The inventory routing problem (IRP) integrates two components of supply chain management, namely, inventory management and vehicle routing. These two issues have been traditionally dealt with problems in the area of logistics separately. However, these issues may reduce the total costs in which the integration can lead a greater impact on overall system performance. The IRP is a well-known NP-hard problem in the optimisation research publication. A vehicle direct delivery from the supplier with and without transhipments (Inventory Routing Problem with Transhipment, IRPT) between customers in conjunction with multi-customer routes in order to increase the flexibility of the system. The vehicle is located at a single depot, it has a limited capacity for serving a number of customers. The thesis is focused on the two main aspects: (1) Development of the optimisation models for the deterministic and stochastic demand IRP and IRPT under ML/OU replenishment polices. On the deterministic demand, the supplier deliveries products to customers whose demands are known before the vehicle arrives at the customers’ locations. Nevertheless, the stochastic demand, the supplier serves customers whose actual demands are known only when the vehicle arrives at the customers’ location. (2) Development of integrated heuristic, biased probability and simulation to solve these problems. The proposed approaches are used for solving the optimisation models of these problem in order to minimise the total costs (transportation costs, transhipment costs, penalty costs and inventory holding costs). This thesis proposed five approaches: the CWS heuristic, the Randomised CWS heuristic, the Randomised CWS and IG with local search, the Sim-Randomised CWS, and the Sim-Randomised CWS and IG with local search. Specifically, the proposed approaches are tested for solving the deterministic demand IRP and IRPT, namely, the IRP-based CWS, the IRP-based Randomised CWS, the IRP-based Randomised CWS and IG with local search. For the transhipment case are called the IRPT-based CWS, the IRPT-based Randomised CWS, and the IRP-based Randomised CWS and IG with local search. On the stochastic demand, these proposed approaches are named the SIRP-based Sim-Randomised CWS, the SIRPT-based Sim-Randomised CWS, the SIRP-based Sim-Randomised CWS and IG with local search, and the SIRPT-based Sim-Randomised CWS and IG with local search. The aim of using the sim-heuristic is to deal with stochastic demand IRP and IRPT, the stochastic behaviour is the realistic scenarios in which demand is used to be addressed using simulation. Firstly, the Sim-Randomised CWS approach, an initial solution is generated by Randomised CWS heuristic, thereafter an MCS is combined to provide further improvement in the final solution of the SIRP and the SIRPT. Secondly, the integration of Randomised CWS with MCS and IG with local search is solved on these problems. Using an IG algorithm with local search improved the solution in which it generated by Randomised CWS. The developed heuristic algorithms are experimented in several benchmark instances. Local search has been proven to be an effective technique for obtaining good solutions. In the experiments, this thesis considers the average over the five instances for each combination and the algorithms are compared. Thus, the IG algorithm and local search outperformed the solution of Sim-Randomised CWS heuristics and the best solutions in the literature. This proposed algorithm also shows a shorter computer time than that in the literature. To the best of the author’ knowledge, this is the first study that CWS, Randomised CWS heuristic, Sim-Randomised CWS and IG with local search algorithms are used to solve the deterministic and stochastic demand IRP and IRPT under ML/OU replenishment policies, resulting of knowledge contribution in supply chain and logistics domain.