INVENTORY MANAGEMENT

Pankaj V. Tadaskar

Roll No. 70

.

WHAT IS INVENTORY?

Stock of items kept to meet future demand

Purpose of inventory management how many units to order when to order

TYPES OF INVENTORY

Raw materials Purchased parts and supplies Work-in-process (partially

completed) products (WIP) Items being transported Tools and equipment

12-3

.

INVENTORY AND SUPPLY CHAIN MANAGEMENT

Bullwhip effect demand information is distorted as it moves

away from the end-use customer higher safety stock inventories to are stored

to compensate Seasonal or cyclical demand Inventory provides independence from

vendors Take advantage of price discounts Inventory provides independence

between stages and avoids work stop-pages

TWO FORMS OF DEMAND

DependentDemand for items used to produce

final products Tyres stored at a MRF plant are an

example of a dependent demand item

IndependentDemand for items used by external

customersMotorcycle appliances, computers,

and houses are examples of independent demand inventory

.

INVENTORY AND QUALITY MANAGEMENT

Customers usually perceive quality service as availability of goods they want and when they want them

Inventory must be sufficient to provide high-quality customer service in TQM

INVENTORY COSTS

Carrying costcost of holding an item in inventory

Ordering costcost of replenishing inventory

Shortage costtemporary or permanent loss of sales when

demand cannot be met

INVENTORY CONTROL SYSTEMS

Continuous system (fixed-order-quantity)

constant amount ordered when inventory declines to predetermined level

Periodic system (fixed-time-period)

order placed for variable amount after fixed passage of time

ECONOMIC ORDER QUANTITY (EOQ) MODELS

EOQ optimal order quantity that will

minimize total inventory costs Basic EOQ model Production quantity model

ASSUMPTIONS OF BASIC EOQ MODEL

Demand is known with certainty and is constant over time

No shortages are allowedLead time for the receipt of

orders is constantOrder quantity is received

all at once

INVENTORY ORDER CYCLE

Demand rate

TimeLead time

Lead time

Order placed

Order placed

Order receipt

Order receipt

Inven

tory

Level

Reorder point, R

Order quantity, Q

0

EOQ COST MODEL

Co - cost of placing order D - annual demand

Cc - annual per-unit carrying cost Q - order quantity

Annual ordering cost =CoD

Q

Annual carrying cost =CcQ

2

Total cost = +CoD

Q

CcQ

2

.

EOQ COST MODEL

TC = +CoD

Q

CcQ

2

= +CoD

Q2

Cc

2

TCQ

0 = +C0D

Q2

Cc

2

Qopt =2CoD

Cc

Deriving Qopt Proving equality of costs at optimal point

=CoD

Q

CcQ

2

Q2 =2CoD

Cc

Qopt =2CoD

Cc

EOQ COST MODEL (CONT.)

Order Quantity, Q

Annual cost ($) Total Cost

Carrying Cost =CcQ

2

Slope = 0

Minimum total cost

Optimal order Qopt

Ordering Cost =CoD

Q

EOQ EXAMPLE

Cc = 0.75/- per item Co = 150/- D = 10,000 item

Qopt =2CoD

Cc

Qopt =2(150)(10,000)

(0.75)

Qopt = 2,000 yards

TCmin = +CoD

Q

CcQ

2

TCmin = +(150)(10,000)

2,000(0.75)(2,000)

2

TCmin = 750 + 750 = 1,500/-

Orders per year = D/Qopt

= 10,000/2,000= 5 orders/year

Order cycle time = 311 days/(D/Qopt)

= 311/5= 62.2 store days

PRODUCTION QUANTITY MODEL

An inventory system in which an order is received gradually, as inventory is simultaneously being depleted

AKA non-instantaneous receipt model assumption that Q is received all at once is

relaxed p - daily rate at which an order is received

over time, a.k.a. production rate d - daily rate at which inventory is demanded

PRODUCTION QUANTITY MODEL (CONT.)

Q(1-d/p)

Inventorylevel

(1-d/p)Q2

Time0

Orderreceipt period

Beginorderreceip

t

Endorder

receipt

Maximuminventory level

Averageinventory level

PRODUCTION QUANTITY MODEL (CONT.)

p = production rate d = demand rate

Maximum inventory level = Q - d

= Q 1 -

Qp

dp

Average inventory level = 1 -

Q2

dp

TC = + 1 -dp

CoD

Q

CcQ

2

Qopt =2CoD

Cc 1 - dp

PRODUCTION QUANTITY MODEL: EXAMPLE

Cc = $0.75 per yard Co = $150 D = 10,000 yards

d = 10,000/311 = 32.2 yards per day p = 150 yards per day

Qopt = = = 2,256.8 yards yards

2CoD

Cc 1 - dp

2(150)(10,000)

0.75 1 - 32.2150

TC = + 1 - = $1,329dp

CoD

Q

CcQ

2

Production run = = = = 15.05 days per orderQp

2,256.8150

PRODUCTION QUANTITY MODEL: EXAMPLE (CONT.)

Number of production runs = = = 4.43 runs/yearDQ

10,0002,256.8

Maximum inventory level = Q 1 - = 2,256.8 1 -

= 1,772 yards

dp

32.2150

QUANTITY DISCOUNTS

Price per unit decreases as order quantity increases

TC = + + PDCoD

Q

CcQ

2

where

P = per unit price of the itemD = annual demand

QUANTITY DISCOUNT MODEL (CONT.)

Qopt

Carrying cost

Ordering cost

Invento

ry c

ost

($)

Q(d1 ) = 100 Q(d2 ) = 200

TC (d2 = $6 )

TC (d1 = $8 )

TC = ($10 ) ORDER SIZE PRICE0 - 99 $10100 – 199 8 (d1)200+ 6 (d2)

QUANTITY DISCOUNT: EXAMPLE

QUANTITY PRICE

1 - 49 $1,40050 - 89 1,100

90+ 900

Co =$2,500

Cc =$190 per computer

D = 200

Qopt = = = 72.5 PCs2CoD

Cc

2(2500)(200)190

TC = + + PD = $233,784 CoD

Qopt

CcQopt

2

For Q = 72.5

TC = + + PD = $194,105CoD

Q

CcQ

2

For Q = 90

REORDER POINT

Level of inventory at which a new order is placed

R = dL

where

d = demand rate per periodL = lead time

REORDER POINT: EXAMPLE

Demand = 10,000 yards/yearStore open 311 days/yearDaily demand = 10,000 / 311 = 32.154 yards/dayLead time = L = 10 days

R = dL = (32.154)(10) = 321.54 yards

SAFETY STOCKS

Safety stockbuffer added to on hand inventory during

lead timeStockout

an inventory shortageService level

probability that the inventory available during lead time will meet demand

VARIABLE DEMAND WITH A REORDER POINT

Reorderpoint, R

Q

LTTime

LT

Inven

tory

level

0

REORDER POINT WITH A SAFETY STOCK

Reorderpoint, R

Q

LTTime

LT

Inven

tory

level

0

Safety Stock

REORDER POINT WITH VARIABLE DEMAND

R = dL + zd L

where

d= average daily demandL= lead timed= the standard deviation of daily demand z= number of standard deviations

corresponding to the service levelprobability

zd L= safety stock

REORDER POINT FOR A SERVICE LEVEL

Probability of meeting demand during lead time = service level

Probability of a stockout

R

Safety stock

dLDemand

zd L

REORDER POINT FOR VARIABLE DEMAND

The carpet store wants a reorder point with a 95% service level and a 5% stockout probability

d = 30 yards per dayL = 10 daysd = 5 yards per day

For a 95% service level, z = 1.65

R = dL + z d L

= 30(10) + (1.65)(5)( 10)

= 326.1 yards

Safety stock = z d L

= (1.65)(5)( 10)

= 26.1 yards

ORDER QUANTITY FOR A PERIODIC INVENTORY SYSTEM

Q = d(tb + L) + zd tb + L - I

where

d = average demand ratetb = the fixed time between ordersL = lead timesd = standard deviation of demand

zd tb + L= safety stockI = inventory level

FIXED-PERIOD MODEL WITH VARIABLE DEMAND

d = 6 bottles per daysd = 1.2 bottlestb = 60 daysL = 5 daysI = 8 bottlesz = 1.65 (for a 95% service level)

Q = d(tb + L) + zd tb + L - I

= (6)(60 + 5) + (1.65)(1.2) 60 + 5 - 8

= 397.96 bottles

THANKS