1. Inventory Management
Multi-Items and Multi-Echelon
Chris Caplice
ESD.260/15.770/1.260 Logistics Systems
Nov 2006

2. Advanced Topics
So far, we have studied single-item single
location inventory policies.
What about . . .
Multiple Items
How do I set aggregate policies?
What if I have to meet a system wide objective?
Multiple Locations – Multi-echelon
Deterministic demand
Stochastic demand
MIT Center for Transportation & Logistics – ESD.260 2 © Chris Caplice, MIT

3. Inventory Planning Hierarchy
Inputs Plan Results
Strategic
Annual/Quarterly
• Transportation costs
• Inventory flow
• Facility fixed and
variable costs Network • Network
configuration
• Inventory costs Design • Capacity
• Service levels
• Item-level flow
• Forecast
• Item classifications
• Lead times
• Inventory locations
Quarterly/Monthly
• Variable and Deployment
Operational Tactical
inventory costs • Target Service levels
• Business policies • Target Reorder points
• Target Safety stock
• Forecasts/Orders • How much and when
• Lead times to replenish
• Handling costs • Reorder Points
Replenishment
• Vendor/volume Reorder Quantities
discounts • Review Periods
Weekly/Daily/Hourly
• Customer orders
• Demand prioritization
• On-hand and
• Assign inventory to
in-routeinventories Allocation orders
• Real transit costs
• Production
schedules
Jeff Metersky, Vice President Chainalytics, LLC
Rosa Birjandi, Asst. Professor Air Force Institute of Technology
MIT Center for Transportation & Logistics – ESD.260 3 © Chris Caplice, MIT

4. 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
MIT Center for Transportation & Logistics – ESD.260 4 © Chris Caplice, MIT

5. 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 ⎞ N = ∑ i =1
n Di
= ∑ i =1
n Di
⎜
⎜ rv ⎟ v i
⎟ Qi 2 ADi
n Qi v i n ⎝ ⎠
TACS = ∑ i =1 = ∑ i =1
i
rv i
2 2
rDi v i r 1
N = ∑ i =1 ∑ Di v i
n n
ADi v i A 1 =
TACS = ∑ i =1 ∑ Di v i
n n
= 2A A 2 i =1
2r r 2 i =1
MIT Center for Transportation & Logistics – ESD.260 5 © Chris Caplice, MIT

6. Exchange Curves
Exchange Curve
$160,000
A/r = 10000
Total Average Cycle Stock Value
$140,000
$120,000
$100,000 Current Operations
$80,000
$60,000
A/r = 10
$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
MIT Center for Transportation & Logistics – ESD.260 6 © Chris Caplice, MIT

7. 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 $2000 in SS – what is our
CSL?
Single Item Exchange Curve
7000
6000
5000
Safety Stock ($)
4000
3000
2000
1000
0
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1
-1000
-2000
-3000
Cycle Service Level
MIT Center for Transportation & Logistics – ESD.260 7 © Chris Caplice, MIT

8. 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
Expected total stockout occasions per year (ETSOPY)
Expected total value short per year (ETVSPY)
TSS = ∑ i =1 k i σ Li v i
n Di Di
ETSOPY = ∑ i =1 ETVSPY = ∑ i =1 σ Li v i G(ki )
n n
P [SOi ]
Qi Qi
MIT Center for Transportation & Logistics – ESD.260 8 © Chris Caplice, MIT

9. Exchange Curves
$3,500
$3,000 k=3
Total Safety Stock ($)
$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
MIT Center for Transportation & Logistics – ESD.260 9 © Chris Caplice, MIT

10. Replenishment in a Multi-Echelon System
Plant
RDC1 RDC2
LDC1 LDC2 LDC3 LDC4
R1 R2 R3 R4 R5 R6 R7 R8
MIT Center for Transportation & Logistics – ESD.260 10 © Chris Caplice, MIT

11. 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.
MIT Center for Transportation & Logistics – ESD.260 11 © Chris Caplice, MIT

12. Impact of Multi-Echelons
CDC
Demand
Pattern
RDC
Ordering
Patterns
RDC
Inventory
Cycles
Customer
Demand
Patterns
Layers of Inventory Create Lumpy Demand
MIT Center for Transportation & Logistics – ESD.260 12 © Chris Caplice, MIT

13. 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
MIT Center for Transportation & Logistics – ESD.260 13 © Chris Caplice, MIT

14. 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
MIT Center for Transportation & Logistics – ESD.260 14 © Chris Caplice, MIT

15. A Distribution Network Example
Plant
Central Warehouse
Regional Warehouse 1 Regional Warehouse 2 Regional Warehouse 3
Retailer A Retailer D Retailer G
Retailer B Retailer E Retailer H
Retailer C Retailer E Retailer I
MIT Center for Transportation & Logistics – ESD.260 15 © Chris Caplice, MIT

16. Central Warehouse Facility
The DRP Plan
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
End Inv 150 50 30 180 150 50 50 150 150
Planned Order 200 200
Regional Warehouse One
Q=50, SS=15, LT=1 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
Plant 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
Central Warehouse Planned Recpt 0 50 0 50 0 50 0 50
End Inv 50 25 50 25 50 25 50 25 50
Planned Order 50 50 50 50
Regional Warehouse 1 Regional Warehouse 2 Regional Warehouse 3 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
Retailer A Retailer D Retailer G Gross Rqmt 20 20 20 20 30 30 30 30
Retailer B Retailer E Retailer H Begin Inv 20 10 30 20 10 20 30 10
Retailer C Retailer E Retailer I Sched Recpt 0 0 0 0 0 0 0 0
Net Rqmt - 10 - - 20 10 - 20
Planned Recpt 30 0 0 30 30 0 30
End Inv 20 10 30 20 10 20 30 10 20
Planned Order 30 30 30 30
Regional Warehouse Three
Q=20, SS=10, LT=1 NOW 1 2 3 4 5 6 7 8
Note: Period Usage
Gross Rqmt
5
15
15
25
10
20
10
20
0
10
15
25
0
10
15
25
Gross Rqmt = Period Usage + SS 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
End Inv 15 10 15 25 15 15 20 20 25
MIT Center for Transportation & Logistics – ESD.260 16 © Chris Caplice, MIT

17. Example: The DRP Plan
Regional Warehouse One Forecast
Q=50 , SS=15 , LT=1
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 Rcpt 0 0 0 0 0 0 0 0
Net Rqmt 15 15 15 15
Plan Rcpt 0 50 0 50 0 50 0 50
End Inv 50 25 50 25 50 25 50 25 50
POR 50 50 50 50
MIT Center for Transportation & Logistics – ESD.260 17 © Chris Caplice, MIT

18. 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
Sched Rcpt 0 0 0 0 0 0 0 0
Net Rqmt 10 20 10 20
Plan Rcpt 0 30 0 0 30 30 0 30
End Inv 20 10 30 20 10 20 30 10 20
POR 30 30 30 30
MIT Center for Transportation & Logistics – ESD.260 18 © Chris Caplice, MIT

19. Example: The DRP Plan
Regional Warehouse Three
Q=20 , SS=10 , LT=1
NOW 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 Rcpt 0 0 0 0 0 0 0 0
Net Rqmt 15 5 10 5
Plan Rcpt 0 20 20 0 0 20 0 20
End Inv 15 10 15 25 15 15 20 20 25
POR 20 20 20 20
MIT Center for Transportation & Logistics – ESD.260 19 © Chris Caplice, MIT

20. The DRP Plan for All Locations
Rolling Up Orders
NOW 1 2 3 4 5 6 7 8
CENTRAL
Period Usage 100 20 50 30 100 0 100 0
POR 200 200
REGION ONE
Period Usage 25 25 25 25 25 25 25 25
POR 50 50 50 50
REGION TWO
Period Usage 10 10 10 10 20 20 20 20
POR 30 30 30 30
REGION THREE
Period Usage 5 15 10 10 0 15 0 15
POR 20 20 20 20
MIT Center for Transportation & Logistics – ESD.260 20 © Chris Caplice, MIT

21. 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
Sched Rcpt 0 0 0 0 0 0 0 0
Net Rqmt 20 50
Plan Rcpt 0 0 200 0 0 0 200 0
End Inv 150 50 30 180 150 50 50 150 150
POR 200 200
MIT Center for Transportation & Logistics – ESD.260 21 © Chris Caplice, MIT

22. 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"
MIT Center for Transportation & Logistics – ESD.260 22 © Chris Caplice, MIT

23. MRP / DRP Integration
Purchase Orders
C C C C C C C C
SA SA SA SA
MRP
A A
MPS Product
CDC
DRP RDC RDC
Retail Retail Retail Retail
Sales/Marketing Plan
MIT Center for Transportation & Logistics – ESD.260 23 © Chris Caplice, MIT

24. 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
MIT Center for Transportation & Logistics – ESD.260 24 © Chris Caplice, MIT

25. 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
MIT Center for Transportation & Logistics – ESD.260 25 © Chris Caplice, MIT

26. 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 LDC2 LDC3 LDC4
R1 R2 R3 R4 R5 R6 R7 R8
MIT Center for Transportation & Logistics – ESD.260 26 © Chris Caplice, MIT

27. A DRP Network Reality
Plant
RDC1 RDC2
SHORTAGES EXCESS
LDC1 LDC2 LDC3 LDC4
R1 R2 R3 R4 R5 R6 R7 R8
Higher than expected demand Lower than expected demand
MIT Center for Transportation & Logistics – ESD.260 27 © Chris Caplice, MIT

28. Optimal Network Utilization
Plant
RDC1 RDC2
SHORTAGES EXCESS
LDC1 LDC2 LDC3 LDC4
R1 R2 R3 R4 R5 R6 R7 R8
MIT Center for Transportation & Logistics – ESD.260 28 © Chris Caplice, MIT

29. Information and Control Impacts
Centralized Decentralized
Control Control
Global Vendor Managed DRP (most cases)
Information Inventory (VMI) Base Stock Control
DRP (some cases)
Extended Base Stock
Control Systems
Local Standard Inventory
Information N/A Policies:
(R,Q), (s,S) etc.
MIT Center for Transportation & Logistics – ESD.260 29 © Chris Caplice, MIT

30. Questions?