8/3/2019 14 Variability
1/38
Variability
The Bull Whip EffectA Vicious Cycle
Build-to-Order, Lean, JIT,
Managing Variability: A different view ofinventory
15.057 Spring 03 Vande Vate 1
8/3/2019 14 Variability
2/38
ExampleProcter & Gamble: Pampers
Smooth consumer demandFluctuating sales at retail stores
Highly variable demand on distributorsWild swings in demand on
manufacturingGreatest swings in demand on suppliers
15.057 Spring 03 Vande Vate 2
8/3/2019 14 Variability
3/38
Illustration
Consumer Sales at Retailer
1000
900
RetailerOrder
Consumerdem
and
800
700
600
500
400
300
200
1000
13579
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
Retailer's Orders to Distributor
1000
900
800
700
600
500
400
300
11
15.057 Spring 03 Vande Vate13
15
17
19
21
23
25
27
29
200
100
013579
31
33
35
37
39
341
8/3/2019 14 Variability
4/38
Illustration
Retailer's Orders to Distributor
1000
900
800
700
600
500
400
300
200
1000
Distributor's Orders to P&G
1000
900
800
700
600
500
400
300
DistributorOr
der
RetailerOrd
er
13579
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
200
100
013579
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
15.057 Spring 03 Vande Vate 4
8/3/2019 14 Variability
5/38
Illustration
Distributors Orders to P&G
1000
P&G
Order
DistributorO
rder900
800
700
600
500
400
300
200
1000
13
15.057 Spring 03 Vande Vate
579
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
P&G's Orders with 3M
1000
5
900
800
700
600
500
400
300
40
200
100
0
37
1
4
7
10
13
16
19
22
28
31
25
34
8/3/2019 14 Variability
6/38
Illustration
Consumer Sales at Retailer
1000
900
Consumerdem
and
P&G
Order
800
700
600
500
400
300
200
100
01
1
3579
11
13
15
17
19
21
23
25
27
29
31
33
35
37
39
41
P&G's Orders with 3M
1000
6
900
800
700
600
500
400
300
10
15.057 Spring 03 Vande Vate4
7
13
16
19
22
28
40
200
100
0
25
31
34
37
8/3/2019 14 Variability
7/38
What Are the Effects?
What problems, costs, challenges doesthis create for the players in thesupply chain?
What problems does this create for theproduct in the market place?
15.057 Spring 03 Vande Vate 7
8/3/2019 14 Variability
8/38
Forecasting
Poorer forecasts
More variability
Less reliable supply
15.057 Spring 03 Vande Vate 8
8/3/2019 14 Variability
9/38
Causes of Bullwhip TodayProduct Proliferation/Mass
CustomizationMore varieties of products
Build-to-OrderProhibits pooling orders to smoothrequirements
LeanPrevents pooling releases to smoothdemand on the supply chain
15.057 Spring 03 Vande Vate 9
8/3/2019 14 Variability
10/38
Why Lean (Just-In-Time)?
Reduces inventoryCapital requirementsEtc
Reduces handlingDirect-to-Line
Improves QualitySee problems quickly
Increases launch speed15.057 Spring 03 Vande Vate 10
8/3/2019 14 Variability
11/38
Why Not Lean?Capacity
Changes in requirements create upstreaminventory
Changes in requirements raise transportcosts
Reliability
Distant suppliers subject to disruption
15.057 Spring 03 Vande Vate 11
8/3/2019 14 Variability
12/38
Release Variability
Daily Receipt
1400
1200
1000
800
600
400
200
0
01-Apr-02 06-Apr-02 11-Apr-02 16-Apr-02 21-Apr-02 26-Apr-02
8/3/2019 14 Variability
13/38
Managing Variability
Capacity Buffer
Inventory Buffer
Time Buffer
15.057 Spring 03 Vande Vate 13
8/3/2019 14 Variability
14/38
Freight Cost
Capacity
Utilized Capacity
R
equired
rateofconveyances
15.057 Spring 03 Vande Vate 14Time
8/3/2019 14 Variability
15/38
Expediting Expedited Service
R
equiredrateofconveyances
Lower Capacity
Utilized Capacity
15.057 Spring 03 Vande Vate 15Time
8/3/2019 14 Variability
16/38
Ideal Supply Chain
Same requirements every dayNo excess capacityNo inventory No service failuresMinimum Cost
15.057 Spring 03 Vande Vate 16
8/3/2019 14 Variability
17/38
Buffer Inventory with Constant Supply
15.057 Spring 03 Vande Vate 17
Volum
e
Time
Variation in Demand
Variation in Buffer
8/3/2019 14 Variability
18/38
A Financial ModelFrom Revenues
Cash Expenses
Cash Acct15.057 Spring 03 Vande Vate 18
8/3/2019 14 Variability
19/38
A Financial ModelFrom Revenues
Cash Expenses
Sell Assets
Invest
Cash Acct15.057 Spring 03 Vande Vate 19
8/3/2019 14 Variability
20/38
ControlsWhen Cash
Invest
balance reachesenoughto bring it
to here
here
15.057 Spring 03 Vande Vate 20
8/3/2019 14 Variability
21/38
Controls
When Cashbalance
falls to here
Sell assetsto bring it
to here
15.057 Spring 03 Vande Vate 21
8/3/2019 14 Variability
22/38
Controls
T
bt
15.057 Spring 03 Vande Vate 22
8/3/2019 14 Variability
23/38
Trade-offs
Opportunity cost of Cash BalanceTransaction costs of investing andselling assets
Set the controls, T, t and b tobalance these costs
15.057 Spring 03 Vande Vate 23
8/3/2019 14 Variability
24/38
Inventory Analogy
Cash Expenses Daily Production reqs.From Revenue Constant suppliesSell Assets Expedited orderInvest Excess Curtailed order
15.057 Spring 03 Vande Vate 24
8/3/2019 14 Variability
25/38
Trade-offs
Opportunitycost of Cash BalanceTransactioncosts ofinvesting andselling assets
Cost ofholding
InventorySupply chain
costs ofexpeditingand curtailingorders
Set the controls, T, t and b
to balance these costs15.057 Spring 03 Vande Vate 25
8/3/2019 14 Variability
26/38
8/3/2019 14 Variability
27/38
Challenges
Data intensive:pi
s and qi
s
Computationally intensive
Alternative
Brownian motionInventory behaves like
a random walk
Model of a particle in spaceTwo parameters: mean and variance
Advanced calculus methods make it easy to work with
15.057 Spring 03 Vande Vate 27
8/3/2019 14 Variability
28/38
Release Variability
Daily Receipt
1400
1200
1000
800
600
400
200
= 367
= 412
68% of time usage is
between 0 and 800
001-Apr-02 06-Apr-02 11-Apr-02 16-Apr-02 21-Apr-02 26-Apr-02
8/3/2019 14 Variability
29/38
The EOQ as a Special Case
Average usage rate Variance in usage 2
Nominal release rate < Since we order less than we consume,
inventory drifts downward
How much should we expedite when it
reaches 0?
15.057 Spring 03 Vande Vate 29
8/3/2019 14 Variability
30/38
Trade offs
Expediting disrupts the supply chain
Fixed cost F for each time we expedite
Variable cost f for each item in the order
holding cost h for inventory
Larger orders mean less frequent but larger disruptions and more inventory
15.057 Spring 03 Vande Vate 30
8/3/2019 14 Variability
31/38
EOQ as Special Case
Order Q
Time between orders is Q/()
Order frequency is ()/Q
Average Inventory is Q/2 + 2/2()
Average Cost is
Expediting Cost: (F+fQ)()/QInventory Cost: h(Q/2 + 2/2())
15.057 Spring 03 Vande Vate 31
8/3/2019 14 Variability
32/38
The Total Cost Formula
hQ/2 + F( )/Q + h2/2( ) + f( )EOQ: Transaction Constant that doesnt depend on Q
EOQ: Inventory
The best Q balances inventory and orderingcosts:
hQ/2 = F( )/QQ2 = 2F( )/hQ = 2F( )/h
15.057 Spring 03 Vande Vate 32
8/3/2019 14 Variability
33/38
Fixed Expediting Quantity
Find the best nominal release rate to get the right frequency of expediting
15.057 Spring 03 Vande Vate 33
8/3/2019 14 Variability
34/38
The Total Cost Formula
hQ/2 + h2/2r + fr + Fr/Q
EOQ: Transaction EOQ: Inventory
Constant that doesnt depend on r
The best drift rate r = balancesinventory and ordering costs:
h2/2r = fr + Fr/Q
r2 = h2Q/2(F+fQ)
r = h2Q/2(F+fQ)15.057 Spring 03 Vande Vate 34
8/3/2019 14 Variability
35/38
Two-sided Version
If inventory grows too large, curtailshipments
Whats too large?
How much should we curtail?If expediting is expensive
create a positive driftorder more than you need
curtail shipments when inventory is too high
15.057 Spring 03 Vande Vate 35
8/3/2019 14 Variability
36/38
Differences
Constant Stream of Releases punctuatedby Expediting and Curtailing
If supplier can see inventory,
can anticipate expedited and curtailed orders
Have to set a lower bound > 0 to protect
against disruptions safety stock
15.057 Spring 03 Vande Vate 36
8/3/2019 14 Variability
37/38
Example: Shipments300
250
200
150
100
50
0
1
8
15
22
29
36
43
50
57
64
71
78
85
92
99
106
113
120
127
134
141
148
155
162
169
176
183
190
197
204
211
218
225
232
239
246
15.057 Spring 03 Vande Vate 37
8/3/2019 14 Variability
38/38
Example: Inventory
1000
900
800
700
600
500
400
300
200
100
0
15 057 Spring 03 Vande Vate 38
Top Related