SAMPLE 2 Basic Format:Font; Times New Roman Size; 10.5pt IJLS of IFLS A Heuristics on a Vehicle Routing Title: Font; Times New Roman Problem for Reuse Systems Size:20pt Name: Font;Times New Roman, Size:12ptColumn Generation Using Affiliation: Font;Times New Roman, Size;12pt, e-mail: Times New Roman, Size:12pt 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 Abstract : and/or recycling systems, effective systems for Font; Times New Roman reverse logistics which disposed products are Size;from 12pt customers are needed Disposed collected transport packages are transported by filling empty capacities of many vehicles which move toward their destinations or return to their point of origins. Keywords: This paper proposes a heuristics which a Font; Times New Roman Lagrangian dual is solved by column generation Size; 12pt method and a feasible solution is constructed from a Italic Lagrangian dual solution, and clarifies the effectiveness of our proposed heuristics from some 25mm numerical examples. Keywords: Vehicle Routing Problem, Reuse System, Title: Font; Times New Roman,Size:20pt Name:Font;Times Roman, Size:12pt Lagrangian Relaxation, ColumnNew Generation. 1. Affiliation: Font;Times New Roman, Size; 12pt, e-mail:Times Introduction New Roman, Size:12pt Recently, on the viewing point of environmental protection, many manufacturers construct reuse and/or recycling systems for disposed products. With the operationsAbstract: of reuse and/for recycling systems, Within 200 words effective systems for reverse logistics which disposed Keyword: from customers are needed products are collected Up to 4 words [1]-[ 4]. In this paper, a vehicle routing problem (VRP) for the reuse system of transport package is considered Disposed transport packages such as 24mm corrugated cardboard, flexible container bag, plastic bobbins and the like are transported by filling empty 18mm Notify vehicles of Thesis 9pt capacities of many which move toward their destinations or return to their point of origins This 10mm 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 Notify of Thesis:the total transportation quantity of maximizes 4 raws disposed transport package by making use of Font; Times New Roman, Size; 9pt empty capacities of feasible vehicles not to Line:0.75pt influence For original Received duties Date, Accepted Date Received Date: September XX, 2007 Accepted Date: December XX, 2007 (2) ProposeParagraph a heuristics : using the column generation Font; Times New Roman method. Size; 12pt 2. Formulating a Vehicle for 1. chapter 1.1Routing section Model 1.1.1 item 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 Content Disposed: transport packages such as Font; Times New Roman corrugated cardboard, flexible container bag, plastic bobbins and theSize; like 10.5pt 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 2 colums package5 in this paper are pointed out 25mm 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 formulate a vehicle routing model for the reuse systems of the transport packages. Fig.1 shows the conceptual diagram of the reuse system of the transport packages Collected point (CP) References [1] A. I. Barrows,,R. Dekker and V. Schoniten, ”A 18mm a case two-level network, for recycling sand: 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 24mm Operationnal Research, Vol.10mm 138, pp.63-75,2002 Shusaku Hiraki Portrait 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)