Designing a multi-modal and variable-echelon delivery system for last-mile logistics

• A novel multi-modal variable-echelon last-mile delivery system is introduced. • The problem is formulated as a mixed integer programming model. • A fast heuristic is proposed which combines biased-randomisation and local search. • Experiments demonstrate the efficiency of the heuristic and benefits of the proposed delivery system. • Customer density and parcels sizes are shown to be critical factors effecting fleet composition. This paper proposes a last-mile logistics delivery system which makes use of multiple localised storage depots and multi-modal delivery options. Multiple localised storage depots facilitate express and instant delivery services. Multi-modal delivery allows for use of alternative green vehicle types for performing deliveries where there may also be vehicle access restrictions. Additionally, when demand density is sufficiently high and parcel sizes small, utilising alternative delivery modes, such as electric cargo bike and porters, can be cost effective in their own right. The proposed model allows for vehicles to rendezvous at kerbside locations (mobile satellites) where parcels can be transferred between vehicles, a feature that is shown to reduce depot stem costs. For the purpose of generality and the potential for higher quality solutions, no fixed echelon or hierarchical structure is placed on the sequence of vehicles transporting any parcel, that is, the problem is one of variable-echelon. The last-mile delivery system described in the paper gives rise to a multi-modal delivery problem using a heterogeneous fleet of vehicles and with synchronisation constraints. The paper presents a mathematical formulation of the problem and a heuristic algorithm. Computational results are presented that validate the mathematical model and the heuristic on a set of benchmark instances, some of which are based on the literature. The paper also describes a new set of benchmark instances derived from real sales data in London, whose results demonstrate potential benefits from using the proposed delivery concept.