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Survey No. 38, Cherlaguda Village, Shamshabad Mandal,

RR District, Hyderabad- 501218

Phone: +91-40-30461661

Email: info@imthyderabad.edu.in

Inventory Management

Vinay Kumar Kalakbandi

Assistant Professor

Operations Management

Operations & Supply Planning PGDM 2017-19

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Why inventories?

• Economies of Scale

• Supply and Demand Uncertainty

• Volume Discounts/Impending Price Rise

• Long Lead Times and Quick Response to Customer’s Demand

• To maintain independence of operations

• To allow flexibility in production scheduling

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Inventory

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Inventory is injurious to your health!

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Get Lean…Get healthy!

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We want to turn our inventory faster than our people

A quote by James D. Sinegal

Co-founder, Costco

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Inventory turns!!!

• Sales/average inventory

• D/AI

• Low or high??

• What is AI/D?

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Independent – Dependent Demand

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Inventory classification

• Classification by form

– Raw Materials (RM)

– Work-in-Process (WIP)

– Finished Goods (FG)

• Classification by Life cycle

– Perishable

– Non-perishable

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Inventory classification by function

• Cyclic stock

– Ordering lot size/2

• Safety stock

– To protect against uncertainties

• Anticipation

– To absorb uneven rates of demand or supply

• Pipeline

– Scheduled receipts or open orders

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Quantity

Time

Safety stock

Cyclic Stock

Pipeline inventory

L

Cyclic, Pipeline and Safety Stocks

Cyclic inventory, pipeline inventory and safety stocks are critically linked to “how much” and “when” decisions in inventory planning

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Costs of Inventory

• Physical holding cost (out-of-pocket)

• Financial holding cost (opportunity cost)

• Transportation cost • Ordering costs

• Low responsiveness

– to demand/market changes – to supply/quality changes

• Obsolescence

• Holding (or carrying) costs

• Fixed costs

• Shortage costs

• Inventory writedown

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Inventory Policy parameters

• WHEN to order?

• HOW MUCH to order?

• In WHAT FORM? (RM, WIP or FG)

• WHERE TO DEPLOY in the supply chain?

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Simplest case

• Perpetual inventory system • Demand for the product is known constant and

uniform throughout the period • Lead time (time from ordering to receipt) is constant • Replenishment is instantaneous • Price per unit of product is constant • Inventory holding cost is based on average inventory • Ordering or setup costs are constant • All demands for the product will be satisfied (no back

orders are allowed) • How would the inventory level look like?

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• What should be the ordering quantity (Q)?

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EOQ model

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Inventory Planning Models

Mean of weekly demand : 200 Standard deviation of weekly demand : 40 Unit cost of the raw material : Rs. 300/- Ordering cost : Rs. 460/- per order Carrying cost percentage : 20% per annum Lead time for procurement : 2 weeks

40033.39960

400,10*460*22

H

DS

weeks252

2

10400

400

EOQ Model Weekly demand = 200 Number of weeks per year = 52 Annual demand, D = 200*52 = 10,400 Carrying cost, Cc = Rs. 60.00 per unit per year Economic Order Quantity =

Time between orders =

Practical issues with the EOQ model

• It may not be possible to

– Order exactly Q*

– Estimate the parameters (D,S,H) accurately

– Instantaneous replenishment

– Price discounts

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Robustness of the EOQ model

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Incorporating Lead time

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Price Discounts

• Why do suppliers give price discounts?

• Compute Q* values

– From lowest price to the highest

– Until valid Q* is obtained

• Compute TRC at this Q* and each price break above this Q*

• Choose the order quantity with least TC

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Reducing inventory

Type of inventory Primary Lever Secondary Lever

Cyclic Reduce Q Reduce ordering and setup cost Increase repeatability

Safety Stock Place orders closer to the time when the must be received

Improve forecasting Reduce lead time Reduce supply uncertainties Increase equipment and labor buffers

Anticipation Vary the production rate to follow the demand rate

Level out demand rates

Pipeline Cut production-disitribution lead time

Forward positioning Selection of suppliers and carriers Reduce Q

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The elephant in the room

Demand uncertainty!!!

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Vinay Kalakbandi

If life were predictable it would cease to be life, and be without

flavor.

Eleanor Roosevelt

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Lets keep it simple first!

• Single period

• Uncertain demand

• Examples?

– Newspapers

– Cakes

– Fashion products?

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Demand characteristics

• Demand follows a discrete probability distribution

• How much would you order?

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Managing the average will make you an average manager!

A quote by

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Understanding Service level

• What if demand follows a normal distribution

– NORM(5,2)

• What area of the demand distribution would you cover?

• Extending the idea to multiple periods

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Lets complicate things!

• What if demand follows

– UNIF(A,B)?

– Normal (𝜇, 𝜎)

• What area of the demand distribution would you cover?

– Service Level

• Extending the idea to multiple periods

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ROP

Q

L

In

ven

tory L

evel

Time

Mean Demand during LT

Inventory Position Physical Inventory

Certain Demand

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ROP

L

In

ven

tory L

evel

Time

Mean Demand during LT

Inventory Position Physical Inventory

Uncertain Demand

Safety Stock

Back to the multi-period setting

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Computing safety stock

)(L

)(L

)1(

Z

)1(

Let the demand during lead time follow a Normal distribution

Standard normal variate corresponding to an area of covered on the left side of the normal curve =

,

Mean demand during lead-time =

Standard deviation of demand during lead-time =

Desired service level =

The probability of a stock out =

Safety stock (SS) is given by SS = )(* LZ

Factors effecting safety stock

• Demand uncertainty (forecast uncertainty) – Reducing demand uncertainty (better forecast)

reduces safety stock required, reducing material cycle time

• Replenishment lead time – Reducing replenishment lead time, improves forecast

accuracy, reducing safety stock required (square root factor)

• Variability of supply lead time – Reducing variability of supply, improves forecast

accuracy, reducing safety stock required

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Relationship between Service Level and Safety Stock

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ROP

SS

Q

L

In

ven

tory L

evel

Time

Safety Stock

Mean Demand during LT

Inventory Position Physical Inventory

Continuous Review (Q) System

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Continuous review policy

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Inventory Planning Models

)(L

)(L 57.5640*2 Standard deviation of demand during L, =

)(L)(* LZ ROP = + = 400 + 93 = 493

Q System Mean weekly demand = 200 Standard deviation of weekly demand = 40 Lead time, L = 2 weeks Mean demand during L,

= 2* 200 = 400

)(* LZ For a service level of 95%, SS = = 1.645*56.57 = 93.05 93

Using EOQ as the fixed order quantity, Q system can be designed as follows: As the inventory level in the system reaches 493, place an order for 400 units. This will ensure in the long run a service level of 95%.

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SS

L

In

ven

tory L

evel

Time

Safety Stock

Inventory Position Physical Inventory

R 2R 3R

QR Q2R Q3R Order Up to Level

S

Periodic Review (P) System

Periodic Review policy

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Inventory Planning Models

)( RL

Using the time between orders derived from the EOQ model as the basis for review period Review period, R = 2 weeks Mean demand during (L + R), = 200*(2 + 2) = 800

For a service level of 95%,

)( RL)(* RLZ Order up to level, S = + = 800 + 132 = 932

)(* RLZ = 1.645*80 = 131.6 132 SS =

)( RL 8040*22 = Standard deviation of demand during (L + R),

P System

The P system can be designed as follows: The inventory level in the system is reviewed every two weeks and an order is placed to restore the inventory level back to 932 units. This will ensure a service level of 95%.

Periodic & Continuous Review Systems

Criterion Continuous Review (Q) System

Periodic Review (P) System

How much to order

Fixed order qty: Q S = μ(L+R) + Zα × σ(L+R) QR = S – IR

When to order

ROP = μ(L) + Zα×σ(L) Every R periods

Safety stock SS = Zα×σ(L) SS = Zα×σ(L+R)

Salient aspects

• Implemented using two

bin system

• Suited for medium and

low value items

• More safety stock

• More responsive to demand

• Ease of implementation

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Effect of variability in Lead time

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Hybrid Inventory Policies

• (s,S) policy – Optional replenishment system

• Periodic review with a order upto level

• Ensures minimum ordering level

• Eliminates continuous review

• Base stock system – Order as much as you sell

– Base stock level = expected demand during lead time + safety stock

– Usually orders are accumulated periodically

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Back to the single period model

What is the Optimal service level?

Happiness is a mysterious thing, to be found somewhere between too little and too much

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Newsvendor model

• Inventory decision under uncertainty

• The “too much/too little problem”: – Order too much and inventory is left over at the end of the

season

– Order too little and sales are lost.

Notation

• Demand D is a random variable

– Cumulative distribution function F(D)

• Wholesale price W

• Selling price R

• Salvage value S (<W)

• How much should the retailer order?

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“Too much” and “too little” costs

• Co = overage cost – The cost of ordering one more unit than what you would have ordered had

you known demand.

– Increase in profit you would have enjoyed had you ordered one unit lesser.

– Co = Cost – Salvage value = W – S =

• Cu = underage cost – The cost of ordering one fewer unit than what you would have ordered had

you known demand.

– Increase in profit you would have enjoyed had you ordered one unit more.

– Cu = Price – Cost = R – W =

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Balancing the risks and benefits

• Risk : Ordering one more unit increases the chance of overage – Expected loss on the Qth unit = Co x F(Q), where F(Q) =

Prob{Demand <= Q)

• Benefit: Ordering one more unit decreases the chance of underage: – Expected benefit on the Qth unit = Cu x (1-F(Q))

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Expected profit maximizing order quantity

• To minimize the expected total cost of underage and overage, order Q units so that the expected marginal cost with the Qth unit equals the expected marginal benefit with the Qth unit:

• Rearrange terms in the above equation ->

• The ratio Cu / (Co + Cu) is called the critical ratio.

– In other terms, (R-W)/(R-S). R and S are determined by the market.

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QFCQFC uo 1)(

uo

u

CC

CQF

)(

What is the Optimal service level?

ou

u

CC

CQdP

)(

Let Co = Cost of over stocking per unit Cu = Cost of under stocking per unit Q = Number of units to be stocked d = Single period demand = The probability of the single period demand being at most Q units

)( QdP

= Service Level

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Selective Control of Inventories • ABC Classification (on the basis of consumption value) • XYZ Classification (on the basis of unit cost of the item)

– High Unit cost (X Class item) – Medium Unit cost (Y Class item) – Low unit cost (Z Class item)

• FSN Classification (on the basis of movement of inventory) – Fast Moving – Slow Moving – Non-moving

• VED Classification (on the basis of criticality of items) – Vital – Essential – Desirable

• On the basis of sources of supply – Imported – Indigenous (National Suppliers) – Indigenous (Local Suppliers)

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ABC Classification

0%

10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

0% 10%

20%

30%

40%

50%

60%

70%

80%

90%

100%

No. of items (%)

Co

ns

um

mp

tio

n v

alu

e (

%)

Class B

Class C

Class A

Inventory Management in Practice

• Problem of Shrinkage

– Stock mismatch

• Inventory Management software

• RFID technology

• IoT tech

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THANK YOU

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