1. Use Branch and Bound method to solve the following Integer linear programming problem. [6] Minimizez=9x, +10x, subject to x, 39, X, 58, 4x; +3x, 240, X, X, 20 and are integers 2. A trip from Chandigarh to Delhi takes six hours by bus. A typical time table of the bus service in both directions is given below: [7] Departure from Route Arrival at Arrival at Route Departure Chandigarh Number Delhi Chandigarh Number from Delhi 6.00 12.00 11.30 5.30 7.30 b 13.30 15.00 2 9.00 11.30 17.30 21.00 3 15.00 19.00 d 01.00 00.30 4 18.30 00.30 6.30 06.00 5 00.00 a 1 e The cost of providing this service by the transport company depends upon the time spent by the bus crew (driver and conductor) away from their places in addition to service time. There are five crews. There is a constraint that every crew should be provided with more than 4 hours of rest before the return trip again and should not wait for more than 24 hours for the return trip. The company has residential facilities for the crew at Chandigarh as well as at Delhi. Find the optimal service line connection. 3. The Farmer's Bank of London is planning to install a new computerized accounts syster. Bank management has determined the activities required to complete the project, the precedence relationships of the activities, and activity time estimates as follows. Represent all the activities 3. The Farmer's Bank of London is planning to install a new computerized accounts system. Bank management has determined the activities required to complete the project, the precedence relationships of the activities, and activity time estimates as follows. Represent all the activities on a network diagram using minimum number of dummy activities. [3] Predecessor Activity A B D E F G Time (in weeks) 5 3 4 5 1 A A B,C B,C DE 1 3 Description Position recruiting System development System Training Equipment Training Manual system set System changeover Computer personnel interface Equipment modification Equipment testing System debugging and installation Equipment changeover DE 1 H F G 1 3 K GI 5 I 4. The Stone River Textile Mill was inspected by OSHA and found to be in violation of a number of safety regulations. The OSHA inspectors ordered the mill to alter some existing machinery to make it safer (e.g., add safety guards); purchase some new machinery to replace older, dangerous machinery; and relocate some machinery to make safer passages and unobstructed entrances make the changes, if the changes were not made 4. The Stone River Textile Mill was inspected by OSHA and found to be in violation of a number of safety regulations. The OSHA inspectors ordered the mill to alter some existing machinery to make it safer (e.g., add safety guards); purchase some new machinery to replace older, dangerous machinery; and relocate some machinery to make safer passages and unobstructed entrances and exits. OSHA gave the mill only 8 weeks to make the changes; if the changes were not made by then, the mill would be fined $100/week of late finishing. Activity Description Normal duration (in weeks) Normal cost (in $) Crash Duration (in weeks) Increment in cost ($) on per week reduction 50 1-2 3 50 2 1-3 5 140 4 60 1-4 2 50 1 30 2-3 5 100 40 N Order new machinery Determine safety changes Receive Equipment Hire new -employees Make changes in the existing machinery Install new machinery Conduct employee safety orientation 3-5 4 100 2 70 2-5 7 115 5 30 4-5 2 55 2 I (a) Determine the normal duration and total cost of the project. [3] (b) Determine the project schedule and total cost of completing the project in 9 weeks. [5] (c) Is it economical to compress the schedule beyond 9 weeks? Justify, [4] (d) What is the minimum cost at which project can be completed? [1] (e) What is the minimum duration of the project with the minimum cost obtained in part (d)? [1] 1. Use Branch and Bound method to solve the following Integer linear programming problem. [6] Minimizez=9x, +10x, subject to x, 39, X, 58, 4x; +3x, 240, X, X, 20 and are integers 2. A trip from Chandigarh to Delhi takes six hours by bus. A typical time table of the bus service in both directions is given below: [7] Departure from Route Arrival at Arrival at Route Departure Chandigarh Number Delhi Chandigarh Number from Delhi 6.00 12.00 11.30 5.30 7.30 b 13.30 15.00 2 9.00 11.30 17.30 21.00 3 15.00 19.00 d 01.00 00.30 4 18.30 00.30 6.30 06.00 5 00.00 a 1 e The cost of providing this service by the transport company depends upon the time spent by the bus crew (driver and conductor) away from their places in addition to service time. There are five crews. There is a constraint that every crew should be provided with more than 4 hours of rest before the return trip again and should not wait for more than 24 hours for the return trip. The company has residential facilities for the crew at Chandigarh as well as at Delhi. Find the optimal service line connection. 3. The Farmer's Bank of London is planning to install a new computerized accounts syster. Bank management has determined the activities required to complete the project, the precedence relationships of the activities, and activity time estimates as follows. Represent all the activities 3. The Farmer's Bank of London is planning to install a new computerized accounts system. Bank management has determined the activities required to complete the project, the precedence relationships of the activities, and activity time estimates as follows. Represent all the activities on a network diagram using minimum number of dummy activities. [3] Predecessor Activity A B D E F G Time (in weeks) 5 3 4 5 1 A A B,C B,C DE 1 3 Description Position recruiting System development System Training Equipment Training Manual system set System changeover Computer personnel interface Equipment modification Equipment testing System debugging and installation Equipment changeover DE 1 H F G 1 3 K GI 5 I 4. The Stone River Textile Mill was inspected by OSHA and found to be in violation of a number of safety regulations. The OSHA inspectors ordered the mill to alter some existing machinery to make it safer (e.g., add safety guards); purchase some new machinery to replace older, dangerous machinery; and relocate some machinery to make safer passages and unobstructed entrances make the changes, if the changes were not made 4. The Stone River Textile Mill was inspected by OSHA and found to be in violation of a number of safety regulations. The OSHA inspectors ordered the mill to alter some existing machinery to make it safer (e.g., add safety guards); purchase some new machinery to replace older, dangerous machinery; and relocate some machinery to make safer passages and unobstructed entrances and exits. OSHA gave the mill only 8 weeks to make the changes; if the changes were not made by then, the mill would be fined $100/week of late finishing. Activity Description Normal duration (in weeks) Normal cost (in $) Crash Duration (in weeks) Increment in cost ($) on per week reduction 50 1-2 3 50 2 1-3 5 140 4 60 1-4 2 50 1 30 2-3 5 100 40 N Order new machinery Determine safety changes Receive Equipment Hire new -employees Make changes in the existing machinery Install new machinery Conduct employee safety orientation 3-5 4 100 2 70 2-5 7 115 5 30 4-5 2 55 2 I (a) Determine the normal duration and total cost of the project. [3] (b) Determine the project schedule and total cost of completing the project in 9 weeks. [5] (c) Is it economical to compress the schedule beyond 9 weeks? Justify, [4] (d) What is the minimum cost at which project can be completed? [1] (e) What is the minimum duration of the project with the minimum cost obtained in part (d)? [1]