  Travel time in urban centers is a significant contributor to the quality of
living of its citizens. Mobility on Demand (MoD) services such as Uber and Lyft
have revolutionized the transportation infrastructure, enabling new solutions
for passengers. Shared MoD services have shown that a continuum of solutions
can be provided between the traditional private transport for an individual and
the public mass transit based transport, by making use of the underlying
cyber-physical substrate that provides advanced, distributed, and networked
computational and communicational support. In this paper, we propose a novel
shared mobility service using a dynamic framework. This framework generates a
dynamic route for multi-passenger transport, optimized to reduce time costs for
both the shuttle and the passengers and is designed using a new concept of a
space window. This concept introduces a degree of freedom that helps reduce the
cost of the system involved in designing the optimal route. A specific
algorithm based on the Alternating Minimization approach is proposed. Its
analytical properties are characterized. Detailed computational experiments are
carried out to demonstrate the advantages of the proposed approach and are
shown to result in an order of magnitude improvement in the computational
efficiency with minimal optimality gap when compared to a standard Mixed
Integer Quadratically Constrained Programming based algorithm.
