Inventory Optimization for Process Network Reliability. Pablo Garcia-Herreros

Transcription

1 Iveory Opimizaio for Process Nework eliabiliy Pablo Garcia-Herreros

2 Iroducio Process eworks describe he operaio of chemical plas Iegraio of complex operaios Coiuous flowraes Iveory availabiliy is cosraied by producio capaciy Iveory chages coiuously (coiuous repleishme)

3 Problem aeme ochasic Iveory Opimizaio Miimize iveory levels ha guaraee high demad saisfacio uder ucerai producio raes eermie a which sages of he process o hold iveory Esablish iveory policies Process ui orage alace holdig cos ad service 3

4 Iveory Policy Iveory depleio:. aisfy demad rae wih available iveory. If iveory is socked-ou cosrai demad saisfacio rae o iveory repleishme rae Iveory repleishme:. epleish iveory a he upsream producio rae. If iveory arge is reached decrease repleishme rae o mach demad rae Iveory policy is characerized by a iveory arge Policy is a combiaio of push ad pull sysem wih iveories as buffer Push Pull Push Pull 4

5 igle Iveory ysem Maximum producio rae () ad demad rae () are radom: Poeial ipu rae o he ak: Poeial oupu rae: Acual ipu ad oupu raes deped o he iveory level ad iveory arge Iveory buffers ipu ad oupu mismaches Iveory level is a radom variable: depeds o he hisory of ad Measure of performace: expeced fracio of demad ha is saisfied (β-service level) 5

6 iscree ime simulaio model Numerical Approach 6

7 Numerical Approach iscree ime opimizaio model: Fid miimum iveory arge () ha provides service level ( β ) for give sample pahs () of radom variables ( ) mi s.. T N T N T N T N ( ) ( ) > < N T T N β ; ; ; 7

8 Case udy Normally disribued producio rae Problem daa: Producio rae: ~ N() To/day emad rae: To/day ervice level:.95 Opimizaio parameers: imulaed ime horizo: 5 days Number of rus: 5 esuls: Opimal iveory arge: E[] 6.55 Var(). 8

9 Case udy Normally disribued producio rae 9

10 Case udy Normally disribued producio rae

11 Processes i Tadem Maximum producio raes ( ad ) ad demad rae () are radom: Poeial ipu rae o ak : Poeial oupu rae from ak : Poeial ipu rae o he ak : Poeial oupu rae from ak : Acual ipu ad oupu raes deped o iveory levels ad arges Iveory levels are radom variables Measure of performace: expeced fracio of demad ha is saisfied

12 Numerical Approach iscree ime simulaio model of wo processes i adem

13 Numerical Approach iscree ime opimizaio model: Fid miimum iveory arges ( ad ) ha provides service level ( β ) for give sample pahs () of radom variables ( ) mi s.. T N T N T N T N T N T N T N T N T N T N ( ) TH [ ] > TH TH ; ; 3 ( ) TH TH TH TH [ ] < TH TH N T T N β

14 Case udy Normally disribued producio raes Problem daa: Producio raes: ~ N() To/day emad rae: To/day ervice level:.95 Opimizaio parameers: imulaed ime horizo: 5 days Number of rus: esuls: Opimal iveory arge: E[ ] 6.83; Var( ) 3. E[ ] 36.; Var( ).64 4

15 Case udy Normally disribued producio raes 5

16 Case udy Normally disribued producio raes 6

17 Coclusios imulaio-opimizaio approaches are suiable for iveory opimizaio i ucerai producio sysems Iveory policy ca be modeled by usig disjucios igifica icreases i iveory are eeded whe variabiliy i adem producio uis is cosidered Iveory is more effecive if sored up-sream: avoids dowsream sarvig 7