COMP SCI / SFWR ENG 4O03 – Operations Research Problem Set 3 – 20 points Handed out: October 27, 2014 Due date: November 26, 2014 ** justify your answers ** 1. Tom hates to wait at stop signs, yield signs and traffic signals while driving. To minimize this aggravation, he has prepared maps of the various regions in which he frequently drives, and measured the average delay (in seconds) at each of the various intersections in these regions. He wants to find a route from location 2 to 4 which minimizes his delay at intersections (regardless of the total distance he has to drive to avoid delays). The details of his map are listed below: From 1 1 2 2 2 3 5 To 3 4 1 3 5 4 4 Delay (in seconds) 3 6 2 7 6 5 7 Model it as a shortest path problem, and solve it using Dijkstra algorithm. 6p 2. Consider the following system of difference constraints. x1 − x2 ≤ 1 x1 − x4 ≤ −4 x2 − x3 ≤ 2 x2 − x5 ≤ 7 x2 − x6 ≤ 5 x3 − x6 ≤ 10 x4 − x2 ≤ 2 x5 − x1 ≤ −1 x5 − x4 ≤ 3 x6 − x3 ≤ −8 Model it as a constraint graph and use Bellman-Ford algorithm to find a feasible solution, or determine that no feasible solution exists. 7p 3. CFS want to transfer oil from its plant to Calgary. The major challenge in oil transmission is to prevent pressure loss. So some pumps are used to increase pressure through several pipelines without any loss if the oil through it is within its capacity. Any oil beyond its capacity will be lost. Moreover each pipeline among pumps has a certain capacity too. You are asked to find out the maximum amount of oil that can be transmitted throughout the network so that no oil loss occurs. The information on the available pumps and pipes is listed below: Pump A B C Capacity 10 20 30 Location CFS CFS CFS Pipe A↔B Capacity 5 A↔C 10 D 40 Calgary A↔D B↔C B↔D C↔D 13 5 7 20 Model it as a maximum flow problem and solve it using Ford-Fulkerson algorithm. 7p • Your solution must reach your instructor or the TA by or before the due date. • You, or your reliable friend must give your work to the TA hand-to-hand or deliver at class to your instructor. • You have to sign your assignment; your signature certifies that the assignment is your work. • If you use some software to reach a solution, provide explanations.