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This paper addresses a new variant of the multi-trip single vehicle routingproblem where the nodes are related to each other through AND-type precedenceconstraints. The problem aims at determining a sequence of trips to visit allthe nodes respecting every precedence constraint within and among the routes soto minimize the total traveling cost. Our motivation comes from routingproblems where a node may have a set of predecessors (not just single oneproposed in the dial-a-ride or pickup and delivery problems) resulting in a setof pairwise relations that specify which customers need to be visited beforewhich other ones. We develop three Mixed Integer Programming (MIP) models toformulate the problem. The models are experimentally compared to determine thebest one. Moreover, a solution approach based on the Logic-Based BendersDecomposition (LBBD) algorithm is developed which allows to decompose theoriginal problem into an assignment master problem and independent sequencingsubproblems. A new valid optimality cut is devised to achieve fasterconvergence. The cut performance is experimentally investigated by comparingwith a recently proposed one in the literature. We further relax the algorithmto find the sub-optimal solution and demonstrate its efficiency. Extensivecomputational experiments are conducted to assess the proposed algorithms interms of solution quality and CPU time.

Decomposition Algorithm for the Multi-Trip Single Vehicle Routing Problem with AND-type Precedence Constraints