Download Supply Chain Management Part II

Managing the flow
of goods and services.
Supply Chain Management
Part II
Supply chain management is the combination
of art and science that goes into improving
the way a company finds the raw components
it needs to make a product or service,
manufactures that product or service and
delivers it to customers.
I need a model of a
supply chain to free
me of this.
A Supply Chain Model
Objective: Determine the least-cost
configuration and activity levels among
suppliers, factories, and distributors.
The Book’s Approach



Use the transportation problem to model
distribution of a single product from plants to
warehouse
Generalized somewhat with the transshipment
problem
Neither integrates suppliers – factories –
warehouses – customers nor addresses multiresources and products
A broken supply chain
A “Real” Supply Chain Model
- the variables


Let Xi,j,k = the number of units of resource i (raw
material, parts, etc.) shipped from supplier j to
factory k
Let Yl,k,m = the number of units of product l
manufactured in factory k for customer m
(warehouse, retail store, region, etc.)
A model prisoner
supplied with a chain.
A Supply Chain Model
– the cost coefficients



Let ci,j,k = the cost of purchasing resource i from
supplier j and shipping to factory k
Let dl,k,m = the cost of manufacturing product l
in factory k and shipping to customer m
The objective function:
Min z   ci , j ,k X i , j , k 
i , j ,k
d
l ,k ,m
Y
l ,k ,m l ,k ,m
A Supply Chain Model
– the first set of parameters
ai,l = the number of units or resource i needed
to produce one unit of product l
bi,j = number of units of resource i available
from supplier j


X
i , j ,k
j
X
k
  ai ,lYl ,k ,m ; i, k
l ,m
i , j ,k
 bi , j ; i, j
Ship each factory
needed resources
Each supplier has
limited resources
A Supply Chain Model
– the second set of parameters


fl = number of production units (machine hrs, labor
hrs, assembly time, etc.) needed to produce one unit
of product l
Fk = number of production units available at factory k
 fY
l l ,k ,m
l ,m
 Fk ; k
production
constraint
Note: There may be more than one production constraint at a factory.
A Supply Chain Model
– the third set of parameters

Dl,m = demand for product l by customer
m
Y
l ,k ,m
k
 Dl ,m ; l , m
I have a big
demand for
product l.
A Request…
Could you make your so called
supply chain model come alive
with a real world example? My
brother, Thomas Maytow, is owner
of a cannery. What can your
model do for him?
Pat Maytow, a fruit picker.
A Real World Example



The T. Maytow Company* produces three types of tomato
products: a tomato paste, (condensed) tomato soup, and tomato
juice.
They operate two canning facilities. One is located in Kokomo,
Indiana and the other is located in Santa Fe, New Mexico.
Final product is distributed to three major distribution centers
located in Pittsburgh, PA, Chicago, IL, and San Diego, CA.
*Owned and operated by Thomas Maytow
The Suppliers

There are three varieties of tomatoes used in
production:




Roma tomatoes
Plum tomatoes
Beefsteak tomatoes
There are two major suppliers:


Taste of the World (Morristown, New Jersey) imported from
tomato fields near Naples, Italy
Sierra Quality Canners from California's central valley
Tomato Distribution

A typical tomato truck holds 50,000 pounds
of tomatoes, which is about 300,000
tomatoes. (6 X 50,000)
Supplier Costs
Type
NJ to
Kokomo
NJ to
Santa Fe
CA to
Kokomo
CA to
Santa Fe
Roma
12
15
-
-
Plum
10
14
15
8
Beefstk
8
10
12
9
Purchase and shipping cost per 1,000 pounds
Supplier Output
Type
Roma
Plum
Beefstk
NJ
140
100
140
CA
-
120
150
1,000 pounds per week
Production & Distribution Costs
Kokomo Santa Fe Kokomo Santa Fe
Paste
Paste
Soup
Soup
Kokomo Santa Fe
juice
juice
Pgh 8
9
6
7
9
10
Chi
10
11
8
9
11
12
SD
12
10
10
8
13
12
$ per canner load
Tomato Production



Tomato Paste - an average of 35 pounds of tomatoes
is needed per canner load of 7 quarts; an average of 21
pounds is needed per canner load of 9 pints. A bushel
yields 10 to 12 quarts of sauce.
Tomato Soup - an average of 26 pounds of tomatoes
is needed per canner load of 7 quarts; an average of 18
pounds is needed per canner load of 9 pints. A bushel
yields 12 to 14 quarts of sauce.
Tomato Juice - An average of 23 pounds of tomatoes
is needed per canner load of 7 quarts, or an average of
14 pounds per canner load of 9 pints. A bushel yields 15
to 18 pounds per canner load of 9 pints. A bushel yields
15 to 18 quarts of juice.
Production Requirements*
Paste Soup
Juice
Roma
12
-
8
Plum
8
8
15
Beefstk 15
18
-
Total
26
23
35
Pounds of tomatoes per canner load (7 quarts)
*The actual blends of tomato variety into finished product is proprietary
Plant Capacities
Plant
Capacity
Kokomo
10,000
Santa Fe
14,000
capacity in canner loads (7 quarts) per week
Distribution Center
Requirements
Paste
Soup juice
Pgh
2,000
3,000 500
Chi
1,000
4,000 1,500
SD
5,000
2,000 3,000
canner loads (7 quarts) per week
The Decision Variables

Let Xi,j,k = the number of tomatoes in 1,000 pounds of
type i shipped from supplier j to factory k
i = roma, plum, beefsteak
j = NJ, CA
k = Kokomo, Santa Fe

Let Yl,k,m = the number of canner loads of product l
produced in factory k for distribution center m
l = paste, soup, juice
m = Pgh, Chi, SD
The Objective Function
Min 12XR_NJ_K + 10XP_NJ_K+ 8XB_NJ_K +
15XR_NJ_S + 14XP_NJ_S + 10XB_NJ_S
+ 15XP_CA_K+ 12XB_CA_K + 8XP_CA_S+
9XB_CA_S
+8YP_K_PGH + 6YS_K_PGH + 9YJ_K_PGH
+9YP_S_PGH + 7YS_S_PGH + 10YJ_S_PGH
+10YP_K_CHI + 8YS_K_CHI + 11YJ_K_CHI
+11YP_S_CHI + 9YS_S_CHI + 12YJ_S_CHI
+ 12YP_K_SD + 10YS_K_SD + 13YJ_K_SD
+10YP_S_SD + 8YS_S_SD + 12YJ_S_SD
Supplier constraints
East Coast Supplier:
XR_NJ_K + XR_NJ_S < 140
XP_NJ_K + XP_NJ_S < 100
XB_NJ_K + XB_NJ_S < 140
West Coast Supplier:
XP_CA_K + XP_CA_S < 120
XB_CA_K + XB_CA_S < 150
Legend X variables
first index
R – Roma
P – Plum
JB– Beefsteak
middle index
NJ – New Jersey supplier
CA – California supplier
last index
K – Kokomo plant
S – Santa Fe plant
units in 1,000 lb of tomatoes
Production constraints
Roma: XR_NJ_K - .012YP_K_PGH - .012YP_K_CHI - .012YP_K_SD .008YJ_K_PGH - .008YJ_K_CHI - .008YJ_K_SD >= 0
XR_NJ_S - .012YP_S_PGH - .012YP_S_CHI - .012YP_S_SD - .008YJ_S_PGH
- .008YJ_S_CHI - .008YJ_S_SD >= 0
Plum: XP_NJ_K + XP_CA_K - .008YP_K_PGH - .008YP_K_CHI .008YP_K_SD - .008YS_K_PGH - .008YS_K_CHI - .008YS_K_SD .015YJ_K_PGH - .015YJ_K_CHI - .015YJ_K_SD >= 0
XP_NJ_S + XP_CA_S - .008YP_S_PGH - .008YP_S_CHI - .008YP_S_SD .008YS_S_PGH - .008YS_S_CHI - .008YS_S_SD - .015YJ_S_PGH .015YJ_S_CHI - .015YJ_S_SD >= 0
Beefsteak: XB_NJ_K +XB_CA_K - .015YP_K_PGH - .015YP_K_CHI .015YP_K_SD - .018YS_K_PGH - .018YS_K_CHI - .018YS_K_SD >= 0
XB_NJ_S +XB_CA_S - .015YP_S_PGH - .015YP_S_CHI - .015YP_S_SD .018YS_S_PGH - .018YS_S_CHI - .018YS_S_SD >= 0
Production Capacity
constraints
in canner loads
Kokomo:
YP_K_PGH + YS_K_PGH + YJ_K_PGH + YP_K_CHI +
YS_K_CHI + YJ_K_CHI + YP_K_SD + YS_K_SD +
YJ_K_SD < 10000
Santa Fe:
YP_S_PGH + YS_S_PGH + YJ_S_PGH + YP_S_CHI +
YS_S_CHI + YJ_S_CHI+ YP_S_SD + YS_S_SD +
YJ_S_SD < 14000
Distribution Center Requirements
Pittsburgh:
YP_K_PGH + YP_S_PGH > 2000
YS_K_PGH + YS_S_PGH > 3000
YJ_K_PGH + YJ_S_PGH > 500
Chicago:
YP_K_CHI + YP_S_CHI > 1000
YS_K_CHI + YS_S_CHI > 4000
YJ_K_CHI + YJ_S_CHI > 1500
San Diego:
YP_K_SD + YP_S_SD > 5000
YS_K_SD + YS_S_SD > 2000
YJ_K_SD + YJ_S_SD > 3000
Legend Y variables
first index
P – paste
S – soup
J – juice
middle index
K – Kokomo
S – Santa Fe
units in canner loads
The Glorious Solution
Min Cost per week =
$207,160.80
VARIABLE
XR_NJ_K
XP_NJ_K
XB_NJ_K
XR_NJ_S
XP_NJ_S
XB_NJ_S
XP_CA_K
XB_CA_K
XP_CA_S
XB_CA_S
YP_K_PGH
YS_K_PGH
YJ_K_PGH
YP_S_PGH
YS_S_PGH
VALUE
49.777775
92.055557
140.000000
86.222229
0.000000
0.000000
0.000000
0.000000
118.944450
141.999985
2000.0000
3000.0000
500.00000
0.000000
0.000000
VARIABLE
YJ_S_PGH
YP_K_CHI
YS_K_CHI
YJ_K_CHI
YP_S_CHI
YS_S_CHI
YJ_S_CHI
YP_K_SD
YS_K_SD
YJ_K_SD
YP_S_SD
YS_S_SD
YJ_S_SD
VALUE
0.000000
1000.0000
2277.778076
1222.221924
0.000000
1722.221924
277.778046
0.000000
0.000000
0.000000
5000.00000
2000.00000
3000.00000
More of the Glorious Solution
Resources (weekly 1,000 lb of tomatoes):
Type
NJ to
Kokomo
NJ to
Santa Fe
CA to
Kokomo
CA to Santa
Fe
Roma
49.78
86.22
Plum
92.06
118.94
Beefstk
140
142.0
Final Product (weekly canner loads):
Kokomo Santa Fe Kokomo Santa Fe Kokomo
Paste
Paste
Soup
Soup
juice
Pgh 2000
3000
500
Chi
2277.78 1722.22
1222.22
SD
1000
5000
2000
Santa Fe
juice
277.78
3000
The End of the Supply Chain
Model
Goods and services flowing
through the supply pipeline
The bottom line:
The supply chain locks in money!