Large scale stochastic inventory routing problems with split delivery and service level constraints

A stochastic inventory routing problem (SIRP) is typically the combination of stochastic inventory control problems and NP-hard vehicle routing problems, which determines delivery volumes to the customers that the depot serves in each period, and vehicle routes to deliver the volumes. This paper aims to solve a large scale multi-period SIRP with split delivery (SIRPSD) where a customer’s delivery in each period can be split and satisfied by multiple vehicle routes if necessary. This paper considers SIRPSD under the multi-criteria of the total inventory and transportation costs, and the service levels of customers. The total inventory and transportation cost is considered as the objective of the problem to minimize, while the service levels of the warehouses and the customers are satisfied by some imposed constraints and can be adjusted according to practical requests. In order to tackle the SIRPSD with notorious computational complexity, we first propose an approximate model, which significantly reduces the number of decision variables compared to its corresponding exact model. We then develop a hybrid approach that combines the linearization of nonlinear constraints, the decomposition of the model into sub-models with Lagrangian relaxation, and a partial linearization approach for a sub model. A near optimal solution of the model found by the approach is used to construct a near optimal solution of the SIRPSD. Randomly Y. Yu ( ) Rotterdam School of Management, Erasmus University Rotterdam, Rotterdam, Netherlands e-mail: [email protected] Y. Yu School of Management, Lanzhou University, Lanzhou, China C. Chu Laboratoire Génie Industriel, Ecole Centrale Paris, Paris, France H. Chen Industrial Systems Optimization Laboratory, Charles Delaunay Institute (FRE CNRS 2848), University of Technology of Troyes, 10010 Troyes, France F. Chu Laboratoire IBISC EA 4526, Université d’Evry Val d’Essonne, 40 rue du Pelvoux CE 1455, 91025 Evry Cedex, Evry, France