By Rais, A.; Alvelos, F.; Carvalho, M.S.
In recent years, many important real-world applications are studied as ‘‘rich’’ vehicle routing problems 27 that are variants and generalizations of the well-known vehicle routing problem. In this paper we address 28 the pickup-and-delivery version of this problem and consider further generalization by allowing trans- 29 shipment in the network. Moreover, we allow heterogenous vehicles and flexible fleet size. We describe 30 mixed integer-programming formulations for the problem with and without time windows for services. 31 The number of constraints and variables in the models are bounded by polynomial size of the problem. 32 We discuss several problem variants that are either captured by our models or can be easily captured 33 through simple modifications. Computational work gave promising results and confirms that transship- 34 ment in network can indeed enhance optimization.