Learning Objectives:

Formulate supply chain problems using advanced optimization modeling $($network flow models, integer LP models, and mixed$-$integer LP models$)($LO $5\mathrm{.}2)$

Solve supply chain problems using advanced optimization modeling $($network flow models, integer LP models, and mixed$-$integer LP models$)($LO $5\mathrm{.}3)$

Interpret results from the output from advanced optimization models $($LO $5\mathrm{.}4)$

Grading

Total Possible Points: $50$ points

Complete the Alaskan Railroad Problem

Alaskan Railroad is an independent, stand$-$alone railroad operation not connected to any other rail service in North America. As a result, rail shipments between Alaska and the rest of North America must be shipped by truck for thousands of miles or loaded onto ocean$-$going vessels and transported by sea. Alaskan Railroad recently began talks with the nation of Canada about expanding its railroad lines to connect with the North American railway system. Figure $1$ summarizes the various rail segments $($associated costs in millions of U$.$S$.$ dollars$)$ that could be built. The North American railroad system currently provides service to New Hazelton and Chetwynd. Alaskan Railroad would like to expand its railway so as to be able to reach one of these cities from Skagway and Fairbanks.

Part $1.$ Implement a network flow model to determine the least expensive way to connect the city of Fairbanks to either New Hazelton or Chetwynd. You should include Skagway and its connections in the network model for Part $1,$ even though Skagway will not be part of the solution. This is recommended so that you can use the same model $($with some modifications$)$ for Part $2.$

Part $2.$ Modify the model from Part $1$ to determine the least expensive way to connect the cities of Fairbanks AND Skagway to either New Hazelton or Chetwynd. If you included Skagway in your model for Part $1,$ you can copy that model for Part $2.$ You will need to modify the model to include Skagway, particularly addressing the cost of any track used by both cities to get to the destination.

Graded Elements:

a$.($PS$1-5$ points$)$ Conceptual understanding of the network and implementation of dummy nodes.

b$.($PS$6-30$ points$)$ Excel Model. The formulas are implemented correctly and produces accurate solutions.

a$.$ Part $1$: $20$ points

b$.$ Part $2$: $10$ points

c$.($PS$8-10$ points $)$ Spreadsheet Design. The model is easy to understand and logical$.$ The various parts of the model are clearly labeled.

SCM $564$: Supply Chain Data Modeling & Analysis Module $5$: Group Problem Set

d$.($PS$3-5$ points$)$ What is the optimal solution? What nodes connect Fairbanks$/$Skayway with the North American Railway system in the optimal solution for Part $1$ and $2?$ What is the cost for each part?