Job-Shop Scheduling Problem with Cost ... - Tribology in Industry

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processed on a certain machine and that mdchine is ... b1' using a certain decision-making rule, e.g. by ... an already accomplished job its delivery time to the.
UDK 621.3.07 ; 621.316.07 G. DIMITRI, L. ZOHAR

Job-ShopSchedulingProblemwith Cost Parametersfor FlexibleManufacturing Svstem

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Keywords:flexible manufacturingsystem,costparameters

l.INTRODUCTION We are concerned r.vith a problem of machine scheduling known as the generaljob-shop scheduling problemlll. A flexiblemanufacturing system(FMS) c o r n p r i s eass e to f n j o b s J , , 1 < i < n , a n d a s e to f m r n a c h i n eN 4 * , 1 < k ( p . Each job (order) consistsof a chainof operations, eachof which needs to be processedduring an uninterruptedperiod on a given machine.Each rnachinecan processat most one operation at a tirne. If, in the course of nranuf-acturirig, one or ntore jobs are ready to be processedon a certain machine and that mdchine is .free,a.jcb hasto be chosenfrom the line and passed on the machine immediateiy. Thus, the manufacturing process prohibits unnecessary idleness. Choosingthejob from the line is carriedout b1' using a certain decision-makingrule, e.g. by Lrrrder-taking a pairwisecomparison[2]. If at a certain rnorneut,more than one job is readyto be servedon the machine.thesejobs are comparedpairwise.The rvinner of the first pair rvill be comparedwith the thirdjob, etc.,until only onejob is left. The latterhas to be chosenfbr the machine. Each operation O,, is carried out under random disturbances_with

pregiven

probabilit-v law

parameterstl and V,, . For eachjob (order) J, , its P r ofess ctr G o I en ko - G in z bttr g D i nti tr i f)epartntent of Industrictl Engineering and Managentent, Ben-Gurion UniversiQ of the Negev Beer-She'u,a,Israel Dr. Laslo Zohar Department of Industrial Engineering and !t4anagement, Negev Acctdemic College of Engineering Beer-Sheva, [srctel

Tribologvin indust{y,Volume 23,No. 1&2, 2001.

due date D, to be accomplishedand deliveredto the customeris pregiven(assumefor sirnplicitythat fbr an already accomplishedjob its delivery time to the customerequals zero). A job cannot start operating before its earliestpossiblemoment Si . If job J,, 1 < i S n, is accomplishedlater than at the due date D, , the systempays to the customera single cost penalty C, togetherwith an additionalcost penalt,v C;' for each tirne unit of the delay. If the job is accomplished beforethe due date,it is not accepted by the customeruntil the deadline.Thus.the systerl is compelledto storethejob until the due dateand to spend C;' per time unit of storage.Note that such systemscover a broad spectrumof a job-shop FMS underrandorndisturbances. To simpli$ the problem,assurxethat the FMS bears neitherexpenses of utilizing the machinesnor other working expenses (electricity, raw materials, personnel,etc.).Thus, the systemhas to cover only penalty and storage expeuses. It can be wellrecognizedthat, given the system'sparametersD, , togethew r ith the C, , C;- and Cl--, 1S.,1