SPC ERA IJBM Vol-2,Issue No-6 Oct.-Dec. -2014 Variables Reduction in Vehicle Routing Problems ~ 86 ~ Variables Reduction in Vehicle Routing Problems Mihir Dash Department of Quantitative Methods, School of Business, Alliance University,Chikkahagade Cross, Chandapura-Anekal Road, Anekal, Bangalore India e-mail: mihirda@rediffmail.com mob: 0919945182465 Abstract - The Vehicle Routing Problem (VRP) and its variants are well-studied in the operations research literature, with several interesting applications in the planning of distribution systems and logistics. The objective is to find a set of delivery routes in a network satisfying some requirements or constraints with minimal total cost. The problem can be modeled as an integer linear programming problem, though with high computational complexity.The present study examines a variables reduction technique which reduces the complexity of the problem for a special class of VRP’s. Keywords: Vehicle routing problem, integer linear programming, computational complexity. Prologue The classical Vehicle Routing Problem (VRP) is a combinatorial optimization problem, identifying the optimal routing of a fixed fleet of vehicles in order to service a given set of customers in a network satisfying some requirements or constraints, with minimal total cost (Dantzig and Ramser, 1959). VRP has many applications in the fields of transportation, distribution and logistics. The VRP can be modeled as an integer linear programming problem. Many solution techniques are available for the classical VRP, but with high computational complexity (Chiang and Russell, 1996; Braysy et al., 2004; Nagy and Salhi, 2007; Choi and Tcha, 2007). There are several variations and specializations of the VRP. The Vehicle Routing Problem with Pickup and Delivery (VRPPD) involves finding optimal routes for a fleet of vehicles to pick up a number of goods from certain pickup locations and drop them off to other delivery locations. The Vehicle Routing Problem with LIFO is similar to the VRPPD, with the additional restriction that at any delivery location, the item being delivered must be the item most recently picked up, in order to reduce the loading and unloading times at delivery locations. The Vehicle Routing Problem with Time Windows (VRPTW) is a variation on the VRP in which the delivery locations have time periods within which the deliveries (or visits) must be made. The Capacitated Vehicle Routing Problem, with or without Time Windows (CVRP or CVRPTW) involves vehicles with limited carrying capacity of the goods that must be delivered. Another generalization of the VRP is the Multiple Vehicle Routing Problem (MVRP), which involves determining a set of routes for m vehicles (Laporte and Semet, 2002; Cordeau et al., 2002, 2004). In practice, VRPs usually involve several types of restrictions. There may be some restrictions on the vehicles. Each vehicle may have a fixed capacity (usually weight and/or volume). Each vehicle may have a