In some cases, companies want to design supply chain networks in which a market is supplied from only one factory referred to as a single source. Companies may impose this constraint because it lowers the complexity of coordinating the network and requires less flexibility from each facility. Min ΣΣ D; C;;X;; + Σfiyi Total cost Exij = 1 Market j Ex≤ Kiyi Factory i j X;; = 1 if Market j is supplied from Factory i and x = o otherwise y₁ = o if Factory i is to be shut down and y₁ = 1 otherwise. j=1,..,6 i=1,...,5 Market constraints Factory constraints

Practical Management Science
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Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
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In some cases, companies want to design supply chain
networks in which a market is supplied from only one factory,
referred to as a single source. Companies may impose this
constraint because it lowers the complexity of coordinating
the network and requires less flexibility from each facility.
Min ΣE D; CijXij + Σfiyi Total cost
Exij = 1
Market j
Exi; ≤ Kiyi Factory i
j=1,..,6
i=1,...,5
Market constraints
Factory constraints
Xij
X¡¡ = 1 if Market j is supplied from Factory i and x;;= o otherwise
y₁ = o if Factory i is to be shut down and y₁ = 1 otherwise.
Transcribed Image Text:In some cases, companies want to design supply chain networks in which a market is supplied from only one factory, referred to as a single source. Companies may impose this constraint because it lowers the complexity of coordinating the network and requires less flexibility from each facility. Min ΣE D; CijXij + Σfiyi Total cost Exij = 1 Market j Exi; ≤ Kiyi Factory i j=1,..,6 i=1,...,5 Market constraints Factory constraints Xij X¡¡ = 1 if Market j is supplied from Factory i and x;;= o otherwise y₁ = o if Factory i is to be shut down and y₁ = 1 otherwise.
City.
Supply city
Baltimore
Cheyenne
Salt Lake City
Memphis
Wichita
Monthly demand (K units)
Demand city
Production & Transportation Cost (SK/ K units)
Atlanta Boston Chicago Denver Omaha Portland
1,675 400 685 1,630 1,160 2,800 18
1,460
100 495
24
1,940 970
2,400 1,425 500 950
1,925
27
380
1,355 543 1,045
665
22
922
1,646
700 508
311
31
10
8
14
6
7
1,200
800
2,321
1,797
11
Monthly Monthly
capacity fixed costs
(SK)
(K units)
7,650
3,500
5,000
4,100
2,200
Transcribed Image Text:City. Supply city Baltimore Cheyenne Salt Lake City Memphis Wichita Monthly demand (K units) Demand city Production & Transportation Cost (SK/ K units) Atlanta Boston Chicago Denver Omaha Portland 1,675 400 685 1,630 1,160 2,800 18 1,460 100 495 24 1,940 970 2,400 1,425 500 950 1,925 27 380 1,355 543 1,045 665 22 922 1,646 700 508 311 31 10 8 14 6 7 1,200 800 2,321 1,797 11 Monthly Monthly capacity fixed costs (SK) (K units) 7,650 3,500 5,000 4,100 2,200
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