October 1997 Presentation Topic (continued)
How many widgets of each kind should the craftsman make each day to maximize profit?
Question 2. A distributor keeps 15 cans of paint in Oshawa and 25 cans in Oakville. Orders come in for 23 cans to Toronto and 17 cans to Hamilton. Shipping costs per can are given in the table below:
Find the cheapest shipping schedule.
Oshawa $1 $3 Oakville $2 $1
Question 3. An oil company requires a fleet of tankers for shipping crude and product between six ports. Four routes must be served daily as follows:
Assume all tankers are identical. The travel time table between ports is shown below. Assume travel time is independent of direction.
Route# From To No. ships needed per day
1 Dhahran New York 3 2 Marseilles Istanbul 2 3 Naples Bombay 1 4 New York Marseilles 1
One day must be added to each end of any route where cargo is carried for loading and unloading. You may find that the solution requires some routes to be travelled empty.
Na. Ma. Is. NY. Dh. Bo.
Naples 1 2 14 7 7 Marseilles 3 13 8 8 Istanbul 15 5 5 New York 17 20 Dhahran 3
What is the smallest fleet that will do the job? Mark on a sketch where the ships should be located at a typical instant of time.
Question 4. Boatco must determine how many how many boats to produce during each of the coming four quarters (3 month periods). The demand is forecast as 40, 60, 75, and 25 during the next 1st to 4th quarters resp. The number to be produced is decided at the beginning of each quarter. Up to 40 boats can be produced in any quarter without overtime at a cost of $400 per boat. Beyond 40 boats overtime costs drive up the cost to $450 per boat. Any boats unsold at the end of a quarter incur a storage and handling cost of $20 each. Devise a production schedule to minimize the total cost of meeting the demand.
Question 5. Machinco has four machines and four jobs to be completed. Each machine must be assigned to complete one job and each assignment incurs a set-up time. The set-up times are shown below. Find the assignment which minimizes total setup time.
Question 6. A company is taking bids on four construction jobs. Three people have placed bids on the jobs as shown in the following table ("*" indicates that the person did not bid on that job).
Job 1 Job 2 Job 3 Job 4
Machine 1 14 15 8 7 Machine 2 2 12 6 5 Machine 3 7 8 3 9 Machine 4 2 4 6 10
Person 1 can do only one job but persons 2 and 3 can each do up to three jobs. Determine the minimum cost assignment of persons to jobs. [Winston 379-4]
Job 1 Job 2 Job 3 Job 4
Person 1 50 46 42 40 Person 2 51 48 44 * Person 3 * 47 45 45
Question 7. Woodco gets an order for 25 3-ft, 20 5-ft, and 15 9-ft pieces of lumber. It fills the order by cutting up stock 8-ft and 16-ft pieces of which it has a vast supply. How should the cutting be done to minimize waste.