INVENTORY MANAGEMENT

2 Feb 2010 Arif Mahmood

Inventory

Inputs

Raw material

Purchased Parts

Maintenance and Repair

Material

Out Puts

Finished Goods

Scrap, Waste

In Process

Partially completed

Subassemblies

Analogy for Inventory

Supply RateInventory Level

Demand Rate

Inventory Level

Buffers Demand Rate from Supply Rate

Inventory Cost Structures Ordering (or setup) cost Carrying (or holding) cost:

Cost of capital Cost of storage Cost of obsolescence, deterioration, and loss

Stock out cost Item costs, shipping costs and other cost

subject to volume discounts

Typical Inventory Carrying Costs

Housing cost: Building rent or depreciation Building operating cost Taxes on building Insurance

Material handling costs: Equipment, lease, or depreciation Power Equipment operating cost

Manpower cost from extra handling and supervision Borrowing costs Taxes on inventory Insurance on inventory

Pilferage, scrap, and obsolescence Overall carrying cost

Costs as % of Inventory Value

Inventory Management Systems

Functions of Inventory Management– Track inventory – How much to order– When to order

Prioritization Inventory Management Approach

– EOQ– Continuous / Periodic

ABC Prioritization

‘A’ items: 20% of SKUs, 80% of Rupee ‘B’ items: 30 % of SKUs, 15% of

Rupee ‘C’ items: 50 % of SKUs, 5% of Rupee Three classes is arbitrary; could be

any number. Percents are approximate. Danger: Rs use may not reflect

importance of any given SKU!

ABC ANALYSIS EXAMPLE

10 20 30 40 50 60 70 80 90 100

Percentage of items

Per

cen

tag

e o

f R

s va

lue

100 —

90 —

80 —

70 —

60 —

50 —

40 —

30 —

20 —

10 —

0 —

+Class C

Class A

+Class B

Annual Usage of Items by Rs Value

Annual Usage in Units Unit Cost RsUsage

%of Total Rs Usage

5,000 1.50 7,500 2.9%1,500 8.00 12,000 4.7%

10,000 10.50 105,000 41.2%6,000 2.00 12,000 4.7%7,500 0.50 3,750 1.5%6,000 13.60 81,600 32.0%5,000 0.75 3,750 1.5%4,500 1.25 5,625 2.2%7,000 2.50 17,500 6.9%3,000 2.00 6,000 2.4%

254,725.00 100.0%

Inventory Management Approaches

A-items– Track carefully (e.g. continuous review)– Sophisticated forecasting to assure

correct levels C-items

– Track less frequently (e.g. periodic review)

– Accept risks of too much or too little (depending on the item)

Economic Order Quantity (EOQ)Model

Demand rate D is constant, recurring, and known Amount in inventory is known at all times Ordering (setup) cost S per order is fixed Lead time L is constant and known. Unit cost C is constant (no quantity discounts) Annual carrying cost is i time the average RS

value of the inventory No stockouts allowed. Material is ordered or produced in a lot or batch

and the lot is received all at once

EOQ Lot Size Choice

There is a trade-off between lot size and inventory level. Frequent orders (small lot size): higher

ordering cost and lower holding cost. Fewer orders (large lot size): lower

ordering cost and higher holding cost.

EOQ Inventory Order CycleDemand rate

0 TimeLead time

Lead time

Order Placed

Order Placed

Order Received

Order Received

Inve

nto

ry

Lev

el

Reorder point, R

Order qty, Q

As Q increases, average inventory level increases,

but number of orders placed decreases

ave = Q/2

Inventory Management EOQ Model

Keeping track of inventory Implied that we track continuously

How much to order? Solve for when the derivative of total cost with

respect to Q = 0: -SD/Q^2 + iC/2 = 0 Q = sqrt ( 2SD/iC)

When to order? Order when inventory falls to the “Reorder Point-

level” R so we will just at the last item as the new order comes in:

R = DL

Re-order Point Example

Demand = 10,000 yds/year

Lead time = L = 10 days

When inventory falls to R, we order so as not to run out before the new order comes in.

R = ?

Re-order Point

Demand = 10,000 yds/yearDaily demand = 10,000 / 365 = 27.4 yds/dayLead time = L = 10 days

R = D*L = (27.4)(10) = 274 yds

Don’t forget to convert to consistent time units!

EOQ Summary

How much to order? Q = sqrt(2DS/iC)

When to order? R = DL

Annual Demand = 1,000 unitsDays per year considered in average

daily demand = 365Cost to place an order = Rs 10

Holding cost per unit per year = Rs 2.50

EOQ and reorder point?EOQ and reorder point?

units 90or units 89.443 = 2.50

)(10) 2(1,000 =

H

2DS = QOPT

units/day 2.74 = days/year 365

units/year 1,000 = d

Lead time = 7 daysCost per unit = Rs15

units 20or 19.18=(7days)day 2.74units/=L d=R point,Reorder _

EOQ Example

Tug of war between acquisition costs and inventory carrying costs

ROP = SSQ + (QUD x ALT) 

Where, 

ROP = Reorder Point 

SSQ = Safety Stock Quantity 

QUD = Quantity Used Daily 

ALT = Average Lead Time (in days)  How much to order. Acquisition costs and inventory carrying costs: when you order bigger quantities less frequently, your aggregate

acquisition costs are low but your inventory costs are high due to higher inventory levels.

Conversely, when order smaller quantities more often, your inventory costs are low but your acquisition costs are higher because you are expending more resources on ordering.

The EOQ is the order quantity that minimizes the sum of these two costs

Safety Stock Formula

order)on items (includes levelinventory current = I

timelead and review over the demand ofdeviation standard =

yprobabilit service specified afor deviations standard ofnumber the= z

demanddaily averageforecast = d

daysin timelead = L

reviewsbetween days ofnumber the= T

ordered be toquantitiy = q

:Where

I - Z+ L)+(Td = q

L+T

L+T

q = Average demand + Safety stock – Inventory currently

on hand

q = Average demand + Safety stock – Inventory currently on hand

17-21

Cost

Regular

Fast

ReviewLocal

Forecast

Inventory

Gain Life a balance

Take the Service to the Patient

Thanks