What Maks Poduction Systm Dsign Had? 1. Things not always wh you want thm whn you want thm wh tanspot and location logistics whn invntoy schduling and poduction planning 2. Rsoucs a lumpy minimum ffctiv siz fixd cost conomis of scal and scop Babbag s Law: nd wok s skill to match most difficult task 3. Things vay both dmand and poduction pocss vaiability caus poblms vaiability can b known o unknown unctainty/andomnss = unknown vaiability andom dmand, machin bakdowns known vaiability can b du to sasonal dmand bad contol of poduction systm 77
Poduction Systm f d ffctiv poduction/svic at capacity of poduction systm offd dmand to poduction systm dpatu at of dmand satisfid by poduction systm t 78
How to Dal with Dmand Vaiability Chang th dmand pocss: Dynamic picing Advtising Rfus som offd dmand duing pak piods Chang th poduction pocss: Poduc complmntay poducts (shad uipmnt batching) Incas flxibility of poduction pocss (automation) Us a buff (only th possibl kinds): 1. Capacity ( > f, poduction at > dmand at) 2. Tim (waiting, svations/appointmnts) 3. Invntoy of finishd goods (not fasibl fo svic poduction) 79
Buffing Cost Capacity Tim Invntoy Poduction Systm Low Low Low Low High Low Low Low High Low High High High Low Low High High Low High Low High High High High Low capacity cost ddicatd capacity fo a singl poduct High capacity cost capacity that is shad btwn multipl poducts uiing st ups/changovs btwn poduction of batchs of ach poduct 80
Simpl Poduction Systm Poduc maks two dcisions: 1. Poduction at 2. Maximum invntoy lvl Contol logic fo poduc: If custom od is waiting, poduc; ls, if I lvl < lvl, poduc; othwis, shutdown poduction. Custom fulfilmnt pocss: If I lvl > 0, fulfill fom I; ls, wait fo od to b poducd (gtting a discount in pic basd on wait tim) 81
Poduction Systm Dsign Modl wh tim TP p c 1 0 0 d d ch k, p unit sals pic c unit opating cost invntoy invntoy capacity 0 (, ) pobability out of stock imum invntoy hld ( ) dlay discount d d dpatu at h invntoy caying at (, ) avag invntoy lvl k capital cost p unit of capacity capacity of poduction systm 82
Invntoy Modl Finit bith dath pocss poduction = bith dmand = dath Poisson dmand and poduction 0 (, ) 1 1 f f 1 f f n n 0 f, pob. n units inv. f (, ) i 0 i1 i1 i i f i f 83
t Dlay Discount CT ( ) 1 g, (discount applid to stimatd cycl tim) d g discount facto 0 g 1 t ( ) cycl tim (singl machin), ui so all dmand can b satisfid CT f 2 2 ca c u = tct t t 2 1 t uuing tim pocss tim u tim vaiability utilization cycl tim (singl machin + Poisson dmand and pocssing) 11 f 1 1 f 1 1 2 1 f f wh u utilization, fo singl machin c t 2 2 a c f ffctiv pocss tim 1, fo singl machin, suad cofficint of vaiation of dmand and pocssing (mo lat) 1, fo Poisson dmand and pocssing 84
Singl Machin Poisson Modl Not: all costs p, c, and k a indpndnt of d and, 0 0 TP p c 1 ch k 1 f wh 0(, ), 0,1 1 1 f CT g ( ) 1, 0,1 t d CT f 1 1 ( ) f i 0 i1 f (, ) i t d d Sinc and assuming, k k in TP TP pck f f d d UB d 85
Exampl of Modl Poduction at and I can b optimizd I 20 Opt I Opt Cap Unit Sals Pic ( p, $/) 70 70 70 Unit Opating Cost ( c, $/) 50 50 50 Unit Capital Cost ( k, $/) 1 1 1 Discount Facto ( g ) 0.2 0.2 0.2 Invntoy Caying Rat ( h ) 0.01 0.01 0.01 Dmand Rat ( f, /h) 10 10 10 Effctiv Poduction Rat (, /h) 15 15 12.0997 Maximum Invntoy ( ) 20 6 6 Pobability Out of I ( π 0) 0.0001 0.031083 0.075074 Cycl Tim ( t CT) 0.2 0.2 0.476259 Dlay Discount ( π d) 0.956352 0.956352 0.899178 Avag I Lvl ( ) 18.00421 4.435163 3.74024 Total Pofit ( TP, $) 175.997 182.5111 184.5164 Upp Bound on TP ( TP UB, $) 190 190 190 Utilization ( u ) 0.666667 0.666667 0.826467 Thoughput ( d, /h) 10 10 10 WIP ( WIP ) 2 2 4.762585 86
Exampl: Impact of Buffing Cost Buffing Cost: High/Low Capacity-Tim-Invntoy (k,g,h ) LLL LLH LHL LHH HLL HLH HHL HHH Unit Sals Pic ( p, $/) 70 70 70 70 70 70 70 70 Unit Opating Cost ( c, $/) 50 50 50 50 50 50 50 50 Unit Capital Cost ( k, $/) 1 1 1 1 5 5 5 5 Discount Facto ( g ) 0.01 0.01 0.7 0.7 0.01 0.01 0.7 0.7 Invntoy Caying Rat ( h ) 0.00015 0.3 0.00015 0.3 0.00015 0.3 0.00015 0.3 Dmand Rat ( f, /h) 10 10 10 10 10 10 10 10 Effctiv Poduction Rat (, /h) 10.1896 11.4127 10.3923 19.0637 10.062 10.629 10.0377 13.0747 Maximum Invntoy ( ) 44 0 97 1 81 0 201 2 Pobability Out of I ( π 0) 0.014272 1 0.000925 0.344072 0.009394 1 0.003311 0.248945 Cycl Tim ( t CT) 5.274262 0.707864 2.54907 0.11033 16.12903 1.589825 26.5252 0.325235 Dlay Discount ( π d) 0.948372 0.992911 0.046467 0.87561 0.850354 0.984149 1.35E 14 0.675992 Avag I Lvl ( ) 25.13087 0 73.81924 0.655928 43.94809 0 113.1733 1.176621 Total Pofit ( TP, $) 189.4746 187.1695 188.8777 162.5376 149.0792 143.6847 148.3004 100.8451 Upp Bound on TP ( TP UB, $) 190 190 190 190 150 150 150 150 Utilization ( u ) 0.981393 0.876217 0.962251 0.524557 0.993838 0.940822 0.996244 0.764836 Both and slctd to imiz TP stictd to non ngativ intgs 87