A Heuristics on a Vehicle Routing
Problem for Reuse Systems
Using Column Generation
Yoshiaki Ishihara*A and Shusaku Hiraki*B
*A Oshima College of Maritime Technology, e-mail:Ishihara oshima-k..ac.jp
*B Hiroshima Shudo University, e-mail:hiraki shudo-u ac.jp
Abstract
This paper aims to propose a heuristics on a vehicle routing problem for the reuse systems of transport packages. With the operations of reuse and/or recycling systems, effective systems for reverse logistics which disposed products are collected from customers are needed Disposed transport packages are transported by filling empty capacities of many vehicles which move toward their destinations or return to their point of origins.
This paper proposes a heuristics which a Lagrangian dual is solved by column generation method and a feasible solution is constructed from a Lagrangian dual solution, and clarifies the effectiveness of our proposed heuristics from some numerical examples.
Keywords: Vehicle Routing Problem, Reuse System, Lagrangian Relaxation, Column Generation.
1 . Introduction
Recently, on the viewing point of environmental protection, many manufacturers construct reuse and/or recycling systems for disposed products. With the operations of reuse and/for recycling systems, effective systems for reverse logistics which disposed products are collected from customers are needed [1]-[ 4].
In this paper, a vehicle routing problem (VRP) for the reuse system of transport package is considered Disposed transport packages such as corrugated cardboard, flexible container bag, plastic bobbins and the like are transported by filling empty capacities of many vehicles which move toward their destinations or return to their point of origins This paper investigates the following subjects in order to propose a heuristics on a vehicle routing problem for the reuse systems of transport packages.
(1) Formulate a vehicle routing model for a mathematical programming problem, which maximizes the total transportation quantity of disposed transport package by making use of empty capacities of feasible vehicles not to influence original duties
(2) Propose a heuristics using the column generation method.
2. Formulating a Vehicle Routing Model for Reuse System
2.1 Characteristics of Reuse Systems of Trans port Packages
In this paper, we consider the vehicle routing problem for the reuse systems of the transport packages Disposed transport packages such as corrugated cardboard, flexible container bag, plastic bobbins and the like are transported by filling empty capacities of many vehicles which move toward their destinations or return to their point of origins The characteristics of the reuse system of transport package5 in this paper are pointed out as follows
(1) Time restriction of the delivery of the transport packages is weaker.
（2) Transport packages are transported as many as possible with feasible vehicles which move toward their destinations or return to their point of origins.
References
[1] A. I. Barrows,,R. Dekker and V. Schoniten, ”A two-level network, for recycling sand: a case study”, European Journal of Operational Research, Vol.110 pp.199-214, 1988
[2] M. Fle,schmann, R. Kulk, and R. Dekker, ”Controlling inventories with stochastic item returns: A basic model”, European Journal of Operationnal Research, Vol. 138, pp.63-75,2002
Shusaku Hiraki is a professor of Faculty of Hiroshima Shudo University. He received his Ph.D. degree in Industrial Engineering from xxxxxxxx University in 1977. His Research interests are in area of production ordering systems and decision support systems. He is a member of The Japan Society of Logistics Systems(JSLS)