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Managing the Supply Chain

Key to matching demand with supply

Cost and Benefits of inventory

Economies of Scale

Inventory management of a retailer: EOQ + ROP

Levers for improvement

Safety Stock

Hedging against uncertainty

Role of lead time

Improving Performance

Centralization & Pooling efficiencies

Postponement

Accurate Response

or supply system

The Operating

System

The Distribution System

Finished Goods

Storage

Raw Material

supply points

Raw Material

Storage

Movement/

Transport

Manufacturing

Movement/

Transport

Movement/

Transport

Movement/

Transport

PLANT 1

WAREHOUSE

A

PLANT 2

WAREHOUSE

B

PLANT 3

WAREHOUSE

C

MARKETS

What is a Supply Chain?

What makes a “good” Supply Chain?

Inventories represent about %34 of current assets for a typical company in the US; %90 of working capital.

For each dollar of GNP in the trade and manufacturing sector, about 40cents worth of inventory was held.

Average logistics cost = 21c/dollar = %10.5 of GNP.

compensation plan

- Base compensation
- Bonuses
- “The Bonus Plan provides for incentive compensation ... based on certain worldwide, site and individual performance measures. Worldwide and site performance are measured based on targets w.r.t. profit before taxes, inventory turns, days sales outstanding and return on assets. The Compensation Committee believes that these factors are indicative of overall corporate performance and shareholder value.” [compensation committee report FY 96]
- Long Term Incentive Compensation

Supply and Demand

- Cost of overstocking
- liquidation
- obsolescence
- holding
- Cost of under-stocking
- lost sales and customer goodwill
- lost margin

- Economies of scale
- Fixed costs of ordering/manufacturing
- Quantity discounts
- Trade Promotions
- Uncertainty
- Information Uncertainty
- Supply/demand uncertainty
- Seasonal Variability
- Strategic
- Flooding, availability

Cycle/Batch stock

Safety stock

Seasonal stock

Strategic stock

- Physical holding cost
- (out-of-pocket)
- Financial holding cost
- (opportunity cost)
- Low responsiveness
- to demand/market changes
- to supply/quality changes

Holding cost (H)

Costs Associated with Batches

- Ordering costs (S)
- Changeover of production line (Set-up)
- Transportation (Delivery)
- Receiving
- Holding costs (H = r C)
- Physical holding cost
- Cost of capital (r)
- Cost of obsolescence

Palü Gear: Retail Inventory Management

Annual jacket revenues at a Palü Gear retail store are roughly $1M. Palüjackets sell at an average retail price of $325, which represents a mark-up of 30% above what Palü Gear paid its manufacturer. Being a profit center, each store made its own inventory decisions and was supplied directly from the manufacturer by truck. For each order up to 5000 jackets, the manufacturer charges a flat fee of $2,200 for delivery. To exploit economies of scale, stores typically orders 1500 jackets each time it places an order. (Palü’s cost of capital is approximately 20%.) What order size would you recommend for a Palü store in current supply network?

Palü Gear: Evaluation of current policy of ordering 1500 units each time

- What is average inventory I?
- I =
- Annual cost to hold one unit H =
- Annual cost to hold I =
- How often do we order?
- Annual throughput R =
- # of orders per year =
- Annual order cost =
- What is total cost?
- TC =

Can we do better ?

Find the most economical order quantity

Method 1 : Enumerate

Economies of Scale: Inventory Build-Up Diagram

- R: Annual demand rate (units/yr),
- Q: Number of jackets per replenishment order
- Number of orders per year = R/Q.
- Average number of jackets in inventory = Q/2 .

Inventory

T = Q/R

Q

R = Demand rate

T

time between

orders

Time t

Order placed,

arrives immediately

Lead time=0

Order placed,

arrives immediately

Lead time=0

R: Demand per year,

S: Setup or Order Cost ($/setup; $/order),

H: Marginal annual holding cost ($/per unit per year), H = r C

Q: Order quantity.

C: Cost per unit ($/unit),

r: Cost of capital (% / yr),

Total annual costs

H Q/2: Annual holding cost

S R /Q:Annual setup cost

QEOQ

Batch Size Q

What do we learn from the EOQ formula ? How does the ordering policy change if …

The product is a success and the demand picks up, now we are selling 4 times the original demand…

The interest rates double up, so does our unit inventory holding costs …

After investing in IT, we manage to reduce our fixed ordering cost by half …

For a Palü Gear retailer

R = 3077 units/ year C = $ 250 / unit

r = 0.20/year S = $ 2,200 / order

Unit annual holding cost = H = $50/unit-yr

Optimalorder quantity = EOQ = 520 units

Number of orders per year = R/Q = 3077/520 = 5.91

Time between orders = Q/R = 8.78 weeks

Annual order cost = (R/Q)S = $13,018/yr

Average inventory I = Q/2 = 260 units

Annual holding cost = (Q/2)H = $13,018/yr

Take-Aways IBatching & Economies of Scale

- Increasing batch size of production (or purchase) increases average inventories (and thus cycle times).
- Average inventory for a batch size of Q is Q/2.
- The optimal batch size trades off setup cost and holding cost.
- To reduce batch size, one has to reduce setup cost (time).
- Square-root relationship between Q and (R, S):
- If demand increases by a factor of 4, it is optimal to increase batch size by a factor of 2 and produce (order) twice as often.
- To reduce batch size by a factor of 2, setup cost has to be reduced by a factor of 4.

Palü Gearcont.

- The lead time from when a Palü Gear retailer places an order to when the order is received is two weeks. If demand is stable as before, when should the retailer place an order?
- I-Diagram:

ROP

Order

arrives

2wks

Order

placed

ROP =

Two Key Decisions of Inventory Management

- How much to order ?
- Answer: EOQ
- 2. When to place an order ?
- Answer: ROPReorder Point
- represents the amount of inventory on hand when we place a new order .
- Delivery Lead Time = 0 (Instantaneous Delivery) then ROP = …….
- Delivery Lead Time > 0 then ROP = …….
- ROP is driven by:
- Delivery Lead Time
- Demand Uncertainty
- Customer Service Level

A Key to Matching Supply and Demand

When would you rather place your bet?

A

B

D

C

A: A month before start of Derby

B: The Monday before start of Derby

C: The morning of start of Derby

D: The winner is an inch from the finish line

Demand uncertainty and forecasting

- Year Demand Forecast Error
- 1 323
- 2 258
- 3 303
- 4 304
- 5 284
- 6 285

Demand uncertainty and forecasting

- Forecasts depend on
- historical data
- “market intelligence”
- Forecasts are usually (always?) wrong.
- A good forecast has at least 2 numbers (includes a measure of forecast error, e.g., standard deviation).
- The forecast horizon must at least be as large as the lead time. The longer the forecast horizon, the less accurate the forecast.
- Aggregate forecasts tend to be more accurate.

Palü Gear:Service levels & Inventory management

- In reality, a Palü Gearstore’s demand fluctuates from week to week. In fact, weekly demand at each store had a standard deviation of about 30 jackets assume normally distributed. Recall that average weekly demand was about 60 jackets; the order lead time is 2 weeks; fixed order costs are $2,200/order and it costs $50 to hold one jacket in inventory during one year.
- Questions:
- If the retailer uses the ordering policy discussed before (ROP =120), what will the probability of running out of stock in a given cycle be?
- The Palü retailer would like the stock-out probability to be smaller. How can she accomplish this?
- Specifically, how does it get the service level up to 95%?

Example: say we increase ROP to 140 (and keep order size at Q = 520)

- On average, what is the stock level when the replenishment arrives?
- What is the probability that we run out of stock before a delivery arrives?
- How do we get that stock-out probability down to 5%?

Consider the lead time between the placement of an order and the arrival of the order. L=2 weeks.

Demand per week, R ~ (60, 30)

The mean demand during the lead time = 2*60 = 120

Standard deviation of demand during lead time

= (30)2 + (30)2

= 30

2

D lead time ~ N (120, 30 )

2

Probability of stock out (i.e.,

Probability that the demand during

lead time is greater than 120 ) = ?

Lead time

demand distribution

120

Mean Demand

During Lead Time

SAFETY STOCK

Increase reorder point

above average demand during lead time, lower the probability of stockout! BETTER SERVICE LEVEL!

Safety stock increase with the service level.

e.g., % 95

ROP

Small variance / SD

%95

ROP

120

Safety stock increases

with the variance (SD) of lead time demand

Higher Variability

Larger SD/ variance

%95

ROP

120

- Safety stockincreases (decreases) with an increase (decrease) in:
- demand variability or forecast error,
- delivery lead time for the same level of service,
- delivery lead time variability for the same level of service.

Palü Gear: Determining the required Reorder Point for 95% service

- DATA:
- R= 60 jackets/ week sR = 30 jackets/ week
- H = $50 / jacket, yearstandard deviation of weekly demand
- S = $ 2,200 / order L = 2 weeks
- QUESTION:
- What should safety stock be to insure a desired cycle service level of 95%?
- ANSWER:
- Determine slead time demand = 42.42
- Required # of standard deviations z* = 1.64
- 3. Reorder Point = 120+1.64*42.42= 190 jackets
- 4. Safety stock Is = 1.64*42.42=70 jackets

z

0

Review of Probability

The standard normal distribution F(z)

- Transform X = N(m,s) to z = N(0,1)
- z = (X - m) / s.
- F(z) = Prob ( N (0,1) <z)
- Transform back, knowing z*:
- X* = m + z*s.

R

L

Inventory on hand

I(t)

EOQ

EOQ

order

order

order

ROP

mean demand during supply lead time:

m = R L

Is

safety stock Is

0

Time t

L

L

Comprehensive Financial Evaluation:Inventory Costs of Palü Gear

1. Cycle Stock (Economies of Scale)

1.1 Optimal order quantity =

1.2 # of orders/year =

1.3 Annual ordering cost per store = $13,009

1.4 Annual cycle stock holding cost. = $13,009

2. Safety Stock (Uncertainty hedge)

2.1Safety stock per store = 70

2.2 Annual safety stock holding cost = $3,500

3. Total Costs for 5 stores = 5 (13,009 + 13,009 + 3,500)

= 5 x $29,500 = $147.5K.

How to find service level (given ROP)?How to find re-order point (given SL)?

- L = Supply lead time,
- D =N(R, sR) = Demand per unit time is normally distributed
- with mean R and standard deviation sR
- DL=N(m, s) = Demand during the lead time is normally distributed
- with mean m = RL and standard deviations s = sRL
- Given ROP, find SL = Cycle service level = P(stock out)
- = P(demand during lead time >ROP)
- = 1-F(z*= (ROP- m)/s) [use table]
- = 1- NORMDIST(ROP, m, s, True) [or Excel]
- Given SL, find ROP = m + Is
- = m + z*s [use table to get z* ]
- = NORMINV(1-SL, m, s) [or Excel]
- Safety stock Is= z*sReorder point ROP = m + Is

Cycle Cost : EOQ: How much to order?

Balance the fixed costs of ordering with the average inventory holding cost.

Total Cycle Cost are quiet robust to misestimating the parameters

Growth brings scale economies, adjust operating policies as markets conditions change.

Safety Stock Cost: Reorder Point : When to place an order?

Uncertainty is nothing but forecasting error.

Determined by the Service Level P(D(lead time)>ROP)

ROP=RxL+Safety Stock

Take-Aways II

Demand Uncertainty & Inventory Management

How can we reduce supply chain costs without sacrificing customer service?

How can we improve customer service without increasing supply chain costs?

- Distribution Centralization
- Product Postponement (HP)
- Process Postponement (Benetton)
- Capacity Analysis (Benetton)

Improving Supply Chain Performance:1. The Effect of Pooling/Centralization

Decentralized Distribution

Is=100

Is=100

Is=100

Is=100

Centralization Distribution

Is= 400

Is=400

Palü Gear’s Internet restructuring: Centralized inventory management

- Weekly demand per store = 60 jackets/ week

with standard deviation = 30 / week

H = $ 50 / jacket, year S = $ 2,200 / order

Supply lead time L = 2 weeks

Service level : 95% availability.

- Palü Gearnow is considering restructuring to an Internet store. So 5 local stores will be closed and a National DC will be opened to distribute direct to customers.

Compare the safety stock in the decentralized and centralized systems

Decentralized

Centralized – 5 stores

Demand R per week

for each store

ms=60

ss=30

Demand during Supplier lead time (L=2)

mltd=

sltd=

Safety Stock for each store (%95 availability)

Total Safety Stock

Demand R per week

for the centralized warehouse

mc=

sc=

Demand During Supplier Lead Time

(L=2)

mltd=

sltd=

Safety Stock for the centralized warehouse

(%95 availability)

Palü Gear’s Internet restructuring: comprehensive financial inventory evaluation

1. Cycle Stock (Economies of Scale)

1.1 Optimal order quantity =

1.2 # of orders/year =

1.3 Annual ordering cost of e-store = $29,089

1.4 Annual cycle stock holding cost = $29,089

2. Safety Stock (Uncertainty hedge)

2.1Safety stock for e-store =

2.2 Annual safety stock holding cost = $7,800.

3. Total Costs for consolidated e-store = 29,089 + 29,089 + 7,800

= $65,980

Learning Objectives: centralization/pooling

- Different methods to achieve pooling efficiencies:
- Physical centralization
- Information centralization
- Specialization
- Raw material commonality (postponement/late customization)
- Cost savings are sqrt(# of locations pooled).

Production

Unique Power

Production

Transportation

Europe

Process I: Unique

Power Supply

N. America

Europe

Process II: Universal

Power Supply

N. America

Make-to-Stock Push-Pull Boundary Make-to-Order

Improving Supply Chain Performance: 2. Postponement & Commonality (HP Laserjet)Tailored Inventories: Postponement

- Simple solution
- Produce all garments as Greige goods (Production cost is 10% higher)
- Tailored solution
- Base load manufactured from colored thread (cheaper but long lead time sourcing)
- Safety stock held as Greige goods and manufactured on demand (10% more expensive but short lead times)

4000

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3500

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0

0

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4000

Postponement and Re-assortment: The Advantage to ForecastingActual total sales

Initial Forecast Updated Forecast after observing 20% of sales after 80%

Each data point represents the forecast and the actual season sales for a particular item (at the style-color level).

Two types of Production Capacities

Speculative Capacity

Long Lead Time cheap

Reactive Capacity

Short Lead Time - expensive

Commit before

observing the demand

Gamble!

Commit after

observing the early sales data

How do we decide on the size of the speculative capacity?

Demand forecast for Christmas jackets

18%

16%

16%

16%

14%

13%

13%

12%

10%

10%

10%

8%

6%

6%

6%

4%

3%

3%

2%

1%

1%

1%

1%

0%

800

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000

3200

Optimal Service Level and Accurate Response to Demand Uncertainty when you can order only once:- Palü Gear’s is planning to offer a special line of winter jackets, especially designed as gifts for the Christmas season. Each Christma-jacket costs the company $250 and sells for $450. Any stock left over after Christmas would be disposed of at a deep discount of $195. Marketing had forecasted a demand of 2000 Christmas-jackets with a forecast error (standard deviation of 500)
- How many jackets should Palü Gear’s order?

Optimal Service Level and Accurate Response: with Excel(1) Performance for a given order Q, say Q = 2000

Optimal Service Level and Accurate Response : with Excel(2) Performance for all possible Q

- 200

D -55

= F(Q)

Suppose you placed an order of 2000 units but you are not sure about whether you should have ordered one more unit.

Incur an overage cost of (c-s) = C with probability p = P(D<=2000)

Earn a margin (p-c) = B with propability (1-p)= P(D>2000)

DP = …..

DP = ..

Expected contribution of an additional unit

E(DP) = ………………..

So? ... Order more?

What is the contribution of ordering an additional unit?

Marginal Benefit

Marginal Cost

220

- Co = - 55

210

200

Expected

Profit ($k)

190

180

170

160

150

+ 200 = Cu

140

130

Order/Stock

Quantity Q

120

1000

1200

1400

1600

1800

2000

2200

2400

2600

2800

3000

Accurate Response: The newsboy model

In general: at the optimal Q

E(DP) <= 0 – no incentives to order more

(1-p)B= pC

SellDo not sell

Equivalently, choose the smallest Q

such that

p = P(D<Q) = F(Q) >= B/ (B+C)

- Example:
- Critical fractile
- B/ (B+C) =
- Find Q by rounding up!
- Q =

Accurate response: Find optimal Q from newsboy model

- Cost of overstocking by one unit = C
- the out-of-pocket cost per unit stocked but not demanded
- “Say demand is one unit below my stock level. How much did the one unit overstocking cost me?” E.g.: purchase price - salvage price.
- Cost of understocking by one unit = B
- The opportunity cost per unit demanded in excess of the stock level provided
- “Say demand is one unit above my stock level. How much could I have saved (or gained) if I had stocked one unit more?” E.g.: retail price - purchase price.

Given an order quantity Q, increase it by one unit if and only if the expected benefit of being able to sell it exceeds the expected cost of having that unit left over.

Marginal Analysis: Order more as long as F(Q) < B/ (B + C)

- = smallest Q such that service level F(Q) > critical fractile B/ (B + C)

Where else do you find newsboys?

- Benefits: Flexible Spending Account decision
- ATM
- Perishable Products (Newspaper, Medical Supplies, Fashion Goods)
- Weddings, Conferences…

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