Northwest Newsprint Inc. is a major producer of Newsprint with pulp mills located in the Pacific Northwest and Canada that supply to various American and Canadian Markets. In an effort to maximize their profit, Northwest asked us to analyze the quantity of newsprint they should ship from three pulp mills to nine different markets. In order to find the optimal amount of tons from each mill to each city, we used an indexing method of the form “X_mc” where “m” stands for “mills” and has values A,B,C, and “c” stands for “centers” with values one through nine. We maximized the sum of the profits from each combination (i.e. Max[P_A1 + P_A2 + … + P_C9] where “P_mc” is equal to [revenue/ton – total cost/ton]*X_mc). The factors considered in total cost include both production and shipping costs that are specific to each mill and center. We chose to use the per-ton approach to the problem because it would be easier to change the values of certain coefficients given an alteration in costs or revenue figures.
After reviewing the Linear Programming Model, we recommend that, in order to increase profits by $4,109,309.10, Northwest Newsprint should do the following:
A. Shipments from Spruce Mills: 1. Increase shipments to Dallas by 50,000 tons 2. Decrease shipments to New Orleans by 46,000 tons 3. Increase shipments to Los Angeles by 911 tons 4. Decrease shipments to Calgary by 2,576 tons
B. Shipments from Naomee Mills: 1. Increase shipments to Seattle by 23,000 tons 2. Decrease shipments to Chicago by 23,720 tons 3. Decrease shipments to Dallas by 29,500 tons 4. Increase shipments to New Orleans by 46,000 tons 5. Increase shipments to Los Angeles by 20,001 tons 6. Decrease shipments to Vancouver by 20,000 tons 7. Increase shipments to Calgary by 2,576 tons
C. Shipments from Duchesne: 1. Decrease shipments to Seattle by 23,000 tons 2. Increase shipments to Chicago by 25,720 tons 3. Decrease shipments to Dallas by 20,500 tons 4. Decrease shipments to Los Angeles by 19,090 tons 5. Increase shipments to Vancouver by 20,000 tons