Shortest Path Operations Research Problem

Consider the following game with two players one at Base 1 and one at Base 2. Each player needs to find a path to the other base but if they run into each other then they both lose. Since they dont know exactly when each will start and dont want to take any chances, they need to find routes for each that do not use any of the same paths (arcs) or intersections (nodes). If the numbers on the arcs represent travel time, formulate a mathematical model to minimize the total time it takes both players to reach the other base.

1. Clearly define all decision variables, the objective function, and all constraints. (10 points)
2. Solve the problem using Excel Solver. (10 points)

Part C: suppose you know they leave at exactly the same time. Formulate and solve a model that allows them to use the same paths/intersections as long as they dont run into each other!

2. Consider the following network: Consider the following game with two players - one at Base 1 and one at Base 2. Each player needs to find a path to the other base but if they run into each other then they both lose. Since they don't know exactly when each will start and don't want to take any chances, they need to find routes for each that do not use any of the same paths (arcs) or intersections (nodes). If the numbers on the arcs represent travel time, formulate a mathematical model to minimize the total time it takes both players to reach the other base. a. Clearly define all decision variables, the objective function, and all constraints. (10 points) b. Solve the problem using Excel Solver. (10 points) Bonus: suppose you know they leave at exactly the same time. Formulate and solve a model that allows them to use the same paths/intersections as long as they don't run into each other! (You can do the bonus at home if you like...)