• A Multi-Vehicle Cyclic Inventory Routing Problem (MV-CIRP) is studied. MV-CIRP the extension of Single-Vehicle CIRP (SV-CIRP). mixed integer nonlinear programming model formulated. Simulated Annealing algorithm proposed to solve both SV-CIRP and MV-CIRP. This paper presents a new variant which aims determine subset customers be visited, appropriate number vehicles used, corresponding cycle ti...

The inventory routing problem (IRP) is an integration of vehicle and management problems. In the recent years, it has increasingly drawn attention researchers because its potentially significant practical value. IRP classified as NP-hard since subsumes (VRP). This fact led to development many heuristic or metaheuristic approaches, although a small number exact methods have been introduced recen...

• We study the Inventory Routing Problem with Time Windows (IRPTW). provide a mixed integer linear programming formulation that includes both arc and routebased variables. develop an efficient branch-price-and-cut algorithm to solve IRPTW optimally. generate two sets of data considering time-varying time-invariant demands at retailers. demonstrate efficacy our solution approach through computat...