Answered step by step
Verified Expert Solution
Question
1 Approved Answer
Part D: 6 marks A factory has five workers, Anne, Bob, Carol, Dave and Ethan. It also has 5 tasks which must be done. Each
Part D: 6 marks A factory has five workers, Anne, Bob, Carol, Dave and Ethan. It also has 5 tasks which must be done. Each worker does the tasks with a different efficiency. Apply the branch and bound strategy to allocate the tasks with minimum overall cost, when each task must be completed by a different worker. The cost for each worker to do the tasks is given in the following table: Task 1 Task 2 Task 3 Task 4 Task 5 Anne $4.00 $8.00 $8.00 $3.00 $4.00 Bob $9.00 $5.00 $5.00 $2.00 $7.00 Carol $4.00 $2.00 $4.00 $1.00 $3.00 Dave $7.00 $9.00 $6.00 $5.00 $8.00 Ethan $3.00 $6.00 $4.00 $4.00 $5.00 a) Describe a suitable method to calculate the lower bound value for all similar problems, where the total number of workers and the total number of tasks are equal? (1 mark) b) Describe a method to calculate a suitable upper bound for similar problems? (1 mark) c) Use the branch and bound strategy to find the most cost-efficient allocation of tasks to workers. Show the details of the expansion and pruning (branch and bound) of the decision tree along with reasons. (4 marks) Part D: 6 marks A factory has five workers, Anne, Bob, Carol, Dave and Ethan. It also has 5 tasks which must be done. Each worker does the tasks with a different efficiency. Apply the branch and bound strategy to allocate the tasks with minimum overall cost, when each task must be completed by a different worker. The cost for each worker to do the tasks is given in the following table: Task 1 Task 2 Task 3 Task 4 Task 5 Anne $4.00 $8.00 $8.00 $3.00 $4.00 Bob $9.00 $5.00 $5.00 $2.00 $7.00 Carol $4.00 $2.00 $4.00 $1.00 $3.00 Dave $7.00 $9.00 $6.00 $5.00 $8.00 Ethan $3.00 $6.00 $4.00 $4.00 $5.00 a) Describe a suitable method to calculate the lower bound value for all similar problems, where the total number of workers and the total number of tasks are equal? (1 mark) b) Describe a method to calculate a suitable upper bound for similar problems? (1 mark) c) Use the branch and bound strategy to find the most cost-efficient allocation of tasks to workers. Show the details of the expansion and pruning (branch and bound) of the decision tree along with reasons. (4 marks)
Step by Step Solution
There are 3 Steps involved in it
Step: 1
Get Instant Access to Expert-Tailored Solutions
See step-by-step solutions with expert insights and AI powered tools for academic success
Step: 2
Step: 3
Ace Your Homework with AI
Get the answers you need in no time with our AI-driven, step-by-step assistance
Get Started