Supply Chain Management Part II Supply chain management is the combination of art and science that...
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Transcript of Supply Chain Management Part II Supply chain management is the combination of art and science that...
Supply Chain ManagementPart 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.
Managing the flow of goods and services.
A Supply Chain Model
Objective: Determine the least-cost configuration and activity
levels among suppliers, factories, and distributors.
I need a model of a supply chain
to free me of this.
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 multi-resources 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 prisonersupplied 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 i j k i j k l k m l k mi j k l k m
z c X d Y
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
, , , , ,,
, , ,
; ,
; ,
i j k i l l k mj l m
i j k i jk
X a Y i k
X b i j
Ship each factoryneeded resources
Each supplier haslimited 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
, ,,
;l l k m kl m
f Y F k productionconstraint
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
, , , ; ,l k m l mk
Y D 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
Production & Distribution Costs
Kokomo Paste
Santa Fe Paste
Kokomo Soup
Santa Fe Soup
Kokomo juice
Santa Fe 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 35 26 23
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, beefsteakj = NJ, CAk = 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, juicem = Pgh, Chi, SD
The Objective FunctionMin 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 < 140XP_NJ_K + XP_NJ_S < 100XB_NJ_K + XB_NJ_S < 140
West Coast Supplier:XP_CA_K + XP_CA_S < 120XB_CA_K + XB_CA_S < 150
Legend X variables
first indexR – RomaP – PlumJB– Beefsteak
middle indexNJ – New Jersey supplierCA – California supplier
last indexK – Kokomo plantS – 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
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
in canner loads
Distribution Center Requirements
Pittsburgh:YP_K_PGH + YP_S_PGH > 2000YS_K_PGH + YS_S_PGH > 3000YJ_K_PGH + YJ_S_PGH > 500
Chicago:YP_K_CHI + YP_S_CHI > 1000YS_K_CHI + YS_S_CHI > 4000YJ_K_CHI + YJ_S_CHI > 1500
San Diego:YP_K_SD + YP_S_SD > 5000YS_K_SD + YS_S_SD > 2000YJ_K_SD + YJ_S_SD > 3000
Legend Y variables
first indexP – pasteS – soupJ – juice
middle indexK – KokomoS – Santa Fe
units in canner loads
The Glorious SolutionMin Cost per week =
$207,160.80
VARIABLE VALUE XR_NJ_K 49.777775 XP_NJ_K 92.055557 XB_NJ_K 140.000000 XR_NJ_S 86.222229 XP_NJ_S 0.000000 XB_NJ_S 0.000000 XP_CA_K 0.000000 XB_CA_K 0.000000 XP_CA_S 118.944450 XB_CA_S 141.999985 YP_K_PGH 2000.0000 YS_K_PGH 3000.0000 YJ_K_PGH 500.00000 YP_S_PGH 0.000000 YS_S_PGH 0.000000
VARIABLE VALUE
YJ_S_PGH 0.000000 YP_K_CHI 1000.0000 YS_K_CHI 2277.778076 YJ_K_CHI 1222.221924 YP_S_CHI 0.000000 YS_S_CHI 1722.221924 YJ_S_CHI 277.778046 YP_K_SD 0.000000 YS_K_SD 0.000000 YJ_K_SD 0.000000 YP_S_SD 5000.00000 YS_S_SD 2000.00000 YJ_S_SD 3000.00000
More of the Glorious Solution
Kokomo Paste
Santa Fe Paste
Kokomo Soup
Santa Fe Soup
Kokomo juice
Santa Fe juice
Pgh 2000 3000 500
Chi 1000 2277.78 1722.22 1222.22 277.78
SD 5000 2000 3000
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):
Resources (weekly 1,000 lb of tomatoes):