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1. Introduction

(FMSsindustatedto mtributithe syof prossue t

s fordingm isimeict-

et al. [7] provided a mathematical model for routing problem.

Contents lists available at ScienceDirect

journal homepage: www.e

Computers & Oper

Computers & Operations Research 38 (2011) 876888the case of failure.1 Tel.:+1 4122683642; fax:+1412 2687139.Lagrangian decomposition technique was used solve the problem.Ghasemzadeh et al. (2009) [8] presented a conict-free schedul-ing and routing in mesh topologies. It can generate the shortestpath for scheduling predicting conicts and select another path in

0305-0548/$ - see front matter & 2010 Elsevier Ltd. All rights reserved.

doi:10.1016/j.cor.2010.08.012

Corresponding author. Tel./fax: +81668506351.E-mail addresses: nishi@sys.es.osaka-u.ac.jp (T. Nishi),

grossmann@cmu.edu (I.E. Grossmann).AGVs for semiconductor fabrication. The interaction betweenproduction and transportation control is discussed by Mantel and

free conditions [4,5]. Singh and Tiwari [6] presented an intelligentagent framework to nd a conict-free shortest-time path. Nishi(1) dispatching, which is to assign tasks to vehicles; (2) routing,which is to select specic paths taken by vehicles; and(3) scheduling, which is to determine the arrival and departure times.

Unlike the classical vehicle routing problem (VRP) formulation,conict-free constraints should be considered for the routing of

performance taking into account for deadlock or conictAGVs. Kim and Tanchoco [3] studied the problem of nconict-free routes in a bidirectional network. The algorithbased on the shortest path methods through the concept of twindow graph. Petri net is used to analyze deadlock and conthe simultaneous optimization problems for production schedul-ing, dispatching and routing for vehicles in the static situation.The production scheduling problems asks an optimal productionsequence and starting time of operations for jobs at machines formulti-stages with respect to a specied technical precedencerelation. The vehicle management problems are classied into

Most of the literature treat one or two of the problems at the sametime. An extensive review has been addressed by Vis [2] foroperational control of AGVs. A widely used technique fordispatching is the simulation. The heuristic rules are used inon-line control systems. For routing and scheduling of AGVs,several techniques have been used to maximize the total systemFlexible manufacturing systemswarehousing systems, and servicetransportations are employing autom(AGVs) for the material handlingefciency of production and disoperation, it is requested to realizefor the simultaneous schedulingtransportation systems. The main i& 2010 Elsevier Ltd. All rights reserved.

), container terminals,ries including hospitalguided vehicle systemsaintain exibility andon. For the efcientnchronized operationsduction systems andreated in this paper is

Landerweerd [1]. In the owshop production systems, theproduction and transportation schedules are usually controlledby a pull type of policy in case of forklifts or conveyor systems.However, for FMSs environment with AGV systems, the optimalmachine schedules highly depend on the selection of dispatchingand routing because it is extremely difcult to predict thetransportation time when the conicts and interferences betweenvehicles cannot be neglected.

Production scheduling, dispatching, routing and schedulingdecisions for AGVs can be made simultaneously or separately.A bilevel decomposition algorithm for sand conict-free routing for automated

Tatsushi Nishi a,, Yuichiro Hiranaka a, Ignacio E. Ga Division of Mathematical Science for Social Systems, Department of Systems Innovati

Toyonaka City, Osaka 560-8531, Japanb Department of Chemical Engineering, Carnegie Mellon University, Pittsburgh, PA 1521

a r t i c l e i n f o

Available online 7 September 2010

Keywords:

Bilevel decomposition

Lagrangian relaxation

Scheduling

Routing

Automated guided vehicle

a b s t r a c t

We address a bilevel decom

routing problems for autom

tardiness of the set of jobs

levels: the upper level ma

subproblem. The master

obtained. Either the soluti

problem is constructed, an

generated to exclude previ

cuts are proposed to reducultaneous production schedulinguided vehicles

ssmann b,1

raduate School of Engineering Science, Osaka University, 1-3 Machikaneyama,

SA

sition algorithm for solving the simultaneous scheduling and conict-free

ed guided vehicles. The overall objective is to minimize the total weighted

ated to these tasks. A mixed integer formulation is decomposed into two

problem of task assignment and scheduling; and the lower level routing

blem is solved by using Lagrangian relaxation and a lower bound is

turns out to be feasible for the lower level or a feasible solution for the

n upper bound is obtained. If the convergence is not satised, cuts are

feasible solutions before solving the master problem again. Two types of

he duality gap. The effectiveness of the proposed method is investigated

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