Definitions
IE 505
Production Planning and Control
●
“Supply Chain Management deals with the
management of materials, information and financial
flows in a network consisting of suppliers,
manufacturers, distributors, and customers”
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“SCM is a set of approaches utilized to efficiently
integrate suppliers, manufacturers, warehouses, and
stores, so that merchandize is produced and
distributed at the right quantity, to the right locations,
at the right time, in order to minimize systemwide
costs while satisfying service level requirements”
-- Stanford SC Forum/ Dr. Hau Lee
Supply Chain Management
Dr. Rakesh Nagi
Department of Industrial Engineering
University at Buffalo (SUNY)
© Rakesh Nagi
UB, Industrial Engineering
-- Dr. Simchi-Levi et al. (1999)
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© Rakesh Nagi
Definitions
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“Call it distribution or logistics or SCM… It is the
sinuous, gritty, and cumbersome process by which
companies move material, parts, and products to
customers. ….”
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“Structured business approach to balance,
synchronize, and synergize all internal and external
resources and assets.” -- CAM-I
“An integrative approach for planning and controlling
the total flow through a distribution channel from
suppliers to end users.” -- Ashraf Alam
-- Fortune Magazine/Henkoff (1994)
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-- Ross (1998)
Includes service organizations in addition to manufacturing
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© Rakesh Nagi
The Supply Chain Umbrella
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Objectives of this Chapter
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© Rakesh Nagi
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Definitions
“SCM is a continuously evolving management
philosophy that seeks to unify the collective
productive competencies and resources of a
business function found both within the enterprise
and outside the firm’s allied business partners
located along intersecting supply channels into a
highly competitive, customer-enriching supply system
focused on developing innovative solutions and
synchronizing the flow of marketplace products,
services, and information to create unique,
individualized sources of customer value”
© Rakesh Nagi
UB, Industrial Engineering
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Provide an appreciation for the most
important issues encountered in managing
complex supply chains.
Present a sampling of the types of
mathematical models used in SCM analysis
Reading Assignment: Snapshot Application pf
Wal-Mart, p. 307
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1
Transportation Problem
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Transportation Problem
Special case of Min Cost Flow Problem
Shipping and Distribution Applications
From plants to warehouses or warehouses to
retailers, respectively
Let there be m plants with known supplies (Si
corresponding to supply point i)
And n warehouses with know demands (Dj
corresponding to demand point j)
Identify flows at min cost to satisfy demand from
given supply (cij is unit shipping cost point i)
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Minimize
n
x
ij ij
i =1 j =1
●
S.t.
n
∑x
m
ij
≤ Si
for
i = 1,2,
ij
≥ Di
for
j = 1,2,
j =1
m
∑x
i =1
xij ≥ 0
7
n
for all i, j
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Transportation Network
8
Transportation Problem
●
cij
S1
m
∑∑ c
D1
For the model to possess a feasible solution,
total supply should be at least as large as
total demand
m
n
∑ Si ≥ ∑ D j
i =1
j =1
S2
D2
●
S3
Plants
© Rakesh Nagi
It is convenient to assume equality by adding
a dummy destination with remaining supply
Warehouses
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© Rakesh Nagi
Transportation Problem
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Standard Simplex
Simplex solution to an LP problem has at
most k positive variables, where k is the
number of independent constraints
Convince yourself that there are M+n-1
independent constraints in the transportation
problem
Also note that a key result in network theory
is that at least one optimal solution to the TP
has integer-valued xij provided Si and Dj are
integers.
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UB, Industrial Engineering
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Step 1: Select a set of m+n-1 routes that
provide an initial basic feasible solution
Step 2: Check whether the solution is
improved by introducing a non basic variable.
If so, go to Step 3; otherwise, Stop.
Step 3: Determine which routes leave the
basis when the variable that you selected in
Step 2 enters.
Step 4: Adjust the flows of the other basic
routes. Return to Step 2.
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2
Initial Solution
Initial Solution
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Northwest corner rule
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Algorithm: Begin by selecting X11 (that is, start in the northwest corner
of the transportation simplex tableau). Thereafter, if Xij was the last
basic variable selected, then next select Xi,j+1 (that is, move one column
to the right) if source i has any supply remaining. Otherwise, next select
Xi+1,j (that is, move one row down).
1
8
●
3
10
2
6
A
4
9
35/0
9
12
13
10
7
20
14
20
9
50/40/20/0
16
5
10
C
Demand
ui
Supply
35
B
Northwest corner rule: Example
45/10/0
20/0
30 40/30/0
30/10/0
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© Rakesh Nagi
10M
30/0
Initial Solution
Minimum Matrix Method
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Algorithm: Find the minimum Cij and assign to Xij the higher of Si or Dj.
Reduce the demand and supply (Si- Xij; Dj- Xij). Repeat until done. Note
that the last arcs chosen could be very expensive.
1
8
2
6
3
12
13
9
16
Vogel’s Approximation
Method
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Algorithm: For each row and column
remaining under consideration,
calculate its difference, which is
defined as the arithmetic difference
between the smallest and next-tothe-smallest unit cost Cij still
remaining in that row or column. (If
two unit costs tie for being the
smallest remaining in a row or
column, then the difference is 0.) In
that row or column having the largest
difference, select the variable having
the smallest remaining unit cost.
(Ties for the largest difference, or for
the smallest remaining unit cost, may
be broken arbitrarily.)
Supply
7
20
50/20/0
5
1 30 40/10/0
10
45/30/0
●
35/15/0
30
14
C
Demand
4
9
20
9
B
3
10
2
15
20/0
30/10/0
30/0
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© Rakesh Nagi
Z=2,460
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© Rakesh Nagi
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Initial Solution
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Initial Solution
Vogel’s approximation method
1
8
2
6
3
10
●
4
9
Supply
35
12
13
7
14
9
16
5
2
B
50
C
Demand
Col Diff
4
30 40/10
45
20
30
30/0
1
3
3
2
1
8
2
6
3
10
4
9
Supply
35
9
12
13
7
14
9
16
5
3
B
50
C
Demand
Col Diff
5
10
45
1
© Rakesh Nagi
30 40/10/0
20/10
3
30
30/0
3
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2
6
A
3
10
4
9
13
7
10
9
12
Supply
Row Diff
2
35/25
3
B
50
14
C
Demand
Col Diff
9
16
5
10
45
1
30 40/10/0
20/10/0
30
6
1
8
Row Diff
2
A
Vogel’s approximation method
1
8
Row Diff
2
A
9
14
Initial Solution
●
A
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2
6
A
3
10
10
9
12
B
C
Demand
Col Diff
4
9
25
13
16
© Rakesh Nagi
20/10/0
2
50/0
5
10
45/0
1
Row Diff
4
5
9
Supply
35/25/0
7
45
14
30/0
3
30 40/10/0
30/0
30/0
3
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3
Initial Solution
For ABC-> 1234 example
● Northwest corner rule
● Minimum Matrix Method
● Vogel’s Approximation
Initial Solution
$1,180
$1,080
$1,020
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© Rakesh Nagi
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Russell's approximation method
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Algorithm: For each source row i remaining under consideration,
determine its ui which is the largest unit cost Cij still remaining in that
row. For each destination column j remaining under consideration,
determine its vj which is the largest unit cost Cij still remaining in that
column. For each variable Xij not previously selected in these rows and
columns, calculate ∆ij = Cij - ui –vj. Select the variable having the largest
(in absolute terms) negative value of ∆ij (Ties may be broken arbitrarily.)
●
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Dual Linear Program is
m
n
Maximize
S i vi + ∑ D j w j
∑
i =1
j =1
S.t. v + w ≤ C
for all i = 1,2, m
i
j
vi
j = 1,2,
ij
where vi , w j
20
Format for Transportation
Simplex
Step 2: Optimality Test
●
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n
are unrestrict ed in sign
wj
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Theorem of complementary slackness gives:
C ij = vi + w j − Cij ≤ 0 if
xij = 0
C ij = vi + w j − Cij = 0 if
xij > 0
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© Rakesh Nagi
0
21
Example
Example
1
2
2
3
3
11
4
7
1
0
6
1
Supply
A
6
B
1
5
8
15
7
5
1
2
A
2
3
2
3
11
4
7
●
0
6
1
1
5
8
1
7
15
4
5
●
Supply
6
1
B
© Rakesh Nagi
●
9
3
Initial Basic Feasible Solution using Vogel’s Approximation = 112
C
Demand
●
10
C
Demand
vi+wj - Cij
6
●
1
●
10
●
9
3
3
2
2
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Finding vi and wj
Set vA = 0 arbitrarily to determine all other
duals
vA + w2 - 6 = 0; so w2 = 6
vC + w2 - 9 = 0; so vC = 3
vC + w4 - 5 = 0; so w4 = 2
vA + w3 - 10 = 0; so w3 = 0
vC + w1 - 9 = 0; so w1 = 6, etc.
© Rakesh Nagi
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4
Example
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Step 3: Identify incoming variable (A2)
1
2
A
2
3
0
1
2
5
1
6
-4
8
-1
1
15
0
0
-5
0
6
3
9
0
5
0
12
1
2
A
1
2
6-z
1
2
3
z
0
B
4
7
5
6
5
8
1+z
C
Demand
15
1
B
3
3
5
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A
2
3
4+z
0
1-z
8
B
5
●
●
4
7
6
8
A
1
B
1
2
15
2
3
1
1
0
6
10
5
8
6
7
C
Demand
●
15
6
A
1
B
10
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C
Demand
© Rakesh Nagi
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A
2
3
0
1
5
0
●
4
7
3
11
Supply
1
6
B
5
●
8
7
7
15
6
0
-1
-5
0
6
3
9
0
12
5
0
8
6+z
7
4
7
3
11
z
6
6
1
1
15
0
5
Supply
1
9
2-z
3
2
2
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1
●
MRP logic to manage distribution systems (Martin, 1990).
Advantage over ROP systems is that it can deal with changing
demand patterns
However it ignores uncertainty
9
1
3
5
●
1
1
C
Demand
v_I
-1
Distribution Resource
Planning (DRP)
Step 4: Adjust the flows – find new basis (cost = 100)
1
2
15
0
Example
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26
1
0
-2
3
2
3
5
2
2
1
6
8
1
2
1-z
1
9
2
3
© Rakesh Nagi
3
Identify which variable leaves (A1)
Supply
1
0
5
0
6
4
7
3
11
-3
0
2
C
w_j
1
0
-5
9
0
12
0
0
5
2
2
4
7
3
11
2
3
-5
9
3
5
B
15
-2
3
0
1
Step 4: Adjust the flows – find new basis (cost = 101)
A
0
2
1
3
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1
2
6
1
5
v_I
-1
Step 3: Identify incoming variable (A3)
Supply
z
3-z
7
10
Example
3
11
5+z
C
Demand
6
© Rakesh Nagi
Step 3: Identify which variable leaves (B2)
1
2
2-z
1
1
0
0
2
C
w_j
25
2
2
4
7
3
11
0
Example
●
9
3
3
0
-2
5
10
6
15
2
3
1
2
2
Supply
1
0
5
0
9
4-z
7
8
5
7
1
2
1
1
1
Step 3: Identify incoming variable (B3)
Supply
A
4
7
6
1
C
Demand
6
3
11
4
0
B
●
3
11
2
3
2
1
Identify which variable leaves (C2)
A
Step 4: Adjust the flows – find new basis (cost = 104)
v_I
1
0
0
2
C
w_j
●
4
7
3
11
0
B
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Example
2
2
10
Step 3: Test for optimality again
1
2
A
2
3
-1
1
B
0
-5
5
© Rakesh Nagi
0
6
-2
8
0
1
C
w_j
4
7
3
11
0
0
2
-5
0
5
4
1
0
15
-1
3
v_I
-2
9
0
11
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© Rakesh Nagi
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5
Delivery Routes in Supply
Chains
Practical Issues in Vehicle
Scheduling
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Vehicle Scheduling Problems are of two
types
¾
¾
●
1.
2.
3.
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Arc-based (e.g., snow removal, garbage
collection)
Node-based (e.g., collection and distribution)
Schrage (1981) list these features:
Frequency Requirements (e.g., daily)
Time Windows
Time dependent travel times
Practical Issues in Vehicle
Scheduling
4.
5.
6.
7.
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Designing Products for
Supply Chain Efficiency
Multidimensional capacity constraints
(weight/volume)
Vehicle types (different capacities and costs)
Split deliveries (more than 1 vehicle to a
customer)
Uncertainty (e.g., traffic conditions, weather,
vehicle breakdowns)
●
Historically Product Design has been “throw
over the wall” to manufacturing.
In recent past we have
●
Now –
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¾ Design For Manufacturing (DFM)
¾ Concurrent Engineering
¾ Design for Logistics (DFL)
¾ Three-dimensional concurrent engineering (3-
DCE): Products, Processes, and Supply Chains
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© Rakesh Nagi
Designing Products for
Supply Chain Efficiency
●
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¾ Product design for efficient transportation and shipment
¾ Delayed differentiation (Postponement of final product
●
●
configuration)
ƒ
●
Benetton: Dyeing sweaters after knitting (“gray stock”)
HP: Localization of printers (correct power supply + plug) can
be done at DC rather than factories
●
Additional issues
●
¾ The configuration of the supplier base
¾ Outsourcing arrangement (3PL)
¾ Channels of distribution (DCs, 3P wholesalers, licensing, or
direct selling)
© Rakesh Nagi
●
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Role of Information in SCM
How logistics considerations enter design
ƒ
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The Case of Pasta Barilla (Harvard B School)
Barilla is an Italian manufacturer of pasta
In late 1980s the head of logistics tried to introduce a
new distribution approach JITD
The idea was to get the distributor sales #s and Barilla
would decide when and how large should the deliveries
be.
At that time distributors would independently place
weekly orders based on std reorder point methods.
This would cause large swings in demand for Barilla’s
factories due to the “Bullwhip Effect”
The change was met with great resistance but adopted
© Rakesh Nagi
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6
Role of Information in SCM
Bullwhip Effect
Role of Information in SCM
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●
●
●
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The Case of Pasta Barilla (cont.)
JITD system was implemented with striking
results
It was a win-win for Barilla and its distributors
This is known as “Vendor Managed
Inventory” or VMI today
Now, Proctor and Gamble has accepted VMI
for Wal-Mart, etc.
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© Rakesh Nagi
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Industry and academics realized that the
orders placed by distributors had much more
variance than sales at retail stores.
P&G coined the term “bullwhip” effect
Where does it come from?
¾ Demand Forecast updating
¾ Order batching at stages causes spiky demands to
previous suppliers
¾ Price fluctuations
¾ Shortage gaming
37
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Bullwhip Effect: Causes
Demand Forecast updating
38
Bullwhip Effect: Causes
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Order Batching
¾ We will see this in MRP systems too, order
batching (EOQ-type) translates a smooth demand
pattern into spiky demand at “lower” levels
●
Price fluctuations
●
Shortage gaming
¾ “forward buying” due to attractive prices
¾ When product is in short supply the manufacturer
places customers on allocation, so the customers
inflate demand to make up for expected shortfall.
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© Rakesh Nagi
Information Sharing
●
Channel Alignment
40
Multilevel Distribution
Systems
Bullwhip Effect: Elimination*
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¾ All parties share POS data (for forecasts also). Fortunately,
IT has helped – EDI, for instance.
¾ Reduction of fixed costs (ordering cost via EDI;
transportation costs by mixed product and LTL shipments or
outsourcing – 3rd party logistics)
●
Price Stabilization
●
Discouragement of Shortage Gaming
¾ Value-pricing rather than promotional pricing
¾ Allocate based on past sales rather than orders.
* Lee, Padmanabhan, and Whang (1997)
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7
Multilevel Distribution
Systems
●
Advantages of intermediate storage
●
Disadvantages
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Reading Assignment § 6.10 pp. 346-351 on
“Designing the SC in a Global Environment”
¾ Risk pooling (aggregate demand has lower variation)
¾ DCs can be designed to meet local needs
¾ Economies of scale in storage and movement
¾ Faster response time
¾ May require more inventory
¾ May increase total order lead times
¾ Could result in higher cost of storage and movement
¾ Could contribute to the bullwhip effect.
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8