OMG 402 - Operations ManagementSpring 1997

CLASS 14:

Supply Chain Management

Harry Groenevelt

March 1997 2

Agenda

• Recap

• The Safety Stock Decision: Living in an Uncertain World

• Echelon Management in a Supply Chain

• Supply Chain Performance

• Supply Chain Insights

3

Recap

• Supply chains: balancing cost vs. service level

• Single Period Decisions:Trading off stockouts vs oversupplyPr{d < Q} G/(L+G)

• Pr{Z z} =

4

The Safety Stock Decision:Living in an Uncertain World

• Safety Stock = buffer against unpredictable variation in supply and demand

• We will discuss:– how to ‘trigger’ an order

(track inventory position, choose a reorder point)

– how to calculate the reorder point and safety stock

March 1997 5

The Safety Stock Decision: Example

De-icing fluid at Anchorage International Airport – Icing poses a constant threat to safety

– Variant of glycol (antifreeze) used to de-iceclears build-up and inhibits ice formation

– Stock-out of fluid grounds planes

6

weeks

demand(gallons/wk.)

35,000 gal.

The Safety Stock Decision

• demand of 35,000 gallons/week• standard deviation of demand

during one week: st = 4,000 gal.• it takes 2 weeks to receive an order• goal: limit stock-outs while we wait for the order

to arrive.

7

The Safety Stock Decision

• Assume that we use an “order point-order quantity” inventory control system. Here’s how it works:– monitor inventory position:

inventory position = inventory on-hand + scheduled receipts – backorders – inventory allocated

– we re-order Q (often, Q = EOQ) when inventory position drops to R

[see also: handout K&R Chapter 12, p. 549.]

8Note: both demand during lead time and lead time itself can be variable

weeks

inventory(gallons) Q Q

re-order point

(R)

orderplaced

orderreceived

inventoryposition inventory

on-hand

leadtime

The Safety Stock Decision

9

Calculating Reorder Point and Safety Stock

• Quantities known:– lead time to receive order = L weeks

(for now, assume this is constant)

– Dt = E[demand during one week]

– t = standard deviation of demand during one week

10

Calculating Reorder Point and Safety Stock

• Find expected demand and variability during lead time:– E[demand during lead time] = E[DL]= _______

– standard deviationof demand during lead time = L= _________

• Re-order point should be higher than E[DL]The extra inventory is safety stock (s)

11

weeks

inventory(gallons)

L L

Q Q

R

safety stock

(s)

E[DL]

what would happen if we set R = E[DL ] ??

Calculating Reorder Point and Safety Stock

12

Calculating Reorder Point and Safety Stock

• R = E[DL]+ s. How large is safety stock, s?

• Safety stock size driven by variability of demand over lead time and specified service level:– Objective 1: Satisfy cycle service level, v

Pr{stockout during lead time} < 1– v

Pr{demand during lead time > R} < 1 – v

– Objective 2: Satisfy fill rate, f proportion of orders not filled immediately < 1 – f

– Objective 3: Balance expected holding costs vs. costs of stock-out

13

Calculating Reorder Point and Safety Stock

• Assume:– L = 2 weeks, Dt = 35,000 gal, t = 4,000 gal

• Then:– E[DL] =

– L =

– R = E[DL] + s

but what should s be ??

14

Calculating Reorder Point and Safety Stock

• Objective 1: Cycle service level v = 0.01 (99% of order cycles do not stock out)– Choose R so that Pr{DL > R } = 0.01, i.e.,

Pr{DL – E[DL] > R – E[DL] } = 0.01

Pr{DL – E[DL] > s } = 0.01

Pr{Z > s/} = 0.01, or s/L = z0.99

R = E[DL] + s = E[DL] + z0.99 L

=

how many stockouts can we expect (on average) per week?

15

Calculating Reorder Point and Safety Stock

• What happens when variability of demand increases?

• What happens when lead time increases?

16

Calculating Reorder Point and Safety Stock: Variable Lead Times

di = demand during week i (a random variable) with mean E[di] = t and variance var(di) = t

2

n = number of weeks in lead time. Given: E[n] and var(n) = n

2

demand during lead time = DL = d1 + d2 + … + dn

We wish to find:

E[DL] = expected demand during lead time

L2 = variance of demand during lead time

17

Calculating Reorder Point and Safety Stock: Variable Lead Times

E[DL] = E[n] t

L2 = E[n] t

2 + t2 n

2

Then, find R as before:

s = zL R = E[DL] + s

Note that management must control many contributors to safety stock:– randomness of demand, t

2

– length of lead time, E[n] – randomness of lead time, n

2

18

which holds less safety stock as a % of demand?what factors may diminish these benefits?

anchorage intl’ anchorage local

anchorage intl’ anchorage local

Calculating Reorder Point and Safety Stock: Economies of Scale

March 1997 19

warehouse echelon

plant echelon

plant

wh1 wh2 wh3

r1 r2 r3 r4 r5 r6 r7 r8 r9

Manage your own level and those below you - your echelon.

Echelon Management in a Supply Chain

March 1997 20

Echelon Management in a Supply Chain

Each stocking point monitors its echelon inventory position

Echelon inventory position =Total on-hand inventory

+ Total inventory in transit within echelon + Orders outstanding with echelon supplier

– Backorders at echelon retailers – Inventory allocated to retail customers

March 1997 21

Echelon Management in a Supply Chain

• What are the advantages of this system?

• What are the barriers to implementation?

March 1997 22

Information and Material

Flow

Inventory Capacity

Drivers of Supply Chain Performance

Performance primarily driven by three attributes:

March 1997 23

Information and Material

Flow

Inventory Capacity

• demand variability and uncertainty

• supply variability and uncertainty

• supply lead time, order lead time

• pipeline information (how much stuff is out there?)

• bottleneck capacity

• set-up costs and times

• product flexibility

• volume flexibility (how much does it cost to ‘ramp up’?)

• safety stock

• pipeline stock (from Little’s Law!)

• cycle inventory (from batching)

• seasonal stock

Drivers of Supply Chain Performance

March 1997 24

Drivers of Supply Chain Performance

Information and

Material Flow

Inventory Capacity

If you change one attribute, others must change as wellto maintain performance.

25

Supply Chain Insights

• Examined components of inventory:– Inventory due to batching (cycle stock)– Inventory as a buffer against variable demand

during lead time (safety stock)

• Cycle stock is a response to order/setup costs, setup times, and capacity constraints;

• Safety stock guards against uncertain demand over lead times in the supply chain.

26

Supply Chain Insights

• Methods to reduce safety stock:– reduce lead time– reduce variability of length of lead time– reduce demand variability– economies of scale

• In the long run, there are interactions between information, inventory and capacity