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ISEN 315

Spring 2011

Dr. Gary Gaukler

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Inventory Control

Deterministic inventory control

Stochastic inventory control

MRP / Lot sizing / JIT Supply chain management

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Reasons for ol!ing Inventories

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Relevant Costs

Holding osts !osts proportional to the"uantity o# inventory held$

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Relevant Costs "#ontinue!$

%rdering ost &or Production ost'$

an include (oth #i)ed and varia(le components$

slope * c

+

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Relevant Costs "#ontinue!$

Penalty or Shortage osts$All costs thataccrue when insufficient stock is available to

meet demand.

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Si%ple E&' (o!el

,ssumptions-

.$ Demand is #i)ed at units per unit time$

$ Shortages are not allo0ed$1$ %rders are received instantaneously$

2$ %rder "uantity is #i)ed at 3 per cycle$

4$ ost structure-

a' 5i)ed and marginal order costs &+ 6 c)' (' Holding cost at h per unit held per unittime$

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Inventory )evels for t*e E&' (o!el

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Cost E+uation for t*e E&' (o!el

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,*e -verage -nnual Cost un#tion G"'$

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,*e -verage -nnual Cost un#tion G"'$

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/roperties of t*e E&' Solution

2KQ

h

=

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Ea%ple

Des7 production rate * 88 per month 9ach des7 needs 28 scre0s

Scre0s cost :8$81 5i)ed delivery charges are :.88 per order 4; interest rate #or holding cost

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Ea%ple

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E&' Cost un#tion

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'uantity Dis#ount (o!els

,ll >nits Discounts- the discount isapplied to ,LL o# the units in the order$

Incremental Discounts- the discount isapplied only to the num(er o# unitsa(ove the (rea7point$

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-llnits Dis#ount &r!er Cost un#tion

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In#re%ental Dis#ount &r!er Cost un#tion

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-llunit Dis#ount

ompute 9%3s #or all discounts

5ind realiza(le 9%3 values

ompare cost o# realiza(le 9%3 0ith costat (rea7points

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-llnits Dis#ount -verage -nnual Cost

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-llunit Dis#ount &pti%ality

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In#re%ental Dis#ount

ost structure-

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In#re%ental Dis#ount

9sta(lish &3' curve

Determine ?cost per unit@ &3'/3

Su(stitute &3'/3 into A&3' ompute A&3' #or each range

Pic7 #easi(le solution 0ith lo0est cost

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-verage -nnual Cost un#tion

for In#re%ental Dis#ount S#*e!ule

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In#re%ental Dis#ount Ea%ple

Demand B88 (ags / year

Setup cost #or ordering- :C

>nit cost >p to 488- :8$18 >p to .888- #irst 488 at :8$18 remaining at :8$E

%ver .888- #irst 488 at :8$18 ne)t 488 at :8$Eremaining at :8$C

Holding cost- 8;

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In#re%ental Dis#ount Ea%ple

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In#re%ental Dis#ount Ea%ple

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In#re%ental Dis#ount Ea%ple

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/roperties of t*e &pti%al Solutions

5or all units discounts the optimal 0ill occur atthe (ottom o# one o# the cost curves or at a(rea7point$ %ne compares the cost at the

largest realiza(le 9%3 and all o# the (rea7pointssucceeding it$

5or incremental discounts the optimal 0illal0ays occur at a realiza(le 9%3 value$

ompare costs at all realiza(le 9%3Fs$