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, v ariables, objective function and constraints. Decision Variables (A-W): Transportation Routes Decision Mill Destination Variables a Chicago 55608 Spruce b 64976 Spruce Dallas c New Orleans 0 Spruce d Denver 23832 Spruce e San Francisco 0 Spruce f Seattle 40727 Naomee g Chicago 0 Naomee h Dallas 27704 Naomee i New Orleans 92680 Naomee j Denver 0 Naomee k 22401 Naomee Los Angeles l San Francisco 52960 Naomee m Vancouver 0 Naomee n Calgary 0 Naomee o Seattle 0 Duchesne p Chicago 0 Duchesne q Dallas 0 Duchesne r New Orleans 0 Duchesne s Denver 0 Duchesne t 189440 Duchesne Los Angeles u San Francisco 0 Duchesne v Vancouver 32581 Duchesne w Calgary 8145 Duchesne *Canadian destinations are highlighted in red
Revenue/Ton
Prod Cost
Ship Cost
$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $
$ 89.77 $ 162.24 $ 166.18 $ 151.77 $ 151.11 $ 46.68 $ 128.82 $ 204.13 $ 195.08 $ 162.83 $ 147.46 $ 115.49 $ 72.42 $ 77.50 $ 52.80 $ 97.17 $ 210.42 $ 200.62 $ 142.82 $ 150.14 $ 124.83 $ 42.17 $ 87.94
$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $
750 750 750 750 750 750 750 750 750 750 750 750 700 700 750 750 750 750 750 750 750 700 700
390 390 390 390 390 415 415 415 415 415 415 415 415 415 415 415 415 415 415 415 415 415 415
$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $
Profit Margin 270.23 197.76 193.82 208.23 208.89 288.32 206.18 130.87 139.92 172.17 187.54 219.51 212.58 207.50 282.20 237.83 124.58 134.38 192.18 184.86 210.17 242.83 197.06
Objective Function: profit margin of each transportation route * tonnes of newsprint 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) Naomee (f-n) Duchesne (o-w)
Total Capacity <= Total Capacity <= Total Capacity <=
166,320 272,340 265,077
1/7/2016
Northwest Newsprint
Constraint 2: Operation Level Spruce (a-e) Naomee (f-n) Duchesne (o-w)
Must operate 6/7 days (85.741% uptime)
Total Operating Level >= Total Operating Level >= Total Operating Level >=
133,056 217,340 212,062
Constraint 3: Distribution Center Volume Seattle Chicago Dallas New Orleans Denver Los Angeles San Francisco Vancouver Calgary
Total Demand = Total Demand = Total Demand = Total Demand = Total Demand = Total Demand = Total Demand = Total Demand = Total Demand =
40,727 55,608 92,680 92,680 23,832 211,841 52,960 32,581 8,145
Q2. LP Solution Results Decision Mill Destination Variables A Chicago - Spruce B 92,680 Spruce Dallas C Spruce New Orleans 73,640 D Denver - Spruce E San Francisco - Spruce F Naomee Seattle 40,727 G Chicago - Naomee H Dallas - Naomee I Naomee New Orleans 19,040 J Denver - Naomee K 111,800 Naomee Los Angeles L Naomee San Francisco 52,960 M Vancouver - Naomee N 8,145 Naomee Calgary O Seattle - Duchesne P 55,608 Duchesne Chicago Q Dallas - Duchesne R New Orleans - Duchesne S Duchesne Denver 23,832 T 100,041 Duchesne Los Angeles U San Francisco - Duchesne V 32,581 Duchesne Vancouver W Calgary - Duchesne *Canadian destinations are highlighted in red
Revenue/Ton
Prod Cost
Ship Cost
$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $
$ 89.77 $ 162.24 $ 166.18 $ 151.77 $ 151.11 $ 46.68 $ 128.82 $ 204.13 $ 195.08 $ 162.83 $ 147.46 $ 115.49 $ 72.42 $ 77.50 $ 52.80 $ 97.17 $ 210.42 $ 200.62 $ 142.82 $ 150.14 $ 124.83 $ 42.17 $ 87.94
$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $
750 750 750 750 750 750 750 750 750 750 750 750 700 700 750 750 750 750 750 750 750 700 700
390 390 390 390 390 415 415 415 415 415 415 415 415 415 415 415 415 415 415 415 415 415 415
$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $
Profit Margin 270.23 197.76 193.82 208.23 208.89 288.32 206.18 130.87 139.92 172.17 187.54 219.51 212.58 207.50 282.20 237.83 124.58 134.38 192.18 184.86 210.17 242.83 197.06
1/7/2016
Northwest Newsprint
Production Before Optimization
Production After Optimization
Δ Production
Spruce
144416
166320
7.05%
Naomee
236472
232672
-0.81%
Duchesne
230166
212062
-4.09%
1.60% Profit $ 121,537,867 $ 125,500,604 The LP solution allocates the production capacity between plants more efficiently to optimize profit based on transportation and production costs. Q3. Freight Discounts
A B C D E F G H I J K L M N O P Q R S T U V W
Decision Variables 92,680 73,640 40,727 19,040 111,800 52,960 8,145 55,608 23,832 100,041 32,581 -
Mill Spruce Spruce Spruce Spruce Spruce Naomee Naomee Naomee Naomee Naomee Naomee Naomee Naomee Naomee Duchesne Duchesne Duchesne Duchesne Duchesne Duchesne Duchesne Duchesne Duchesne
Destination Chicago Dallas New Orleans Denver San Francisco Seattle Chicago Dallas New Orleans Denver Los Angeles San Francisco Vancouver Calgary Seattle Chicago Dallas New Orleans Denver Los Angeles San Francisco Vancouver Calgary
Production Before Optimization
Revenue/Ton
Prod Cost
Ship Cost
$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $
$ 89.77 $ 162.24 $ 166.18 $ 151.77 $ 151.11 $ 46.68 $ 128.82 $ 204.13 $ 195.08 $ 162.83 $ 147.46 $ 115.49 $ 72.42 $ 77.50 $ 52.80 $ 97.17 $ 210.42 $ 200.62 $ 142.82 $ 150.14 $ 124.83 $ 42.17 $ 87.94
$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $
750 750 750 750 750 750 750 750 750 750 750 750 700 700 750 750 750 750 750 750 750 700 700
100K Tonne Discount (NM/DU-LA)
Δ Production
Spruce
144416
166320
7.05%
Naomee
236472
232672
-0.81%
Duchesne
230166
212062
-4.09%
$ 121,537,867
$ 129,896,305
3.32%
Profit
390 390 390 390 390 415 415 415 415 415 394 415 415 415 415 415 415 415 415 394 415 415 415
$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $
Profit Margin 270.23 197.76 193.82 208.23 208.89 288.32 206.18 130.87 139.92 172.17 208.29 219.51 212.58 207.50 282.20 237.83 124.58 134.38 192.18 205.61 210.17 242.83 197.06
1/7/2016
Northwest Newsprint
Based on the optimal solution Northwest Newsprint can benefit from the 5% reduced ship rates for shipments above 100,000 tonnes on the Naomee-Los Angeles and Duchesne- Los Angeles. Q4. Delivery Swap Given the distribution map and transportation costs it is evident that the transportation route between Naomee Mills and New Orleans could benefit from a delivery swap arrangement. Under the optimized solution, this would require the least amount of production (19,040 tonnes) to be transferred to one of the US mills.
Q5. Convert Machine at Naomee Converting the 58,000 tonne machine at Naomee would decrease the production capacity and operating level at the Naomee facility subject to the highlighted constraints below: Constraint 1: Production Capacity Spruce (a-e) Naomee (f-n) Duchesne (o-w)
Total Capacity <= Total Capacity <= Total Capacity <=
Constraint 2: Operation Level Spruce (a-e) Naomee (f-n) Duchesne (o-w)
166,320 214,340 265,077
Must operate 6/7 days (85.741% uptime)
Total Operating Level >= Total Operating Level >= Total Operating Level >=
133,056 183,777 212,062
1/7/2016
A B C D E F G H I J K L M N O P Q R S T U V W
Northwest Newsprint
Decision Variables 92,680 73,640 40,727 19,040 111,800 52,960 8,145 55,608 23,832 100,041 32,581 -
Mill Spruce Spruce Spruce Spruce Spruce Naomee Naomee Naomee Naomee Naomee Naomee Naomee Naomee Naomee Duchesne Duchesne Duchesne Duchesne Duchesne Duchesne Duchesne Duchesne Duchesne
Destination Chicago Dallas New Orleans Denver San Francisco Seattle Chicago Dallas New Orleans Denver Los Angeles San Francisco Vancouver Calgary Seattle Chicago Dallas New Orleans Denver Los Angeles San Francisco Vancouver Calgary
Revenue/Ton
Prod Cost
Ship Cost
$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $
$ 89.77 $ 162.24 $ 166.18 $ 151.77 $ 151.11 $ 46.68 $ 128.82 $ 204.13 $ 195.08 $ 162.83 $ 147.46 $ 115.49 $ 72.42 $ 77.50 $ 52.80 $ 97.17 $ 210.42 $ 200.62 $ 142.82 $ 150.14 $ 124.83 $ 42.17 $ 87.94
$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $
750 750 750 750 750 750 750 750 750 750 750 750 700 700 750 750 750 750 750 750 750 700 700
Production Before Optimization
58,000 Tonne Reduction @ Naomee
Spruce
144416
166,320
7.05%
Naomee
236472
214,340
-0.81%
Duchesne
230166
230,394
-4.09%
$ 121,537,867
$ 127,907,714
2.55%
Profit
390 390 390 390 390 415 415 415 415 415 394 415 415 415 415 415 415 415 415 394 415 415 415
$ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $ $
Profit Margin 270.23 197.76 193.82 208.23 208.89 288.32 206.18 130.87 139.92 172.17 208.29 219.51 212.58 207.50 282.20 237.83 124.58 134.38 192.18 205.61 210.17 242.83 197.06
Δ Production
Converting the Naomee Mills machine would only increase profits by 2.55% as compared to the possible 3.32% that could be achieved through optimal route design alone. However, given that Groundwood specialties is a faster-growing segment currently operating at 96% capacity; Northwest could use this opportunity to create additional capacity in the Groundwood segment at a minimal cost, with less than 1% reduction in profits.
1/7/2016
Northwest Newsprint
Q6. Optimistic vs Pessimistic Demand Conditions Production Before Optimization
Optimistic Demand
Spruce
144416
166,320
7.05%
Naomee
236472
272,340
-0.81%
Duchesne
230166
236,928
-4.09%
Δ Production
8.69% Profit $ 121,537,867 $ 144,659,511 Under optimistic demand conditions there are favorable increases in productivity and profit. Production Before Optimization
Pessimistic Demand
Spruce
144416
166,320
7.05%
Naomee
236472
272,340
-0.81%
Duchesne
230166
236,928
-4.09%
Δ Production
-10.77% Profit $ 121,537,867 $ 97,899,782 Under pessimistic demand conditions there is no feasible solution for optimization based on the allocated demand constraints leading to a 10.77% decrease in production and profits.
