.