In this research, a new variant of the vehicle routing problem with time windows is studied where a given number of dispersed customers are related to each other through AND/OR precedence constraints.This generalization is necessary for problems like order picker routing models in which the target locations cannot be reached in any sequences, but AND/OR relations need to be taken into account in retrieving requested items. In such an application, a node cannot be visited before its AND-type predecessors, while at least one of its OR-type predecessors needs to be reached before that. We propose a Mixed Integer Linear Programming (MILP) model to formulate the problem. In addition, a meta-heuristic algorithm based on the hybridization of Iterated Local Search and Simulated Annealing approach is developed, which lead to reasonable results in terms of CPU time and solutions accuracy for a set of instances extended from the well-known Solomon benchmark. A different perturbation procedure and several simple and fast neighborhoods are applied to make a good balance between the diversification and intensification of the search. To improve the hybrid algorithm’s performance, Taguchi’s method (Peace, 1993) is used to tune the algorithm parameters. A comprehensive computational analysis is conducted to assess the performance of the developed algorithm.