Goals. Discrete control concepts. History. Frederick Taylor: Chapter 5 Gunnar Lindstedt

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1 Goals Discrete cotrol cocepts Chapter 5 Guar Lidstedt Goal: you should Uderstad how idustrial productio is orgaized ad the reasos why Be able to calculate a suitable productio rate ad ivetory for a certai product with productio disturbaces Be able to schedule the productio of a umber of products i several machies Some calculatios o Moday Feb. 5 History First decades of 20th cetury Productio drive - push systems Customer demad ifiite Orgaized as mass productio The maager had the resposibility for all critical decisios Worker oly a productio uit Frederick Taylor: "All possible brai work should be removed from the shop floor ad cetred i the plaig or layig-out departmet. I my system the worker is told miutely what he is to do ad how he is to do it, ad ay improvemet he makes upo the istructios give to him is fatal to success." 1

2 Taylorism The ma limits the machies Divide work ito uit operatios The productivity ca icrease by cotrollig the ma Ma = machie Ma ot appreciated See Charlie Chapli s Moder Times A chage i attitude eeded Hery Ford Took over Taylor s ideas However, he raised the workers salaries People queuig to be employed by Ford Problems: Workers turover i 191: 80% I 1970: half of those recruited to work o Chrysler s productio lie had left withi 90 days Ma still ot fully appreciated Brai power of workers ot utilized History After 1970s Global perspective The customers market - pull systems Customer demad limited => competitio Diversified ad flexible productio Iitiatives from the shop floor Decisios much more decetralized Decisios take o the shop floor Japaese philosophy Koosuke Matsushita (Japa) "We are goig to wi ad the idustrial west is goig to lose; there's othig much you ca do about it because the reasos for your failure are withi yourselves. Your firms are built o the Taylor model; eve worse, so are your heads. With your bosses doig the thikig while the workers wield the screwdrivers, you're coviced deep dow that this is the right way to ru a busiess... 2

3 Matsushita (co d) For you, the essece of maagemet is gettig the ideas out of the heads of the bosses ad ito the hads of the labour. We are beyod the Taylor model; busiess, we kow, is ow so complex ad difficult, the survival of firms so hazardous i a eviromet icreasigly competitive ad fraught with dager, that their cotiued existece depeds o the day-to-day mobilizatio of every ouce of itelligece." The Japaese philosophy Simplify Itegrate processes as well as decisios Maximize the adequate techology Appreciate the worker ad his/her braipower The classical trasfer lie Fudametal cocepts raw material A B C D fiished product Chapter 5 Starvig - o iput product Blockig - ca ot deliver fiished product

4 Itroducig buffers Parallel operatios machie ceter raw material A B C D fiished product raw material ABCD ABCD ABCD ABCD buffers fiished product Productio ca still cotiue! Flexible maufacturig cell Properties raw material ABCD ABCD ABCD ABCD fiished Need advaced cotrol computers to product be fully utilized! Structure Series size Flexibility Sesitivity Trasfer lie Medium Low High Trasfer lie High Low Medium with buffer Parallel Low High Low ceters FMS Medium High Low 4

5 Just-i-time (JIT) productio Market demads flexibility Fashio, seasos, treds, etc. Large ivetory Costly, iflexible Buffers hide productio problems Symptom of bad sychroizatio Solutio: produce ecessary quatity at the right momet => JIT JIT Goals of JIT: Fid ad elimiate the losses ad problems Simplify o all levels Material hadlig systems (e.g. Kaba) Iformatio techology JIT No buffers Pull system, meet customer demads No waitig time Remove the bottleecks ad set-up time No errors Quality cotrol i all operatios No failures Prevetive maiteace No paper Admiistrative simplificatios Productio cotrol Chapter 14 5

6 Criteria for productio cotrol Time scales i productio cotrol Miimize the productio time time scale Miimize the productio costs Satisfy delivery dates years moths market ecoomy order predictios maagemet productio plas strategic level Miimize buffers ad ivetory Miimize idle time Miimize average waitig time weeks hours - days secods - miutes resources material material orders resource plaig productio cotrol sequece cotrol machie sychroisatio tactical plaig operatioal level Levels of cotrol Log term plaig Productio level (log term plaig) Fidig the right productio rate Fidig a appropriate ivetory to meet demad Cell level (short term plaig) Routig (which way?) Schedulig (i what order?) Machie level Cotrol of sequetial operatios (PLC) Cotrol of cotiuous processes/movemet (e.g. PID) d u 6

Hedgig poit strategy How to fid the optimal size of ivetory Strategy for plaig productio rate o a hourly ad daily (ad loger) basis Machies will break ad productio will be disturbed

mea time to repair (MTTR), T r We also eed to defie the time period for the aalysis, T ad the umber of failures, N f : N f T T T f r Oe breakdow Hedgig poit calculatios UT g(h) c p

7 Hedgig poit strategy How to fid the optimal size of ivetory Strategy for plaig productio rate o a hourly ad daily (ad loger) basis Machies will break ad productio will be disturbed Keep the expected average x j ( close to zero Hedgig poit strategy To get the optimal buffer size (H) we eed to estimate: The demad, d The mea time betwee failures (MTBF), T f The mea time to repair (MTTR), T r We also eed to defie the time period for the aalysis, T ad the umber of failures, N f : N f T T T f r Oe breakdow Hedgig poit calculatios UT g(h) c p HT N r H f U d c H 2 pn f 2d H 2 2(U d) c N f 2 dg(h)/ dh 0 (dt r H) 2 U d U d g(h)= c p (positive area) + c (egative area) Miimize g(h)! c p c H d T c p c r d c p c U UT f d(t f T r ) 7

8 Hedgig poit cotrol strategy Short term plaig dx u( d( dt u( U if x( H u( d if x( H u( 0 if x( H I practice, the cotrol law has to be somewhat more sophisticated! Routig A products path through the machies Not treated here, assumed to be kow Schedulig The order i which differet products are produced. Sequecig The book is a bit cofusig o this Complexity Criteria for schedulig Type of plat Flow shop, job shop Arrival patter Dyamic, static Level of detail Failure rates, ucertaity Flow shop Job shop Productio time Average time i shop Idle time of machies Waitig time Average lateess of product How late (or early) is the product i respect to due date => miimizig costs (operatig, ivetory) 8

9 The sequecig problem Determie the order of operatios for a certai family of products products to be produced by m machies Productio system (routig) is give ad the same for all jobs, i.e. flow shop All jobs available at start Buffers may be used Oe machie ad jobs (/1) Waitig + processig time for 1 job: P i = W i + t i Total time for job k to be completed: k F k P i i 1 The mea flow time (MFT) i the shop: 1 1 F Fk P1 ( P1 P2 )... ( P1... P ) k 1 1 F i 1 ( i 1) P i Oe machie ad jobs (/1) MFT is miimized if P 1 P 2 P that is, the shortest job first. Oe machie ad jobs (/1) Lateess, defied as: L i =F i -d i where d i is the due date for job i Mea lateess: 1 1 L Lk ( Fk dk ) MFT k 1 k 1 d is the average due date. d 9

10 Oe machie ad jobs (/1) Miimizig mea lateess is the same as miimizig MFT Miimizig the maximum lateess: d 1 d 2 d Prioritizig Sometimes it is ecessary to prioritize a job. Weight ca be used to order the productio: P1 w 1 P2 w 2 P w Two machies ad jobs (/2) Two machies ad jobs (/2) Two cases: Without buffer betwee machies With buffer betwee machies m1 m1 buffer m2 m2 The maximum total productio time for all jobs: Fmax P i,1 P,2 F max i 1 ad P P i,2 i 1 sice P i,2 must wait for P i,1 to fiish. 1,1 10

11 Processig time - Gatt chart Miimizig the processig time M1 M2 M1 M2 J1 J2 J J4 J5 J6 M M With buffer betwee m1 ad m Without buffer betwee m1 ad m M2 has to wait util M1 is fiished. M1 has to wait util there is space i M2. Johso s procedure Choose the shortest time of P i,1 ad P i,2 If shortest job time is o M1 put this job first else put this job last Elimiate the job from the list ad repeat Miimizig the processig time / problem M1 M2 M1 M2 From Johso s procedure: J4 J5 J2 J6 J J1 M M Total time: 7 Idle time M1: 2 Idle time M2: 2 Total time: 45 Idle time M1: 10 Idle time M2: 10 Ca be solved uder certai coditios: Same order for all jobs, i.e. flow shop If M2 (the machie i the middle) is completely domiated by either M1 or M This is true if: mip i,1 maxp i,2 or mip i, maxp i,2 11

12 / problem Itroduce virtual machies M1 ad M2 P i,1 = P i,1 + P i,2 ad P i,2 = P i,2 + P i, Flexible maufacturig If the order of operatios is ot the same for all jobs? Ca be solved i some special cases Optimal solutio ofte ot possible Graphical approaches used Apply Johso s procedure Two jobs ad m machies (2/m) Two jobs ad m machies (2/m) Fidig the shortest path 45 degree agle Ca be exteded to /m Computer solutio 12

13 Productio cotrol - summary Log term plaig- hedgig poit Short term schedulig Fid miimum mea flow time The geeral /m problem ot solved /2 (/) possible for flow shops /2 (/) sometimes possible for job shops 2/m difficult for job shops 1

Integer Programming (IP)

Integer Programming (IP) Iteger Programmig (IP) The geeral liear mathematical programmig problem where Mied IP Problem - MIP ma c T + h Z T y A + G y + y b R p + vector of positive iteger variables y vector of positive real variables