<p> In this thesis, we have considered the vehicle routing problem with pickup and delivery which is a generalization of the capacitated vehicle routing problem (CVRP). The vehicle routing problem with pickup and delivery (VRPPD) arises whenever pickup demand and delivery demand is to be satisfied by the same vehicle. The problem is encountered in many real life situations including reverse logistics. We consider three variants of VRPPD, namely, the vehicle routing problem with back-hauls (VRPB), the vehicle routing problem with back-hauls and mixed-load (VRPBM) and the vehicle routing problem with simultaneous pickup and delivery (VRPSPD). </p> <p> The inherent complexity of VRPPD makes it an NP -hard problem. It is not possible to solve an NP-hard problem in polynomial time unless P = NP. Therefore, heuristics and metaheuristics are used to produce a good quality solution within reasonable CPU time. We develop ant colony algorithms for VRPB, VRPBM and VRPSPD. We have improved the existing ant-colony algorithms by applying better local search schemes and by adding new features such as construction rule and the trail updating criteria. We also develop saving based heuristics for single and multi-depot versions of VRPSPD. Checking feasibility of a given route is an important issue in VRPSPD because of the fluctuating load on the vehicle. We have proposed the cumulative net-pickup approach for this purpose. One important feature of this approach is that it checks the feasibility of an altered route in constant time. </p> <p> The proposed heuristics and metaheuristics are evaluated by solving benchmark problem instances available in literature and then comparing the solutions with the solutions produced by the existing algorithms. Our computational experiment has shown that the proposed heuristics and metaheuristics give better or equally good results in comparison to the existing solution procedures. </p> / Thesis / Doctor of Philosophy (PhD)