© 2003 Anita Lee-Post Inventory management Part 3 By Anita Lee-Post.

© 2003 Anita Lee-Post

Inventory managementPart 3

By

Anita Lee-Post


EPQ assumptions• Same as the EOQ except: inventory arrives in

increments & is drawn down as it arrives


EPQ: Total cost equation

p

dH

QS

Q

DTC

p

dQI

HI

SQ

DTC

SQ

D

HI

Q

Q

12

rate production daily :p and rate, demand daily :d where

1)p

Qd( - Q used Total - produced Total

year per unit per cost Holding :H

order per cost etupOrdering/S :S

Demand Annual :D where

2 Q, at cost Total

cost etupordering/s Annaul

,2

cost holding Annual

max

max

max


EPQ: Total cost equation continued

rate production Daily :p

demand Daily :d

year per unit per cost Holding :H

run production per cost Setup :S

demand Annual :D where

daysEPQ

run Production

p

d-1H

2DS EPQ where

EPQ at costs setup annual holding annual 2 or

p

d-1

2 EPQ, at cost Minimal

p

SEPQ

DTC

HEPQ

SEPQ

DTC

EPQ

EPQ


EPQ exampleGiven:• Annual demand = 15,000• Setup cost = $500 per production run• Holding cost = $50 per item per year• Number of working days per year = 240• Annual production rate = 25,000(a) What is the EPQ?(b) What is the total cost at EPQ?(c) What is the maximum inventory level?(d) What is the total number of production run in a year?(e) What is the length of production run?(f) What is the time between production?(g) What is the length of time with no production?


EPQ example continued

days 6 8-14 run production no with time of Length (g)

days 41 18

240 run production between Time (f)

days 824025000

866

p

EPQ t run, production of Length (e)

18 866

15000

EPQ

demand Annual year a in runs production of number Total (d)

34625000

1500018661I inventory,Maximum (c)

$17320 500866

150002

2 EPQ at cost Total (b)

866

25000

15000150

500150002

d-1H

2DS EPQ (a)

p

max

p

dEPQ

SEPQ

D

p


DQ assumptions

• Same as the EOQ, except:– Unit price depends upon the quantity ordered

• Adjusted total cost equation:

price unit :P

year peritem per cost Holding :H

order per cost etupOrdering/S :S

demand Annual :D where

2PDH

QS

Q

DTCQD


QD procedure

1. Calculate the EOQ at the lowest price

2. Determine whether the EOQ is feasible at that price (will the vendor sell that quantity at that price?)

3. If yes, stop – if no, continue

4. Check the feasibility of EOQ at the next higher price

5. Continue until you identify a feasible EOQ


QD procedure continued

6. Calculate the total costs (including purchase price) for the feasible EOQ model

7. Calculate the total costs of buying at the minimum quantity allowed for each of the cheaper unit prices

8. Compare the total cost of each option & choose the lowest cost alternative


QD example #1

Given: • annual demand = 100 units• Ordering cost = $45 per order• Holding cost per year = 20% of item cost• Quantity discounts:

Order quantity Cost per item

50 or less $18

51 to 59 $16

60 or more $12


QD example #1 continuedThe lowest cost per item is $12 if ordered 60 units or more

Order at 62 units at a time is the recommended policy

1347$12005.735.73

10012$12$2.02

6245$

62

100

2

feasible found is EOQ The

item per $12 of price discounted

lowest the for qualifies time a units 62 Ordering

units 62122.0

4510022

PDHEOQ

SEOQ

DTC

H

DSEOQ

EOQ


QD example #2



50 or less $18

51 to 99 $16

100 or more $12


QD example #2 continued

• The lowest cost per item is $12 if ordered 100 units or more

infeasible found is EOQ The

item per $12 of price discounted the for

qualify not does time a units 62 Ordering

units 62122.0

4510022

H

DSEOQ



• The next lowest cost per item is $16 if ordered between 51 to 99 units



qualifies time a units 54 Ordering

units 54162.0

4510022

H

DSEOQ


QD example #2 continuedCost comparisons:


cost total lower a yields

365,1$120012045

10012$12$2.02

10045$

100

100

2

770,1$16008585

10016$16$2.02

5445$

54

100

2

100

100

54

Q

Q

EOQ

TC

PDHQ

SQ

DTC

PDHEOQ

SEOQ

DTC


QD example #3



55 or less $18

56 to 99 $16

100 or more $12



• The lowest cost per item is $12 if ordered 100 units or more




units 62122.0

4510022

H

DSEOQ



• The next lowest cost per item is $16 if ordered between 56 to 99 units




units 54162.0

4510022

H

DSEOQ



• The remaining cost per item is $18 if ordered less than 56 units


item per $18 at time a units 50 Ordering

units 50182.0

4510022

H

DSEOQ


QD example #3 continuedCost comparisons:


cost total lowest the yields

365,1$120012045

10012$12$2.02

10045$

100

100

2

771,1$16008190

10016$16$2.02

5645$

56

100

980,1$18009090

10018$18$2.02

5045$

50

100

100

100

56

50

Q

Q

Q

EOQ

TC

PDHQ

SQ

DTC

TC

TC

© 2003 Anita Lee-Post Inventory management Part 3 By Anita Lee-Post.

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Transcript of © 2003 Anita Lee-Post Inventory management Part 3 By Anita Lee-Post.