Inventory Management
Multi-Items and Multi-Echelon
Chris Caplice
ESD.260/15.770/1.260 Logistics Systems
Nov 2006
Advanced Topics
So far, we have studied single-item single
location inventory policies.
What about . . .
„
Multiple Items
Š How do I set aggregate policies?
Š What if I have to meet a system wide objective?
„
Multiple Locations – Multi-echelon
Š Deterministic demand
Š Stochastic demand
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© Chris Caplice, MIT
Inventory Planning Hierarchy
Annual/Quarterly
Quarterly/Monthly
Weekly/Daily/Hourly
Operational Tactical
Strategic
Inputs
Plan
• Transportation costs
• Facility fixed and
variable costs
• Inventory costs
• Service levels
Network
Design
• Inventory flow
• Network
configuration
• Capacity
Deployment
• Item-level flow
• Item classifications
• Inventory locations
• Target Service levels
• Target Reorder points
• Target Safety stock
Replenishment
• How much and when
to replenish
• Reorder Points
Reorder Quantities
• Review Periods
• Forecast
• Lead times
• Variable and
inventory costs
• Business policies
• Forecasts/Orders
• Lead times
• Handling costs
• Vendor/volume
discounts
Results
• Customer orders
• On-hand and
in-routeinventories
• Real transit costs
• Production
schedules
Allocation
• Demand prioritization
• Assign inventory to
orders
Jeff Metersky, Vice President Chainalytics, LLC
Rosa Birjandi, Asst. Professor Air Force Institute of Technology
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© Chris Caplice, MIT
Inventory Policies for Multiple Items
Aggregate constraints are placed on total inventory
„
„
Avg total inventory cannot exceed a certain budget ($ or Volume)
Total number of replenishments per unit time must be less than a certain
number
Inventory as a portfolio of stocks – which ones will yield the highest
return?
Cost parameters can be treated as management policy variables
„
„
„
„
There is no single correct value for holding cost, r.
Best r results in a system where inventory investment and service level
are in agreement with overall strategy.
Cost per order, A, is also not typically known with any precision.
Safety factor, k, is set by management.
Exchange Curves
„
„
Cycle Stock - Trade-off between total cycle stock and number of
replenishments for different A/r values
Safety Stock – Trade-off between total safety stock and some
performance metric for different k values
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Exchange Curves
Set notation for each item:
„
„
„
„
„
A = Order cost common for all items
r = Carrying cost common for all items
Di = Demand for item i
vi = Purchase cost of item i
Qi = Order quantity for item i
Need to find:
Total average cycle stock (TACS) and Number of replenishments (N)
⎛ 2 ADi ⎞
⎜⎜
⎟⎟ v i
rv i ⎠
n Qv
n
TACS = ∑ i =1 i i = ∑ i =1 ⎝
2
2
ADi v i
A 1
n
n
=
TACS = ∑ i =1
∑ Di v i
r 2 i =1
2r
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N = ∑ i =1
n
N = ∑ i =1
n
Di
Di
n
= ∑ i =1
Qi
2 ADi
rv i
rDi v i
=
2A
r 1
n
∑ Di v i
A 2 i =1
© Chris Caplice, MIT
Exchange Curves
Exchange Curve
Total Average Cycle Stock Value
$160,000
A/r = 10000
$140,000
$120,000
Current Operations
$100,000
$80,000
A/r = 10
$60,000
$40,000
$20,000
$-
100
200
300
400
500
Number of Replenishments
Exchange curve for 65 items from a hospital ward.
Current operations calculated from actual orders.
Allows for management to set A/r to meet goals or budget,
Suppose TACS set to $20,000 – we would set A/r to be ~100
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Exchange Curves
Now consider safety stock, where we are trading off SS
inventory with some service metric
Different k values dictate where we are on the curve
Suppose that we only have budget for $2000 in SS – what is our
CSL?
Single Item Exchange Curve
7000
6000
Safety Stock ($)
5000
4000
3000
2000
1000
0
-1000
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
-2000
-3000
Cycle Service Level
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© Chris Caplice, MIT
Exchange Curves
Set notation for each item:
„
„
„
„
„
σLi = RMSE for item i
ki = Safety factor for item i
Di = Demand for item i
vi = Purchase cost of item i
Qi = Order quantity for item i
Need to find:
„
„
Total safety stock (TSS) and
Some service level metric
Š Expected total stockout occasions per year (ETSOPY)
Š Expected total value short per year (ETVSPY)
TSS = ∑ i =1 k i σ Li v i
n
ETSOPY = ∑ i =1
MIT Center for Transportation & Logistics – ESD.260
n
8
Di
P [SOi ]
Qi
ETVSPY = ∑ i =1
n
Di
σ Li v i G(ki )
Qi
© Chris Caplice, MIT
Exchange Curves
$3,500
k=3
Total Safety Stock ($)
$3,000
$2,500
k=1.6
$2,000
$1,500
$1,000
$500
$-
100
200
300
400
500
600
700
800
Expected Total Stockout Occasions per Year
Exchange curve for same 65 items from a hospital ward.
Allows for management to set aggregate k to meet goals or budget,
Suppose TSS set to $1,500 – we would expect ~100 stockout events per
year and would set k= 1.6
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© Chris Caplice, MIT
Replenishment in a Multi-Echelon System
Plant
RDC1
RDC2
LDC1
R1
LDC2
R2
R3
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LDC3
R4
R5
10
LDC4
R6
R7
R8
© Chris Caplice, MIT
What if I Use Traditional Techniques?
In multi-echelon inventory systems with
decentralized control, lot size / reorder
point logic will:
„
„
„
Create and amplify "lumpy" demand
Lead to the mal-distribution of available stock,
hoarding of stock, and unnecessary stock outs
Force reliance on large safety stocks,
expediting, and re-distribution.
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© Chris Caplice, MIT
Impact of Multi-Echelons
CDC
Demand
Pattern
RDC
Ordering
Patterns
RDC
Inventory
Cycles
Customer
Demand
Patterns
Layers of Inventory Create Lumpy Demand
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© Chris Caplice, MIT
What does a DRP do?
Premises
„
„
„
„
Inventory control in a distribution environment
Many products, many stockage locations
Multi-echelon distribution network
Layers of inventory create "lumpy" demand
Concepts
„
„
„
„
Dependent demand versus independent demand
Requirements calculation versus demand forecasting
Schedule flow versus stockpile assets
Information replaces inventory
"DRP is simply the application
of the MRP principles and techniques
to distribution inventories“
Andre Martin
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© Chris Caplice, MIT
DRP Requirements
Information Requirements:
„
„
„
„
Base Level Usage Forecasts
Distribution Network Design
Inventory Status
Ordering Data
DRP Process:
„
„
„
„
Requirements Implosion
Net from Gross Requirements
Requirements Time Phasing
Planned Order Release
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A Distribution Network Example
Plant
Central Warehouse
Regional Warehouse 1
Regional Warehouse 2
Retailer A
Retailer B
Retailer C
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Retailer D
Retailer E
Retailer E
15
Regional Warehouse 3
Retailer G
Retailer H
Retailer I
© Chris Caplice, MIT
The DRP Plan
Central Warehouse Facility
Q=200, SS=0, LT=2
NOW
1
2
3
4
5
6
7
8
Period Usage
100
20
50
30
100
0
100
0
Gross Rqmt
100
20
50
30
100
0
100
0
Begin Inv
150
50
30
180
150
50
50
150
Sched Recpt
0
0
0
0
0
0
0
0
Net Rqmt
-
-
20
-
-
-
50
-
Planned Recpt
0
200
0
0
0
200
0
180
150
50
50
150
150
End Inv
150
Planned Order
50
30
200
200
Regional Warehouse One
Q=50, SS=15, LT=1
Plant
Central Warehouse
NOW
1
2
3
4
5
6
7
8
Period Usage
25
25
25
25
25
25
25
25
Gross Rqmt
40
40
40
40
40
40
40
40
Begin Inv
50
25
50
25
50
25
50
25
Sched Recpt
0
0
0
0
0
0
0
0
Net Rqmt
-
15
-
15
-
15
-
15
0
50
0
50
0
50
0
50
25
50
25
50
25
50
25
50
Planned Recpt
End Inv
50
Planned Order
Regional Warehouse 1
Regional Warehouse 2
Retailer D
Retailer E
Retailer E
Retailer G
Retailer H
Retailer I
50
50
50
Regional Warehouse Two
Regional Warehouse 3
Q=30, SS=10, LT=1
Retailer A
Retailer B
Retailer C
50
NOW
1
2
3
4
5
6
7
8
Period Usage
10
10
10
10
20
20
20
20
Gross Rqmt
20
20
20
20
30
30
30
30
Begin Inv
20
10
30
20
10
20
30
10
Sched Recpt
0
0
0
0
0
0
0
0
Net Rqmt
-
10
-
-
20
10
-
20
Planned Recpt
End Inv
20
Planned Order
10
30
0
0
30
30
0
30
30
20
10
20
30
10
20
30
30
30
30
Regional Warehouse Three
Q=20, SS=10, LT=1
Note:
Gross Rqmt = Period Usage + SS
1
2
3
4
5
6
7
8
Period Usage
5
15
10
10
0
15
0
15
Gross Rqmt
15
25
20
20
10
25
10
25
Begin Inv
15
10
15
25
15
15
20
20
Sched Recpt
0
0
0
0
0
0
0
0
Net Rqmt
-
15
5
-
-
10
-
5
Planned Recpt
0
20
20
0
0
20
0
20
10
15
25
15
15
20
20
25
End Inv
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15
© Chris Caplice, MIT
Example: The DRP Plan
Regional Warehouse One
Q=50 , SS=15 , LT=1
NOW
Forecast
1
2
3
4
5
6
7
8
Period Usage
25
25
25
25
25
25
25
25
Gross Rqmt
40
40
40
40
40
40
40
40
Begin Inv
50
25
50
25
50
25
50
25
0
0
0
0
0
0
0
0
Sched Rcpt
Net Rqmt
15
Plan Rcpt
End Inv
50
POR
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15
15
0
50
0
50
0
50
0
50
25
50
25
50
25
50
25
50
50
50
17
50
50
© Chris Caplice, MIT
Example: The DRP Plan
Regional Warehouse Two
Q=30 , SS=10 , LT=1
NOW
1
2
3
4
5
6
7
8
Period Usage
10
10
10
10
20
20
20
20
Gross Rqmt
20
20
20
20
30
30
30
30
Begin Inv
20
10
30
20
10
20
30
10
0
0
0
0
0
0
0
0
20
10
Sched Rcpt
Net Rqmt
10
Plan Rcpt
End Inv
20
POR
MIT Center for Transportation & Logistics – ESD.260
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0
30
0
0
30
30
0
30
10
30
20
10
20
30
10
20
30
30
30
18
30
© Chris Caplice, MIT
Example: The DRP Plan
Regional Warehouse Three
Q=20 , SS=10 , LT=1
NOW
1
2
3
4
5
15
10
10
0
15
0
15
Gross Rqmt
15
25
20
20
10
25
10
25
Begin Inv
15
10
15
25
15
15
20
20
0
0
0
0
0
0
0
0
15
5
0
20
20
0
0
20
0
20
10
15
25
15
15
20
20
25
20
20
Period Usage
Sched Rcpt
Net Rqmt
Plan Rcpt
End Inv
15
POR
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5
6
7
8
10
20
5
20
© Chris Caplice, MIT
The DRP Plan for All Locations
Rolling Up Orders
NOW
1
2
3
4
5
Period Usage
100
20
50
30
100
POR
200
6
7
8
CENTRAL
0
100
0
25
25
25
200
REGION ONE
Period Usage
25
POR
50
25
25
25
50
25
50
50
REGION TWO
Period Usage
10
POR
30
10
10
10
20
30
30
10
0
20
20
20
30
REGION THREE
Period Usage
POR
MIT Center for Transportation & Logistics – ESD.260
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15
20
20
20
10
20
15
0
15
20
© Chris Caplice, MIT
Example: The DRP Plan
Central Warehouse
Q=200 , SS=0 , LT=2
NOW
1
2
3
4
5
6
7
8
Period Usage
100
20
50
30
100
0
100
0
Gross Rqmt
100
20
50
30
100
0
100
0
Begin Inv
150
50
30
180
150
50
50
150
0
0
0
0
0
0
0
0
Sched Rcpt
Net Rqmt
20
Plan Rcpt
End Inv
POR
150
50
0
0
200
0
0
0
200
0
50
30
180
150
50
50
150
150
200
MIT Center for Transportation & Logistics – ESD.260
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© Chris Caplice, MIT
Results and Insights
DRP is a scheduling and stockage algorithm
-- it replaces the forecasting mechanism above the
base inventory level
DRP does not determine lot size or safety stock
-- but these decisions must be made as inputs to the
process
DRP does not explicitly consider any costs
-- but these costs are still relevant and the user must
evaluate trade-offs
DRP systems can deal with uncertainty somewhat
-- using "safety time" and "safety stock"
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© Chris Caplice, MIT
MRP / DRP Integration
Purchase Orders
C
MRP
C
C
SA
C
C
SA
C
C
SA
C
SA
A
A
MPS
Product
CDC
RDC
DRP
Retail
RDC
Retail
Retail
Retail
Sales/Marketing Plan
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© Chris Caplice, MIT
Evolution of Inventory Management
Traditional Replenishment Inventory:
„
„
„
„
Lot Size/ Order Point Logic
Single item focus
Emphasis on cost optimization
Long run, steady state approach
The MRP / DRP Approach:
„
„
„
„
Scheduling emphasis
Focus on quantities and times, not cost
Multiple, inter-related items and locations
Simple heuristic rules
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© Chris Caplice, MIT
Evolution of Inventory Management
MRP / DRP have limited ability to deal with:
„
„
„
„
„
„
Capacity restrictions in production and distribution
“set-up” costs
fixed and variable shipping costs
alternative sources of supply
network transshipment alternatives
expediting opportunities
Next Steps in MRP/DRP
„
„
„
„
Establish a time-phased MRP/MPS/DRP network
Apply optimization tools to the network
Consider cost trade-offs across items, locations, and
time periods
Deal with shortcomings listed above
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© Chris Caplice, MIT
A DRP Network Plan
What happens when actual demand in the short term doesn’t follow
the forecast exactly…..
How should I re-deploy my inventory to take the maximum advantage
of what I do have?
Plant
RDC1
RDC2
LDC1
R1
LDC2
R2
R3
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LDC3
R4
R5
26
LDC4
R6
R7
R8
© Chris Caplice, MIT
A DRP Network Reality
Plant
RDC1
RDC2
SHORTAGES
LDC1
R1
EXCESS
LDC2
R2
R3
LDC3
R4
R5
Higher than expected demand
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LDC4
R6
R7
R8
Lower than expected demand
© Chris Caplice, MIT
Optimal Network Utilization
Plant
RDC1
RDC2
SHORTAGES
LDC1
R1
EXCESS
LDC2
R2
R3
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LDC3
R4
R5
28
LDC4
R6
R7
R8
© Chris Caplice, MIT
Information and Control Impacts
Centralized
Control
Vendor Managed
Global
Information Inventory (VMI)
DRP (some cases)
Extended Base Stock
Control Systems
Local
Information
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N/A
29
Decentralized
Control
DRP (most cases)
Base Stock Control
Standard Inventory
Policies:
(R,Q), (s,S) etc.
© Chris Caplice, MIT
Questions?