|M.Sc Student||Hallufgil Davy|
|Subject||Deterministic Inventory Routing with Lateral Transshipments|
|Department||Department of Industrial Engineering and Management||Supervisor||Mr. Michael Masin|
In this research, we consider a two-level supply chain, where the first and second levels consist of an outside supplier and a set of retailers, respectively. Each retailer faces dynamic deterministic demand for multiple types of products over a finite planning horizon. A homogenous fleet of large vehicles located at the supplier satisfies the periodical demands of each retailer, whereas, smaller vehicles located at each retailer are responsible for transshipment within a period. The cost structure of this system consists of fixed vehicle costs, variable vehicle-dependent transportation cost, fixed cost for replenishment and transshipment, unit ordering cost, inventory holding and shortage costs. We call this problem IRP-LIT. In order to develop a strong mixed integer linear programming formulation of the problem, we follow an evolutionary process. We start with simpler problems, Basic Dynamic Deterministic Inventory Routing Problem (Problem BIRP) and Multi-item Dynamic Deterministic Inventory Routing Problem with Backlogging (Problem EIRP). Their valid inequalities are incorporated into Problem IRP-LIT with slight modification. For the first two problems, we have applied only standard branch and bound method, whereas for Problem IRP-LIT, we have applied additional two solution techniques, namely, Lagrangian relaxation method, and Benders' decomposition method. A comprehensive numerical study has been performed to evaluate the effect of strengthening and the performance of the solution techniques. Our results indicate that (1) valid inequalities improve LP relaxation lower bound significantly for each problem type, (2) Lagrangian relaxation method outperforms other techniques as problem size increases and (3) transshipment decreases total cost in most of the cases.