# OPM 330-Quantitative Methods For Business

### Question:

A company is planning to ship goods from its headquarters in Riyadh to a customer in Dammam. The cost (including time and shipping costs) from one location to another is as follows: A (1,2) \$70, B (1,5) \$120, C (1,3) \$30, D (2,4) \$50, E (3,4) \$20, F (3,5) \$80, G (4,5) \$40, H (3,6) \$110, I (2,6) \$90, J (5,6) \$20 and K (4,6) \$80

a. Add the route letter (A, B, …, K) and cost (in dollars) in the above network representation. Distinguish arc types by adding small end arrows to one-way arcs.

b. State the objective function (assuming that xij = 1, if the arc from node i to node j is on the shortest route and xij = 0, otherwise; for all i,j).

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c. Define all constraints.