4
Network Design
in the Supply
Chain (Part2)
PowerPoint presentation to accompany
Chopra and Meindl Supply Chain Management, 5e
Global Edition
Copyright ©2013 Pearson Education.
1-1
5-1
Network Optimization Models
TelecomOne & HighOptic Case
Demand City
Production and Transportation Cost
per Thousand Units (Thousand $)
Supply
City
Monthly
Capacity
(Thousand
Units) K
Monthly
Fixed Cost
(Thousand
$) f
Atlanta
Boston
Chicago
Denver
Omaha
Portland
Baltimore
1,675
400
985
1,630
1,160
2,800
18
7,650
Cheyenne
1,460
1,940
970
100
495
1,200
24
3,500
Salt Lake
City
1,925
2,400
1,450
500
950
800
27
5,000
Memphis
380
1,355
543
1,045
665
2,321
22
4,100
Wichita
922
1,646
700
508
311
1,797
31
2,200
10
8
14
6
7
11
Monthly
demand
(thousand
units) Dj
Allocating demand to
production facilities
Case1: TelecomOne & HighOptic are two
independent companies.
n = number of factory locations
m
= number of markets or demand points
D j = annual demand from market j
xij =quantity shipped
from factory i to
market j
K i = capacity of factory i
cij = cost of producing and shipping one unit from factory i
to market j
n
m
Minå å cij xij
i=1 j=1
subject to
n
x
i 1
ij
m
x
j 1
ij
 D j for j  1,..., m
 Ki for i  1,..., n
生產設施的需求分配

市場由哪個工廠服務？

工廠使用哪個供應來源？
受限於：
xij =每年自工廠 i 至市場
j 之裝運數量
5-4
Case1: TelecomOne & HighOptic are
two independent companies.

Optimal demand allocation
TelecomOne
HighOptic
Atlanta
Boston
Chicago
Denver
Omaha
Port
land
Baltimore
0
8
2
Memphis
10
0
12
Wichita
0
0
0
Salt Lake
0
0
11
Cheyenne
6
7
0
Capacitated Plant Location
Model
Case2: TelecomOne & HighOptic are
merged into one company TelecomOptic.
Decision variables
yi = 1 if plant i is open, 0 otherwise
xij = quantity shipped from
plant i to market j
n
n
Minå f i yi + å
i=1
i=1
m
åc x
ij ij
j=1
subject to
n
x
i 1
ij
m
x
j 1
ij
 D j for j  1,..., m
 Ki yi for i  1,..., n
yi  0,1 for i  1,..., n, x ij  0
Case2: TelecomOne & HighOptic are
merged into one company TelecomOptic.
Case2: TelecomOne & HighOptic are
merged into one company TelecomOptic.
Case2: TelecomOne & HighOptic are
merged into one company TelecomOptic.
Case2: TelecomOne & HighOptic are
merged into one company TelecomOptic.
Capacitated Model With
Single Sourcing

Market supplied by only one factory

Modify decision variables
yi = 1 if factory i is open, 0 otherwise
xij = 1 if market j is supplied by factory i, 0 otherwise
n
n
m
Minå f i yi + å å D j cij xij
subject to
i=1
i=1 j=1
n
åx
ij
= 1 for j = 1,...,m
i=1
m
åD x
i ij
£ K i yi for i = 1,...,n
j=1
xij , yi Î {0,1}
單一供應來源的最適工廠位址模型

yi = 1
如果工廠
設於 i地，否則為
受限於：
0

xij = 1
如果市場 j
是由工廠 i 供貨，
否則為 0
5-12
Locating Plants and
Warehouses Simultaneously
Locating Plants and
Warehouses Simultaneously

Model inputs
m
n
l
t
Dj
Ki
Sh
We
fi
fe
chi
cie
cej
=
=
=
=
=
=
=
=
=
=
=
=
number of markets or demand points
number of potential factory locations
number of suppliers
number of potential warehouse locations
annual demand from customer j
potential capacity of factory at site i
supply capacity at supplier h
potential warehouse capacity at site e
fixed cost of locating a plant at site i
fixed cost of locating a warehouse at site e
cost of shipping one unit from supply source h to factory i
cost of producing and shipping one unit from factory i to
warehouse e
= cost of shipping one unit from warehouse e to customer j
Locating Plants and
Warehouses Simultaneously
Decision variables
Yi
Ye
xej
xie
xhi
=
=
=
=
=
1 if factory is located at site i, 0 otherwise
1 if warehouse is located at site e, 0 otherwise
quantity shipped from warehouse e to market j
quantity shipped from factory at site i to warehouse e
quantity shipped from supplier h to factory at site i
Objective Function:
n
t
i 1
e1
l
n
n
t
t
m
Min  fi yi   f e ye    chi xhi   cie xie   cej xej
h 1 i 1
i 1 e 1
e1 j 1
Locating Plants and
Warehouses Simultaneously
Constraints:
subject to
n
åx
hi
£ Sh for h = 1,...,l
i=1
åx
ej
£ We ye for e = 1,...,t
j=1
l
t
åx – åx
hi
h=1
ie
³ 0 for i = 1,...,n
e=1
t
åx
ie
n
£ Ki yi for i = 1,...,n
m
åx – åx
ie
ej
j=1
t
åx
ej
= D j for j = 1,...,m
e=1
e=1
i=1
m
³ 0 for e = 1,...,t
yi , ye Î {0,1},xej ,xie ,xhi ³ 0
Accounting for Taxes, Tariffs,
and Customer Requirements

A supply chain network should maximize
profits after tariffs and taxes while meeting
customer service requirements

Modified objective and constraint
n
m
n
n
m
Max  rj xij –  fi yi –  cij xij
i 1 j 1
n
åx
ij
i=1
i 1
i 1 j 1
£ D j for j = 1,...,m
Making Network Design
Decisions In Practice

Do not underestimate the life span of
facilities

Do not gloss over the cultural implications

Do not ignore quality-of-life issues

Focus on tariffs and tax incentives when
locating facilities