1/7/2016 Northwest Newsprint
Q1. Northwest Newsprint as a Linear Program Formulation
To formulate the Northwest Newsprint production-distribution problem as a linear function we need to
define the decision variables, objective function and constraints.
Decision Variables (A–W): Transportation Routes
Decision
Variables
Mill
Destination
Revenue/Ton
Prod Cost
Ship Cost
Profit
Margin
a
55608
Spruce
Chicago
$ 750
$ 89.77
$ 390
$ 270.23
b
64976
Spruce
Dallas
$ 750
$ 162.24
$ 390
$ 197.76
c
0
Spruce
New Orleans
$ 750
$ 166.18
$ 390
$ 193.82
d
23832
Spruce
Denver
$ 750
$ 151.77
$ 390
$ 208.23
e
0
Spruce
San Francisco
$ 750
$ 151.11
$ 390
$ 208.89
f
40727
Naomee
Seattle
$ 750
$ 46.68
$ 415
$ 288.32
g
0
Naomee
Chicago
$ 750
$ 128.82
$ 415
$ 206.18
h
27704
Naomee
Dallas
$ 750
$ 204.13
$ 415
$ 130.87
i
92680
Naomee
New Orleans
$ 750
$ 195.08
$ 415
$ 139.92
j
0
Naomee
Denver
$ 750
$ 162.83
$ 415
$ 172.17
k
22401
Naomee
Los Angeles
$ 750
$ 147.46
$ 415
$ 187.54
l
52960
Naomee
San Francisco
$ 750
$ 115.49
$ 415
$ 219.51
m
0
Naomee
Vancouver
$ 700
$ 72.42
$ 415
$ 212.58
n
0
Naomee
Calgary
$ 700
$ 77.50
$ 415
$ 207.50
o
0
Duchesne
Seattle
$ 750
$ 52.80
$ 415
$ 282.20
p
0
Duchesne
Chicago
$ 750
$ 97.17
$ 415
$ 237.83
q
0
Duchesne
Dallas
$ 750
$ 210.42
$ 415
$ 124.58
r
0
Duchesne
New Orleans
$ 750
$ 200.62
$ 415
$ 134.38
s
0
Duchesne
Denver
$ 750
$ 142.82
$ 415
$ 192.18
t
189440
Duchesne
Los Angeles
$ 750
$ 150.14
$ 415
$ 184.86
u
0
Duchesne
San Francisco
$ 750
$ 124.83
$ 415
$ 210.17
v
32581
Duchesne
Vancouver
$ 700
$ 42.17
$ 415
$ 242.83
w
8145
Duchesne
Calgary
$ 700
$ 87.94
$ 415
$ 197.06
*Canadian destinations are highlighted in red
Objective Function: profit margin of each transportation route * tonnes of newsprint shipped along
each of these routes = a*270.23+b*197.76+c*193.82+d*208.23+e*208.89+f*288.32+g*206.18+h*130.
87+i*139.92+j*172.17+k*187.54+l*219.51+m*212.58+n*207.50+o*282.20+p*2
37.83+q*124.58+r*134.38+s*192.18+t*184.86+u*210.17+v*242.83+w*197.06
Constraint 1: Production Capacity
Spruce (a–e)
Total Capacity <=
166,320
Naomee (f–n)
Total Capacity <=
272,340
Duchesne (o–w)
Total Capacity <=
265,077
1/7/2016 Northwest Newsprint
Constraint 2: Operation Level → Must operate 6/7 days (85.741% uptime)
Spruce (a-e)
Total Operating Level >=
133,056
Naomee (f-n)
Total Operating Level >=
217,340
Duchesne (o-w)
Total Operating Level >=
212,062
Constraint 3: Distribution Center Volume
Seattle
Total Demand =
40,727
Chicago
Total Demand =
55,608
Dallas
Total Demand =
92,680
New Orleans
Total Demand =
92,680
Denver
Total Demand =
23,832
Los Angeles
Total Demand =
211,841
San Francisco
Total Demand =
52,960
Vancouver
Total Demand =
32,581
Calgary
Total Demand =
8,145
Q2. LP Solution Results
Decision
Variables
Mill
Destination
Revenue/Ton
Prod Cost
Ship Cost
Profit
Margin
A
–
Spruce
Chicago
$ 750
$ 89.77
$ 390
$ 270.23
B
92,680
Spruce
Dallas
$ 750
$ 162.24
$ 390
$ 197.76
73,640
$ 750
$ 166.18
$ 390
$ 193.82
D
–
Spruce
Denver
$ 750
$ 151.77
$ 390
$ 208.23
E
–
Spruce
San Francisco
$ 750
$ 151.11
$ 390
$ 208.89
F
40,727
Naomee
Seattle
$ 750
$ 46.68
$ 415
$ 288.32
–
$ 750
$ 128.82
$ 415
$ 206.18
H
–
Naomee
Dallas
$ 750
$ 204.13
$ 415
$ 130.87
I
19,040
Naomee
New Orleans
$ 750
$ 195.08
$ 415
$ 139.92
J
–
Naomee
Denver
$ 750
$ 162.83
$ 415
$ 172.17
K
111,800
Naomee
Los Angeles
$ 750
$ 147.46
$ 415
$ 187.54
52,960
$ 750
$ 115.49
$ 415
$ 219.51
–
$ 700
$ 72.42
$ 415
$ 212.58
8,145
$ 700
$ 77.50
$ 415
$ 207.50
O
–
Duchesne
Seattle
$ 750
$ 52.80
$ 415
$ 282.20
–
$ 750
$ 210.42
$ 415
$ 124.58
R
–
Duchesne
New Orleans
$ 750
$ 200.62
$ 415
$ 134.38
S
23,832
Duchesne
Denver
$ 750
$ 142.82
$ 415
$ 192.18
T
100,041
Duchesne
Los Angeles
$ 750
$ 150.14
$ 415
$ 184.86
U
–
Duchesne
San Francisco
$ 750
$ 124.83
$ 415
$ 210.17
32,581
$ 700
$ 42.17
$ 415
$ 242.83
–
$ 700
$ 87.94
$ 415
$ 197.06
