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The Last Mile Problem (LMP) refers to the provision of travel service from thenearest public transportation node to a home or office. We study the supply side of thisproblem in a stochastic setting, with batch demands resulting from the arrival of groupsof passengers at rail stations or bus stops who request last-mile service. Closed-formbounds and approximations are derived for the performance of Last Mile TransportationsSystems as a function of the fundamental design parameters of such systems. An initialset of results is obtained for the case in which a fleet of vehicles of unit capacity providesthe Last Mile service and each delivery route consists of a simple round-trip between therail station and bus stop and the single passenger’s destination. These results are thenextended to the general case in which the capacity of a vehicle is an arbitrary, buttypically small (under 10) number. It is shown through comparisons with simulationresults, that a particular strict upper bound and an approximate upper bound, both derivedunder similar assumptions, perform consistently and remarkably well for the entirespectrum of input values and conditions simulated. These expressions can therefore beused for the preliminary planning and design of Last Mile Transportation Systems,especially for determining approximately resource requirements, such as the number ofvehicles/servers needed to achieve some pre-specified level of service.


Last mile problem, queuing, batch demands, waiting time bounds, cyclic assignment


OS and Networks | Software Engineering

Research Areas

Intelligent Systems and Decision Analytics


Tristan VIII, San Pedro de, Atacama, Chile



City or Country

San Pedro de, Atacama, Chile

Creative Commons License

Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 4.0 License.