Lecture 3. Matching Supply With Demand

Supply Chain Management

Lecture 3

Matching Supply With

Demand

Professor Kihoon Kim

BUSS211 OM


Contents

Littles Law (Flow Time vs. Inventory Amount)

Matching Supply with Known Demand

Steamed Oyster-Rice Game

Matching Supply with Unknown Demand

Postponement & Bullwhip Effect


Costs of not Matching Supply and Demand

Cost of overstocking

liquidation, obsolescence, holding

Cost of under-stocking

lost sales and resulting lost margin

What are the causes (challenges) driving this mismatch?

Uncertainty

Timing

Number of SKUs


The Grocery Industry 1985-1992

Number of products in average supermarket

1985 11,036

1990 16,486

1992 20,000

2004 ??

2008 ??

1975 1992 2008

2,000

20,000


Even Toothpaste


A Key to Matching Supply and Demand

When would you rather place your bet?

A B C D

A: A month before start of Derby (horse racing) B: The Monday before start of Derby C: The morning of start of Derby D: The winner is an inch from the finish line


Timing: Flow Time

Buffer Operation

Waiting Processing

Long Flow Time makes it hard to match supply with demand.


Operational Flows (Littles Law)

Throughput R

Inventory I

I = R T Flow time T = Inventory I / Throughput R

FLOW TIME T


Why do Buffers Build?

Why hold Inventory?

Economies of scale

Fixed costs associated with batches

Quantity discounts

Trade Promotions

Uncertainty

Information Uncertainty

Supply/demand uncertainty

Seasonal Variability

Strategic

Flooding, availability

Cycle/Batch stock

Safety stock

Seasonal stock

Strategic stock


Matching Supply with Known Demand

How to find the right Cycle/Batch stock quantity?


What Characterizes Inventory Systems?

1. Demand

Known Vs. Uncertain (Random)

Constant Vs. Variable (Aggregate planning, MRP): the rate of demand

2. Lead Time: time that elapses from placement of order until its arrival.

During the lead time, a shortage can happen.

3. Review Cycle: Continuous vs. Periodic

4. Treatment of Excess Demand.

Backorder all Excess Demand

Lose all excess demand

Backorder some and lose some

5. Inventory that changes over time

perishability

obsolescence


Cost of Holding Inventory

Physical holding cost

(out-of-pocket)

Financial holding cost

: Max{Cost of capital r (%/yr), Annual opportunity cost }

Low responsiveness (hard to measure)

to demand/market changes

to supply/quality changes

Ex: a) Physical Cost of Space (ex:3%) b) Taxes and Insurance (ex: 2 %) c) Breakage Spoilage and Deterioration (ex: 1%) d) Opportunity Cost of alternative investment: cost of capital (ex: 18%) Total: 24% (of unit price)


Order Cost

Fixed order cost (regardless

of order size)

Setup cost

Transportation cost

Temporary workers wages

Variable order cost

: price of a good # of units ordered

# of units

Order Cost

Fixed Cost


Penalty (or Shortage) Cost

All costs that accrue when insufficient stock is available to meet

demand. These include:

Loss of revenue for lost demand

Costs of bookkeeping for backordered demands

Loss of goodwill for being unable to satisfy demands when they

occur.

Generally assume cost is proportional to number of units of excess

demand.

If the demand is known, shortage cost is generally irrelevant; Only

when the demand is random, we incorporate shortage cost in

calculating an optimal number of units to order.


Production with large batchesProduction with small batches

Cycle

Inventory

End of

Month

Beginning of

Month

Cycle

Inventory

End of

Month

Beginning of

Month

Produce Sedan

Produce Station wagon


Cycle

Inventory

End of

Month

Beginning of

Month

Cycle

Inventory

End of

Month

Beginning of

Month

Produce Sedan



Cycle

Inventory

End of

Month

Beginning of

Month

Cycle

Inventory

End of

Month

Beginning of

Month

Produce Sedan



Cycle

Inventory

End of

Month

Beginning of

Month

Cycle

Inventory

End of

Month

Beginning of

Month

Produce Sedan


Batch Size (order size) vs. Inventory Level


Economic Order Quantity (EOQ) Model

Assumptions:

1. Demand is fixed at l units per unit time.

2. Shortages are not allowed.

3. Orders are received instantaneously. (this will be relaxed later).

4. Order quantity is fixed at Q per cycle. (can be proven optimal.)

5. Cost structure:

a) Fixed and Variable order costs (K + cx)

b) Holding cost: h per unit per unit time.


Inventory Cycle

Inventory, units

Time, t

Q

T

downward slope


Total Inventory Cost

Variable Order Cost

Holding CosFixed Order Cost

( )2

K: setup cost per order

c: order cost per unit

: demand rate per unit time (# of units)

h: holding cost per unit per unit time

t

K hQTC Q c

Q

where

ll

l


Economic Order Quantity

: Demand per year,

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

h : Marginal annual holding cost ($/per unit per year),

Q : Order quantity.

c : Cost per unit ($/unit),

i : Cost of capital (%/yr),

h = i c.

The order quantity that minimizes total

supply chain cost is:

h Q/2: Annual holding cost

Order Size Q

Total annual costs

K /Q:Annual setup cost

EOQ

2K hl

2*

KQ

h

l


Balancing between order cost and holding cost

Hyundai Sonata has been sold at a rate of 1000 cars/month

during the past year. Hyundai Sonata has released a new

version, and they expect it to be sold at the same rate. The new

Sonata costs $12,000. A dealer needs to determine how many

new Sonatas they are going to buy regularly to balance

between order-processing costs and inventory-holding

costs? You can use the information below:

Order (setup) cost: $1000 per order

Holding cost: 10% of the variable cost (annually)


Calculating EOQ

Which information they need to calculate EOQ?

Order cost

Fixed order cost: $1,000

Variable cost per unit: $12,000

Holding cost: 10% of the variable cost (annually)

EOQ?

What will happen to EOQ if order cost quadruples?


Role of Lead Time: Reorder Point (ROP)

An order can generally takes some time to be fulfilled by a 3rd

party.

Need to order in advance

When to order?

Reorder point is the inventory amount that indicates the time to order

If it takes 3 days for the order to arrive at the dealer shop, when the

dealer should order?

3 days:= 0.1 month

0.1 month < 0.1414 (cycle time)

0.1x1000=100 (Reorder Point)


Annual jacket revenues at a Pal Gear retail store are roughly $1M. Pal jackets sell at an average retail price of $325, which represents a mark-up of 30% above what Pal Gear paid its manufacturer. Being a profit center, each store made its own inventory decisions and was supplied directly from the manufacturer by truck. A shipment up to a full truck load, which was about 1500 jackets, was charged a flat fee of $2,200. To exploit economies of scale, stores typically ordered full truck loads. (Pals cost of capital is approximately 20%.)

What order size would you recommend for a Pal store in current supply network?

retailer manufacturer

Pal Gear Case


Pal Gear: evaluation of current policy of ordering Q =

1500 units each time

1. What is average inventory I?

I = Q/2

Annual cost to hold one unit H =

Annual cost to hold I = Holding cost Inventory

2. How often do we order?

Annual throughput =

# of orders per year = Throughput / Batch size

Annual order cost = Order cost # of orders

3. What is total cost? (excluding annual variable order cost)

TC = Annual holding cost + Annual order cost =

4. What happens if order size changes?


Find most economical order quantity: Spreadsheet for a Pal Gear retailer

$-

$20,000

$40,000

$60,000

$80,000

$100,000

$120,000

$140,000

$160,000

0 100 200 300 400 500 600 700 800 900 1000

Order (batch) size Q

Setup Cost

Holding Cost

Total Cost

Number of units per

order/batch Q

Number of Batches per Year: R/Q

Annual Setup Cost

Annual

Holding Cost

Annual

Total Cost

50 62 $135,385 $1,250 $136,635

100 31 $67,692 $2,500 $70,192

150 21 $45,128 $3,750 $48,878

200 15 $33,846 $5,000 $38,846

250 12 $27,077 $6,250 $33,327

300 10 $22,564 $7,500 $30,064

350 9 $19,341 $8,750 $28,091

400 8 $16,923 $10,000 $26,923

450 7 $15,043 $11,250 $26,293

500 6 $13,538 $12,500 $26,038

510 6 $13,273 $12,750 $26,023

520 6 $13,018 $13,000 $26,018

530 6 $12,772 $13,250 $26,022

540 6 $12,536 $13,500 $26,036

550 6 $12,308 $13,750 $26,058

600 5 $11,282 $15,000 $26,282

650 5 $10,414 $16,250 $26,664

700 4 $9,670 $17,500 $27,170

750 4 $9,026 $18,750 $27,776

800 4 $8,462 $20,000 $28,462

850 4 $7,964 $21,250 $29,214

900 3 $7,521 $22,500 $30,021

1000 3 $6,769 $25,000 $31,769


Optimal Economies of Scale:

For a Pal Gear retailer

= 3077 units/ year c = $ 250 / unit

i = 0.20/year K = $ 2,200 / order

Unit annual holding cost = h = 0.20/yr x $250 = $50/yr

Optimal order quantity = Q = sqrt(2 x 3077 x 2200/50) = 520

Number of orders per year = /Q = 5.9

Time between orders = Q/ = 0.17yr = 8.8weeks

Annual order cost = ( /Q)K = $13,008.87/yr

Average inventory I = Q/2 = 260

Annual holding cost = (Q/2)h =$13,008.87/yr

Average flow time T = I/R = 0.084 yr = 4.4weeks

If the lead time is 2 weeks, when they should order?


Optimal Economies of Scale:

Managerial Insights

How cut inventories (economically smart)? Reduce Fixed Order Cost

Budgeting for growth

Last FY: Sales = $100M Inventories = $20M

Next year: Sales = $400M Inventories = ?

Centralized inventory management

22EOQ EOQ

KQ TC K h c

h

ll l


Summary of Matching Supply with Known Demand

Increasing batch size Q of order (or production) increases average

inventories (and thus flow times).

Average inventory for a batch size of Q is Q/2.

The optimal batch size minimizes supply chain costs by trading off setup

cost and holding cost and is given by the EOQ formula.

To reduce batch size, one must reduce setup cost (time).

Economies of scale are manifested by the square-root relationship between

QEOQ and (, K):

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.


Matching Supply with Unknown Demand

How to find the right safety stock quantity?


Oyster-Rice in a Hot stone pot

For it to be delicious, Oysters should be fresh enough


Time to make the Oyster-Rice

The demand for Oyster-Rice is random but the distribution does not vary from day to day.

For simplicity, you tell your staff to make the same number of the oyster-rice each day that you are out of town.

How many oyster rices should they prepare?

To maximize the profits

We will simulate the demand for the oyster-rice by

The team(s) that earns the maximum profit is the winner(s)!

Distribution of Daily Demand

0%

2%

4%

6%

8%

10%

12%

14%

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Demand

Pro

babilit

y


Summary data

Distribution of Daily Demand

0%

2%

4%

6%

8%

10%

12%

14%

3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Demand

Pro

babilit

y

Retail price = $7 Cost = $3 Leftover price = $1

Mean demand = 10.5


Demand Distribution Information

D P(Dem = D) P(Dem D)

3 0.5% 0.5%

4 1.4% 1.9%

5 2.8% 4.6%

6 4.6% 9.3%

7 6.9% 16.2%

8 9.7% 25.9%

9 11.6% 37.5%

10 12.5% 50.0%

11 12.5% 62.5%

12 11.6% 74.1%

13 9.7% 83.8%

14 6.9% 90.7%

15 4.6% 95.4%

16 2.8% 98.1%

17 1.4% 99.5%

18 0.5% 100%


Suppose we prepare 11 pots of oyster-rice

We spend 11 $3 = 33 to prepare them.

Overstock: If demand is 8, we sell 8 at $7 for $56 and sell (11 8) at $1 for $3.

Total profit is $26.

Understock: If demand is 13, we sell 11 at $7 for $77 and we have no leftovers.

Total profit is $44.

Same profit as when demand is exactly 11.


Safety Stocks

Q

Time t

ROP

L

R

L

order order order

mean demand during supply lead time:

mL = R L

safety stock Is

Inventory on hand

I(t)

Q

Is

0

L


Safety Stocks Service Levels

Raise ROP until we reach appropriate SL

To do numbers, we need:

Mean m and stdev s of demand during lead time

Either Excel or tables with z-value such that CSL = F(z)

mean ROP

F(z)

demand during supply lead time

Stock-out probability

Cycle Service Level (CSL)

Is = z s

0 z


1. How to find service level (given ROP)?

2. How to find re-order point (given SL)?

1. Given ROP, find SL = P(no stock out)

= P(demand during lead time < ROP)

= F(z*= (ROP- mL)/sL) [use table]

= NORMDIST(ROP, mL, sL, True) [or Excel]

2. Given SL, find ROP = mL + Is

= mL + z*sL [use table to get z

* ]

= NORMINV (SL, mL, sL) [or Excel] Safety stock Is = z

*sL ; Reorder point ROP = mL + Is

L Lead time

D Demand per unit time Mean: R Std. Dev.: sR

DL Demand during lead time Mean: mL Std. Dev.: sL

mL = RL sL = sR L


Palu Gear:

Determining the required Safety Stock for 95% service

DATA:

R = 59 jackets/ week sR = 30 jackets/ week

h = $50 / jacket-year

K = $ 2,200 / order L = 2 weeks

QUESTION: What should safety stock be to insure a desired cycle service level of

95%?

ANSWER:

1. Required # of standard deviations z* for SL of 95% = 1.65

2. Determine std. dev. of demand during lead time: s L = sR L = 30 2 = 42

3. Answer: Safety stock Is = z* sL = 1.65 42 = 70


Total Inventory Costs of Pal Gear

1. Cycle Stock (Economies of Scale)

1.1 Optimal order quantity = 520

1.2 # of orders/year = 5.9

1.3 Annual ordering cost per store = $13,009

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

2. Safety Stock (Uncertainty hedge)

2.1 Safety stock per store = 70

2.2 Annual safety stock holding cost = $3,500.

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

= $29,500


Summary of safety stocks

Safety stock is a hedge against uncertainty

Which factors drive safety stock ? level of service z

Impact of increased service level on required safety stock

demand variability or forecast error sR,

delivery lead time L for the same level of service,

delivery lead time variability for the same level of service.

LzI Rs s*


Goal of a Supply Chain Match Demand with Supply

It is hard Why?

Hard to anticipate demand, Forecasts are wrong Why?

There is lead time. Why?

Lead time (flow time) = Activity

time+ Waiting Time Because there is waiting time...

Why there is waiting time?

Because there is inventory in the SC ( Littles Law)

Why do we hold inventory?

Rules of Forecasting

1.Forecasts are probability distributions: Use at least two numbers (mean and s)

2. Shorter forecasts are less uncertain

3.Aggregate forecasts are less uncertain

Uncertainty

To hedge against forecast error, increase inventories so that we keep

safety stock Is = z s R L

Implications:

As long as you are in the flat region of total cost you are fine.

Growth brings economies of scale, hence should reflect that

into ordering decisions.

To reduce the order size n times, one has to cut the fixed cost per

order by n 2 times (the square root formula!)

Matching supply with demand:

Summary

Economies of Scale

Manage the trade-off between - ordering cost and inventory holding cost. Use:

order quantity: 2

EOQ

KQ

h

l


Implications:

Where does sR come from?

Customer Demand Uncertainty Customer Demand Uncertainty Normal Variations

Supply Chain Management Summary Contd: How deal with Uncertainty?

1. Is service level SL (or z) appropriate?

2. Reduce lead time L

3. Reduce uncertainty per period sR

How do we deal with it?

1. Better forecasting 2. Pooling: - physical centralization - information - specialization - substitution - commonality 3. Postponement (& Pooling) 4. Quick response: - reduce leadtime and its

variability

Balance overstocking and understocking Newsvendor formula gives optimal service level:

SL* = Cu / (Co+Cu)

Lecture 3. Matching Supply With Demand

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