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Lecture 12

InventoryManagement

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Types of Inven tory

Raw material

Purchased but yet not processed

Work- in-process

Undergone som e change but not c ompleted

Maintenance/repair/operat ing (MRO)

Necessary to keep m ach inery and proc esses

product ive

Finished goods

Completed product awai t ing shipment

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Hold ing , Order ing , and

Setup Costs Hold ing costs - the costs o f hold ing

or carrying inventory over time

Order ing cos ts - the costs of

placing an order and receiv ing

goods

Setup costs - cos t to p repare a

mach ine or pro cess for

manu factur ing an o rder

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Invento ry Models for

Independent Demand

Basic econom ic order quant i ty

Product ion o rder quant i ty

Quant i ty d iscount m odel

Need to determ ine when and how

much to order

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Basic EOQ Model

1. Demand is known, cons tant , and

independent

2. Lead t ime is known and cons tan t

3. Receipt of inventory is ins tantaneous and

complete

4. Quant it y d iscounts are not poss ib le

5. Only var iab le costs are setup and ho ld ing

6. Stockouts can be completely avo ided

Impor tant assumpt ions

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Invento ry Usage Over Time

Figure 12.3

Orderquanti ty = Q(maximum

inventorylevel)

Inven

tory

leve

l

Time

Usage rate Averageinventoryon hand

Q2

Min imuminventory

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Minim izing Costs

Object ive is to m inim ize total costs

Table 11.5

Annua

lcos

t

Order qu ant i ty

Curve for totalcost of ho ld ing

and setup

Hold ing costcurve

Setup (or ord er)cost curve

Min imumtota l cost

Opt imal

orderquant i ty

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The EOQ Model

Q = Number of pieces per order

Q* = Optimal num ber of pieces per order (EOQ)

D = Annual demand in uni ts for the Inventory i tem

S = Setup or order ing cost for each order

H = Holding or carrying cost per un it per year

Ann ual setup cost = (Number of orders p laced per year)x (Setup o r order cos t per order)

Annual demand

Number of uni ts in each orderSetup o r ordercos t per order=

= (S)D

Q

Ann ual setup cost = SD

Q

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The EOQ Model

Q = Number of pieces per order

Q* = Optimal num ber of pieces per order (EOQ)

D = Annual demand in uni ts for the Inventory i tem

S = Setup or order ing cost for each order

H = Holding or carrying cost per un it per year

Annua l ho ld ing cost = (Average inventory level)x (Holding cos t per unit per year)

Order quanti ty

2= (Hold ing co st per uni t p er year)

= (H)Q

2

Ann ual setup cost = SD

Q

Annual ho ld ing cost = H

Q

2

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The EOQ Model

Q = Number of pieces per order

Q* = Optim al number of pieces per ord er (EOQ)

D = Ann ual demand in uni ts for the Inventory i tem

S = Setup or order ing cost for each order

H = Holding or carrying cos t per unit per year

Opt imal order quant i ty is found when annual setup cos t

equals annual hold ing cos t

Ann ual setup cost = SD

Q

Annual ho ld ing cost = H

Q

2

D

Q

S = HQ

2Solving for Q*

2DS = Q2H

Q2= 2DS/H

Q* = 2DS/H

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An EOQ Example

Determ ine opt imal num ber of needles to o rder

D = 1,000uni tsS = $10per orderH

= $.50per un it per year

Q* =2DSH

Q* =2(1,000)(10)

0.50= 40,000 = 200uni ts

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An EOQ Example

Determ ine opt imal num ber of needles to o rder

D = 1,000un its Q* = 200uni tsS = $10per orderH

= $.50per un it per year

= N = =

Expectednum ber oforders

Demand

Order quant i ty

D

Q*

N = = 5orders per year1,000200

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An EOQ Example

Determ ine opt imal num ber of needles to o rder

D = 1,000un its Q* = 200uni tsS = $10per order N = 5orders per yearH = $.50per un it per year

= T =

Expectedtime between

orders

Number of work ingdays per year

N

T = = 50 days between o rders250

5

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An EOQ Example

Determ ine opt imal num ber of needles to o rder

D = 1,000un its Q* = 200uni tsS = $10per order N = 5orders per yearH = $.50per un it per year T = 50days

Total annual cost = Setup cos t + Holding cost

TC = S + HD

Q

Q

2

TC = ($10) + ($.50)1,000

200

200

2

TC = (5)($10) + (100)($.50) = $50 + $50 = $100

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Reorder Po ints

EOQ answers the how much question

The reorder poin t (ROP) tells when to

order

ROP =Lead t ime for a

new o rder in daysDemandper day

=d x L

d =D

Number of wo rking days in a year

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Reorder Poin t Example

Demand = 8,000DVDs per year250wo rking day yearLead t im e for orders is 3work ing days

ROP =d x L

d =D

Number of wo rking days in a year

= 8,000/250 = 32uni ts

= 32un i ts per day x 3days = 96uni ts