  This paper develops a computationally efficient algorithm for the Multiple
Vehicle Pickup and Delivery Problem (MVPDP) with the objective of minimizing
the tour cost incurred while completing the task of pickup and delivery of
customers. To this end, this paper constructs a novel 0-1 Integer Quadratic
Programming (IQP) problem to exactly solve the MVPDP. Compared to the
state-of-the-art Mixed Integer Linear Programming (MILP) formulation of the
problem, the one presented here requires fewer constraints and decision
variables. To ensure that this IQP formulation of the MVPDP can be solved in a
computationally efficient manner, this paper devises a set of sufficient
conditions to ensure convexity of this formulation when the integer variables
are relaxed. In addition, this paper describes a transformation to map any
non-convex IQP formulation of the MVPDP into an equivalent convex one. The
superior computational efficacy of this convex IQP method when compared to the
state-of-the-art MILP formulation is demonstrated through extensive simulated
and real-world experiments.
