1 270J/ESD 273J
1.270J/ESD.273J
Logiistitics and
d Di
Disttrib
ibutition Systtems
Dynamic Economic Lot Sizing Model
1
Outline
{
The Need for DELS
{
DELS without capacity constraints:
z
z
{
ZIO policy;
policy;
Shortest path algorithm.
DELS with capacity constraints:
z
z
Capacity
C
it constrained
t i d producti
d tion sequences;
Shortest path algorithm.
2
Strategic Sourcing Inputs
Supplier
constraints, costs,
fixed orders, etc
Product info and
BOM
WH cost, capacity,
safety stock targets,
and current on
on-hand
hand
position
Transportation
costs, rules for
shipping out of
territory overflow
facilities
Mfg constraints, costs, run
rules, fixed production
schedules, set
set-ups,
etc.
schedules
ups tooling,
tooling etc
by time period
Current demand
forecast by
y forecast
location by time period
3
Key Drivers in Sourcing Decisions
ƒ Purchase prices
ƒ Availability at different
times of the year
ƒ Freight costs for
existing and
potential lanes
p
ƒ Duties for different
customer countries
Raw Materials
Freight
g
& Duties
ƒ
ƒ
ƒ
ƒ
Suppliers
Plants
Warehouses
Customers
Production
Capabilities
Sourcing
Decisions
Mfg
Costs
Locations
Products
ƒ Product attributes
ƒ BOM information
ƒ
ƒ Special rules and
constraints
ƒ What can be made
where, tooling, etc.
ƒ Mf
Mfg speed
ds &
capacities
ƒ Setups, batches, yield
loss, etc.
ƒ Production costs
ƒ Allocation of fixed &
variable overheads
ƒ Economies of scale
Demand
ƒ Demand by product
by customer
ƒ Monthly or weekly
forecasts
4
Strategic Sourcing Outputs
Amount purchased
from each supplier
supplier,
where and when it
should be shipped
Throughput by WH by
product by time period,
ending inventory by
period, costs by period
Strategic sourcing minimizes
total supply chain costs
subject to all constraints
Total volume and
cost on each lane
in each time period
What products should be
made where,, made when,,
and shipped to where
Total landed cost by
time period
byy
p
customer/product
5
Dase Study:
Strategic Sourcing
ICI LOCATIONS
Canada
CA 2
OH
PA
CA 1
GA
TX 2
Pacific
Ocean
Atlantic Ocean
Mexico
TX 1
Gulf of Mexico
0
800 km
0
500 km
PR
PR
Image by MIT OpenCourseWare.
6
Background
„
Sold product throughout US to variety of customers
z
z
z
„
Wide variety of product
z
z
z
„
4,000 different SKU’s
1500 different base products (could be labeled differently)
Many low-volume products
Batch Manufacturing
z
„
Direct to customers/distributors
Through their own stores
Through retailers
Manufacturing
M
f t i done
d
iin b
batch,
t h so th
there significant
i ifi
t economies
i off scale
l if a
single product is made in one location
Mfg Capability
z
z
Each plant had many different processes
Many plants can produce the same problem
7
Business Problems
„
Are products being made in the right location?
„
Should plants produce a lot of products to serve the local
market or should a plant produce a few products to
to
minimize production costs?
„
Should we close the high cost plant?
„
How sh
hould
ldwe manage allll th
the low vollume SKU’
SKU’s?
?
8
Key Driver - Data Collection
Raw Material Costs
Variable Mfg. Costs
•Invoice cost
•Freight cost
•% shrinkage
•Difficulty - Medium
•Variable Mfg
Mfg. costs by process/by site
•Difficulty - High
Technical Capability
p
y
•Product Family
•Difficulty - High
Manufacturing Capability
Key Drivers
Yield Loss
•% of lost volume per 100 units
•Site Specific
•Difficulty - Low
•Demonstrated Capacity
•Difficulty - High
Interplant Freight Costs
•Average run rates in from site to site
•Difficulty - Low
9
Process Change
Existing Process
Sourcing decisions currently made in isolation
Ö Decisions are made for small groups of
products
Excel is the primary decision tool – Many drawbacks
Ö Excel does not capture the many different
trade-offs that exist in the supply chain
E l can only
l calculate
l l t the
th costs
t ffor a given
i
Ö Excel
decision; it cannot make decisions
No formal data collection process
Ö Data not collected systematically across the
supply chain to make these decisions
New Process
Sourcing decisions made in context of entire supply
chain
Ö Decisions are made considering the entire
supply chain
Sourcing decisions are made using Master Planning
Ö Optimization model provides global
optimization capability
Model automatically updates for on-going decision
making
Ö Developed process for automatically updating
and maintaining the model so the decisions
can be made on an on-going basis
Built 2 Models
1. Model for all the base products
2.
SKU s
2 Model for low volume SKU’s
10
Results
„
Savings
z
z
z
„
Details
z
z
„
Identified
Id
tifi d immediate
i
di t llow volume
l
SKU moves
Identified $4-$10M in savings for moving base products
Identified negotiation opportunities for raw materials
Moved 20% more volume into the high
g cost p
plant
80% of savings were from 10% of the production moves
Implementation
z
z
z
Implementation done in phases, starting with the easiest and highest
value changes first
Expect 3
3-5
5 months to complete analysis
analysis, another 3
3-6
6 months to
implement
Expect to adjust plans as you go forward
11
More Volume to High Cost Plant
„
Baseline
z
z
„
O ti i ti
Optimization
z
z
„
Product
P
d t A:
A 20% off th
the volume,
l
45% off th
the variable
i bl costt
Product B: 80% of the volume, 55% of the variable cost
Product A: 5% of the volume, 15% of the variable cost
Product B: 95% of the volume, 85% of the variable cost
Net change was an increase in total volume
12
Case Study 3: Optimizing S&OP at PBG
{Make
M k
{PBG
Operates
57 Plants in the
U.S. and 103
Plants Worldwide
{Sell
S ll
{Over
125 Million
8 oz. Servings
are Enjoyed by
Pepsi
p Customers
Each Day!
{Deliver
D li
{240,000
Miles are
Logged Every Day to
Meet the Needs of
Our Customers
{Service
S i
{Strong
Customer Service
Culture Identified
as “Customer
Connect”
PBG Structure - The PBG Territory
Central
WA
MT
OR
ND
ME
ID
WY
NV
UT
CA
CO
MN
SD
Great West
West
PA
IL
OH
IN
MO
KY
WV
SC
AR
MS
TX
AL
VA
NC
TN
OK
NM
NY
MI
IA
NE
KS
AZ
WI
GA
LA
AK
VT
NH
CT
MA
RI
Atlantic
NJ
DE
MD
Southeast
Atlantic
Central
Great West
FL
West
Southeast
Image by MIT OpenCourseWare.
{PBG
accounts for 58% of the domestic Pepsi Volume…the other 42% is
{g
generated through
g a network of 96 Bottlers
{Each
BUs act independently and meet local needs
Challenges and Objective
„
Problem: How should the firm source its products to
minimize cost and maximize availability?
„
Objjective: Determine where products should be produced
to reduce overall supply chain costs and meet all relevant
business constraints
15
©Copyright 2008 D.
Simchi-Levi
Optimization Basics
{Tradeoffs
associated with optimizing a network…
{Would
like to minimize the number of
products produced at a location to
maximize product run size
{Capacity
Constraints
{High
Hi h
costt
plants may be
close to key
markets
{Would
like to maximize the
number of products produced at a
location to minimize transportation
costs
16
Image by MIT OpenCourseWare.
©Copyright 2008 D.
Simchi-Levi
Optimization Scenario
„
Optimized Central BU model:
Total Cost
Category
MFG Cost
Trans Cost
Total Cost
Baseline
$ 2,610,361.00
$
934,920.00
$ 3
3,545,281.00
545 281 00
Optimized
$ 2,596,039.00
$
857,829.00
$ 3,453,868.00
3 453 868 00
Difference
% savings
$ 14,322.00
0.6%
$ 77,091.00
9.0%
$ 91,413.00
2.6%
91 413 00
2 6%
Production Breakdown
Plant
Burnsville
Howell
Detroit
Units Produced
Baseline
Optimized
% change
2 444 277 00
2 457 688 00
2,444,277.00
2,457,688.00
1%
3,509,708.00
3,828,727.50
8%
2,637,253.00
2,304,822.50
-14%
©Copyright 2008 D. SimchiLevi
17
Multi Stage Approach
„
Stage 1-2: 2005-6
POC
z
z
„
Stage 3: 2007 Annual
Operating Plan (AOP)
z
z
„
6 months
2 Business Units
Model USA
Full year model
St
Stage
4
4: Q1 – Q4 2007
z
z
Quarter based model
Package / Category
Image by MIT OpenCourseWare.
©Copyright 2008 D. SimchiLevi
18
Impact
„
„
„
„
Creation of regular meetings bringing together Supply
chain, Transport, Finance, Sales and Manufacturing
functions to discuss sourcing and pre-build strategies
Reduction in raw material and supplies inventory from $201
to $195 million
A 2 percentage point decline in in growth of transport miles
even as revenue grew
An additional 12.3 million cases available to be sold due to
reduction in warehouse out-of-stock levels
To put the last result in perspective,
perspective the reduction in warehouse out-of-stock
out-of-stock levels
effectively added one and a half production lines worth of capacity to the firm’s
supply chain without any capital expenditure.
19
Outline
{
The Need for DELS
{
DELS without capacity constraints:
z
z
{
ZIO policy;
policy;
Shortest path algorithm.
DELS with capacity constraints:
z
z
Capacity
C
it constrained
t i d producti
d tion sequences;
Shortest path algorithm.
20
Assumptions
{
{
{
{
{
{
{
{
Finite horizon: T periods;
Varying demands: dt, t=1,…,T;
t=1
T;
Linear ordering cost: Ktδ(yt)+ctyt ;
Linear holding cost: ht ;
Inventoryy level at the end of period t,,I t
No shortage;
Zero lead time;
Sequence of Events: Review, Place Order,
O d Arrives,
Order
A i
D
Demand
d iis R
Realized
li d
21
Wagner-Whitin (W-W) Model
22
Zero Inventory Ordering Policy (ZIO)
{
Any optimal policy is a ZIO policy, that is,
It-1· yt=0,
0 for tt=1,…,T.
1
T
{
Time independent costs: c, h.
{
Time dependent costs: ct, ht.
23
ZIO Policy ↔ Extreme Point {
Definition: Given a polyhedron P, A vector x is an extreme point if we cannot find two other
other
vectors y, z in P, and a scalar λ,0≤λ≤1, such that
x =λy+(1-λ)z
λy+(1-λ)z.
Consider the linear programming
problem of minimizing c’x over a polyhedron P,
then either the optimal cost is equal to -∞
∞, or
there exists an extreme point which is optimal.
{ Theorem:
24
Min-Cost Flow Problem
S
y1
yt
2
1
d1
It-1
yT
t
T-1
T
dT
dt
25
Implication of ZIO
{
Each order covers exactly the demands
of several consecutive periods
periods.
{
Order times sufficient to decide on order
quantities.
26
Network Representation
1
i
t
T+1
j−1
j−1
j−1
⎧
⎪ K i + ci ∑ d t + ∑ hk ∑ d t , 1 ≤ i < j ≤ T +1
lij = ⎨
t =i
k =i
t =k
⎪⎩
+∞
o.w.
27
Shortest Path Algorithm
{
{
Complexity of the shortest path algorithm: O(T2).
{
With a sophisticated algorithm, O(T lnT).
28
Outline
{
The Need for DELS
{
DELS without capacity constraints;
z
z
{
ZIO policy;
policy;
Shortest path algorithm.
DELS with capacity constraints;
z
z
Capacity
C
it constrained
t i d producti
d tion sequences;
Shortest path algorithm.
29
DELS with Capacity Constraints
30
DELS model with capacity: description
y1≤ C1
2
1
d1
yT≤ CT
yt≤ Ct
t
T-1
dt
T
dT
31
Feasibility of DELS with capacity
32
Inventory Decomposition Property
33
Structure of Optimal Policy
34
Production Sequence Sij
S
yi+1≤ Ci+1
i+1
di
i+2
yj≤ Cj
yt≤ Ct
t
j-1
dt
j
djj-11
35
Network Representation
1
j
i
T 1
T+1
lij ?
36
Calculation of Link Costs {
Time-dependent capacities: difficult;
{
Time-independent capacities: Ct=C.
{
Let m and f such that mC+f =di+1+…+jdt,
where m is a nonnegative integer and 0≤f<C
0≤f<C, k
define Yk = ∑t =i+1 yt ,i < k ≤ j.
0 f ,C,C
C C + f ,2
2C
C,..., mC + f }}
.
then Yk ∈ {0,
37
Calculation of Link Costs
Yi+1=yi+1
0
Yi+2=yi+1 +yi+2
… Yj=yi+1 +…+yj
0
0
0
f
f
p
C
C
C
C+f
C+f
2C
2C
mC+f
38
Complexity: equal capacity
{
Computing link cost lij: shortest path algorithm:O((j-i)2).
{
Determining
i i the
h optimal
i l production
d i sequence between
all pairs of periods: O(T2)× O(T2) = O(T4).
{
Shortest path algorithm on the whole network : O(T2).
{
Compllexit
ity for finding
di an opti
timallso lution
l ti for DELS
model with equal capacity: O(T4) + O(T2) = O(T4).
{
With a sophisticated algorithm: O(T 3) .
{
Not appli
licabl
ble to problems
bl
wiithh time-d
i
dependdent capaciity
constraints, why?
39
Tree-Search Method
yT+1=0
yT= min{CT, dT}
yT=0
yT-1=0
yT= min{CT-1, dT-1+dT}
yT-1=0
yT= min{CT-1, dT-1+dT -yT}
{
Effective with time
time-dependent
dependent capacity constraints.
constraints
{
Not polynomial.
p y
40
ZICO Policy
{
Theorem: Any optimal policy is a ZICO policy,
It-1 · (Ct-yyt) · yt = 0,
0 for tt=1,…,T.
1 T
{
Corollary: If (y1, y2,… yT) represents an optimal
solution, and t = max{j: yj>0}, then
yt = min{Ct, dt +…+dT}.
41
MIT OpenCourseWare
http://ocw.mit.edu
ESD.273J / 1.270J Logistics and Supply Chain Management
Fall 2009
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