Executive Summary for Northwest Newsprint Inc.

This report contains information regarding our analysis and recommendations for a variety of business decisions that Northwest is considering. We were asked to determine optimal production and distribution decisions for 1995 for each of Northwest’s production and distribution centers. More specifically, we used sensitivity reports and excel solver to determine whether or not a significant improvement could be made to the company’s original production plan.

We began by defining Northwest’s decision variables, objective function, and constraints (refer to appendix question 1 for details). After applying excel solver, we found that the company was not operating optimally. We then performed sensitivity analysis to determine the optimal point that the company should be operating at to maximize profit and minimize costs. We then subject our model to changes in production and shipping cost structure, and production capacity and demand structure. We found that decreasing shipping rates on the Duchesne-San Francisco route would increase the amount of profit generated. We also found that by expanding operations at the Los Angeles facilities would result in a major increase in profit. Finally, we considered whether to implement a cash-back incentive to clients at both the Dallas and the Los Angeles locations. We concluded that we should not support such an incentive at either location, as it would ultimately lead to a loss. All numerical data and models are provided in the appendix of this report. Please refer to them as needed.

 

Analysis

Question 2:

We calculated Northwest’s original profit margins and multiplied them by the number of tonnes delivered to find the profit they were making without optimization. We then subtracted that value from our optimal profit to find how much additional profit Northwest could have realized. We found that Northwest could have made an additional $3,962,737.90 profit by maximizing.

Question 3:

Northwest’s optimal solution does not change because of this change in transportation cost. This is because it’s still within the flexibility interval. The interval allows for an increase of $6.66, but the actual change is only about $5.00. The profit doesn’t change because Northwest continues to choose not to use the Duchesne-San Francisco shipping route, and because the increase is still within the flexibility interval.

Question 4:

The flexibility interval for the Duchesne-Los Angeles route allows for a decrease of 2.86. The shipping company’s decision to decrease their costs by 10.14 is outside of the allowable decrease, which means that the optimal solution needs to be changed. Upon resolving for the optimal solution, we found that Northwest’s profit would increase by $1,124,822.67, giving a total profit of $126,625,427.77.

 

Question 5:

A 5% increase in the minimum operations requirement at Naomee Mills results in a 13,617 tonnes increase in the minimum production requirement. This increase is less than the allowable increase of 14800.4 shown in the sensitivity report. Therefore, there is no change that needs to be made to the optimal solution. The profit does not change both because the optimal solution doesn’t change and the shadow price is 0.

Question 6: Northwest would choose Los Angeles. The sensitivity report shows that the increase in demand of 10,000 is less than the allowable increase for both Dallas and LA, so using the shadow price is acceptable.  The shadow price for the Los Angeles constraint is greater than that of Dallas, indicating that any change within the flexibility interval will result in a higher profit. The increase in profit is $1,875,400.

Question 6, continued:

No, Northwest should not implement the $2 million “cash back” incentive at either location. This is because the $2 million incentive would be greater than the additional profit generated at both locations.

 

Appendix

Question 1:

Decision Variables:

 

X = transportation and production costs

First Subscript Number: Producing Mill (Shipped From)

1= Spruce Mills, 2= Naomee Mills, 3= Duchesne

 

Second Subscript Number: Distribution Center (Shipped To)

1= Seattle, 2= Chicago, 3= Dallas, 4= New Orleans, 5= Denver, 6= Los Angeles, 7= San Francisco, 8=Vancouver, 9= Calgary

 

(i.e. X₂₅ would indicate transportation and production costs from Naomee Mills to Denver)

 

 

X₁₂

X₁₃

X₁₄

X₁₅

X₁₇

X₂₁

X₂₂

X₂₃

X₂₄

X₂₅

X₂₆

X₂₇

X₂₈

X₂₉

X₃₁

X₃₂

X₃₃

X₃₄

X₃₅

X₃₆

X₃₇

X₃₈

X₃₉

 

 

Objective Function:

 

270.23(X₁₂) + 197.76(X₁₃) + 193.82(X₁₄) + 208.23(X₁₅) + 208.89(X₁₇) + 288.32(X₂₁) + 206.18(X₂₂) + 130.87(X₂₃) + 139.92(X₂₄) + 172.17(X₂₅) + 187.54(X₂₆) + 219.51(X₂₇) + 212.58(X₂₈) + 207.5(X₂₉) + 282.2(X₃₁) + 237.83(X₃₂) + 124.58(X₃₃) + 134.38(X₃₄) +192.18(X₃₅) + 184.86(X₃₆) + 210.17(X₃₇) + 242.83(X₃₈) + 197.06(X₃₉) = PROFIT

 

Constraints:

 

X₂₉ + X₃₉ = 40,727 (Seattle)

X₁₂+ X₂₂ + X₃₂ = 55,608 (Chicago)

X₁₃ +X₂₃+X₃₃ = 92,680 (Dallas)

X₁₄+ X₂₄ +X₃₄ = 92,680 (NO)

X₁₅ + X₂₅ + X₃₅ = 23,832 (Denver)

X₂₆+ X₃₆ = 211,841 (LA)

X₁₇ + X₂₇ + X₃₇ = 52,960 (San Francisco)

X₂₈ + X₃₈ = 32,581 (Vancouver)

X₂₉ + X₃₉ = 8,145 (Calgary)

 

Sum of X_1X ≤ 166,320 & ≥ 133,056 (1 = Spruce Mills)

Sum of X_2X ≤ 272,340 & ≥ 217,872 (2 = Naomee Mills)

Sum of X_3X ≤ 265,077 & ≥ 212,062 (3 = Duchesne)

Question 2:

Old profit: $121,537,867.20

Optimal profit (using excel solver): $125,500,605.10

New – Old = increase in profit

(125,500,605.10 – 121,537,867.20) = $3,962,737.90

 

Question 4:

Optimal profit before resolving: $125,500,605.10

Optimal profit after resolving (using excel solver): $126,625,427.77

New – Old = increase in profit

(126,625,427.77 – $125,500,605.10) = $1,124,822.67

 

Question 6:

Shadow price for LA constraint = 187.54

Shadow price for Dallas constraint = 143.86

Increase of 10,000 tons of newsprint per year

(shadow price X quantity increased = increase in profit)

 

Increase in profit if expansion takes place at LA distribution center:

(187.54 X 10,000) = 1,875,400

 

Increase in profit if expansion takes place at Dallas distribution center:

(143.86 X 10,000) = 1,438,600

 

1,875,400 > 1,438,600, therefore, profit increases more in LA than in Dallas.

 

Question 6, continued:

Additional increase in profit at LA distribution center = $1,875,400

Additional increase in profit at Dallas distribution center = $1,438,600

Cash Back Incentive = 2,000,000

 

1,875,400 < 2,000,000

1,438,600 <2,000,000

 

Therefore, a cash back incentive amount of 2 million will lead to a loss.