A. Inventory model. Why are we interested in it? What do we really study in such cases.

Transcription

1 Some general yem model.. Inenory model. Why are we nereed n? Wha do we really udy n uch cae. General raegy of machng wo dmlar procee, ay, machng a fa proce wh a low one. We need an nenory or a buffer or emporary orage. Producer proce Conumer proce Sock on-hand How much o ock? How much o order? When o order? Fr a mple model. mple pcure needed. ngleem model. One complee cycle profle Sock On-hand me

2 n mproemen on he bac model. Place order Now. Sock On-hand Safey leel me e ry he mple model fr. ypcal profle may look lke (oer mulple cycle) f he demand conan. Sock Volume T Tme Th a mple deermnc model. Here D demand rae (conan oer me) ock-orderng co (once per cycle) T cycle lengh n day.. nenory carryng co per em per un me

3 opmum order amoun erage ock on hand n a cycle I I() he amoun of ock aalable a me. T T 0 I( )d where In our cae, I( ) D. Thu, I Therefore, nenory carryng co durng a cycle The oal relean co per cycle T The relean co per un cycle, C ( T ) T Bu T. Therefore, D T D C. nd a he opmum order amoun dc D D 0 * d * ( ) * *, D * called Economc Order uany (EO). Th EO model. Can we relax ome of he aumpon? Make our model more realc?

4 Irregular bu deermnc demand Sock On-hand Irregular & conan Demand D Tme me, demand d. Suppoe a 0we e enough nenory o la un of me. n exenon. Sochac demand rae wh he probably of demand drbuon gen. Sock On-hand Sochac Demand D Tme llow occaonal horage! Pay n goodwll f horage occur. Order f ock goe below he reorder pon. llow leadme for replenhmen f ochac.

5 Sock On-hand Sochac Demand D Tme Typcal Inenory profle under hee aumpon. We can expand he cope of he model progreely. If h become mahemacally nracable, ry o mulae. ock H Irregular demand Bu known Tme me demand d. Oher aumpon, a before. 0, we hae uffcen ock o la un of me. Then he relean co per un me (noe ha H he area under he demand cure)

6 n d d H ) ( C (Why appearng n he formula? Conder he area of a rapezum uch a h ) If ) ( C were opmum, ) C( ) ( C. Th mple d d )d ( opmum, when he nequaly afed. Sochac Inenory model d e I area e ) ( d

7 Safey leel ock y ead me umpon. a. Probablc demand. g. demand rae D b. Reorder when ock reache leel. Order an opmal c. ead me no conan d. Replenhmen a he end of lead me mmedae e. Shorage co ncurred when nenory negae. I Cper un ock per un me. f. Order co & nenory holdng co are a before, namely and, repecely. g. p ( y ) he probably ha y un demanded durng lead me. Some compuaon.. Wha he aerage nenory durng lead me?

8 O C y Safey leel B erage olume of he nenory durng erage hegh of OBC ( O BC ) y Expeced nenory durng ( y )p( y ) B. Nex, we compue expeced nenory leel afer a replenhmen unl nex reorder fer replenhmen, nenory leel M M aerage conumpon durng lead me reorder pon he nenory Therefore, he aerage nenory leel ( M ) ( M )

9 C. Nex, we compue me-duraon. M T T M T expeced me neral beween order arral and reorder pon T Cycle me,.e. me neral beween wo conecue arral ( M ) M Then, T D D M T T Therefore, T D D D. Nex, we compue he expeced horage co. Expeced horage durng lead me y> ( y )p( y ) S Shorage

10 Noe ha ( y )p( y ) ( y ) p( y ) y 0 y 0 y M S ( y ) p( y ) Now we compue he relean nenory co X per cycle. X ( M )T ( M S )(T T ) C S Toal relean con per un me C X T D M M CD S Opmum, * * C obaned from 0 D DC S( M ) and olng for. ll hee model peran o a ngle-em nenory. Nex conder he pobly o wo or more-em nenory (mul-nenory) yem, wh he addonal conrol feaure:

11 ume replenhmen for all em from a ngle ource. If any one em rgger a replenhmen order o go ou, check f any oher em from h uppler could be ordered now een f han ouched he reorder pon. e.g. B In h cae, perhap, replenhmen order for boh and B could go ou a he ame me. Bu no n he followng cae, perhap! B Perhap, we could carry ou mulaon o decde he order quany of each em gen ha hey could ofen, bu no alway, be launched earler n adance.