A MATHEURISTIC SAMPLING APPROACH FOR LOCATION INVENTORY ROUTING PROBLEM - JAYA AZIZ (NIM: 23415029), IWAN
We consider a model in which a single commodity is distributed through a two echelon network that includes one production facility, a set of candidate intermediate facilities and a larger set of clients facing a sequence of demands over a discrete and finite planning horizon. The corresponding optimization problem aims at jointly minimizing the costs of opening distribution centers (DC) on a subset of the intermediate facilities, managing both their inventories and the clients and transporting the units through the network, from the production unit to its final destination. The resulting problem therefore lies at the intersection of facility location, vehicle routing and inventory management problems. It is known as the Location Inventory Routing Problem (LIRP) and is an NP-hard problem. We focus on two variants of the above model. In the first one, direct trips are performed between the production center and each DC (upper echelon). At the lower echelon, independent distribution routes starting at each DC deliver goods to one or several customers and return to the DC. In the second one, the upper echelon consists of routes starting from the production center and visiting one or several DCs before returning to the production center. The lower echelon assumes a fixed cost for delivering each client from a DC. This can model the cost of direct shipment to each client, or a fixed incentive to each client for picking the goods directly at DCs. In both variants, the routes are restricted by several business constraints, e.g. limitation of route duration, maximum number of clients on a route. The objective function includes a fixed cost for each DC opened, fixed route costs for direct shipments, holding costs and the cost of circular routes. We solve instances of both mathematical models with IBM Ilog Cplex 12.We present and discuss numerical experiments based on a collection of generated instances, and conclude with managerial insights and possible practical use of our models.