EGR 549 – Problem 10, page 538Page 1 of 4
April 22, 2007
By: Kristofer Olsen
Parisay’s notes in red.
Solve problem 10 on page 539. Use TSP option of WinQSB (Network modeling module > TSP). Print input and output results. Write a report to explain output.
A manufacturer of printed circuit boards uses programmable drill machines to drill six holes in each board. The x and y coordinates of each hole are given below. A drilling order was determined to minimize the time the drill machine spends moving between holes.
xyHole
12 1
31 2
53 3
72 4
83 5
The time (in seconds) it takes to travel from one hole to the next is same as the distance between the holes and is given in the following table.
Distance between Holes for example:
D13 = SQRT[(1-5)^2 + (2-3)^2)] = 4.13
Hole12345
1- 2.236 4.123 6.000 7.071
2 2.236 - 2.828 4.123 5.385
3 4.123 2.828- 2.236 3.000
4 6.000 4.123 2.236- 1.414
5 7.071 5.385 3.000 1.414-
WinQSB Input (option I):
WinQSB input (option II):
WinQSB Output:
Report:
Meeting consumer demand is important to the manufacturer of printed circuit boards, and consumer demand is higher than what is currently being produced. To increase the capacity for production, an analysis needed to be made on the automation processes so that time saving applications could be determined and implemented. All of the processes were analyzed and what follows is one of the highlights of the analysis.
As it was suggested that a study be conducted to determine how the production processes could be made more efficient, one of the processes that was studied was the drilling process. As a result of the study, a new program for drilling the holes is recommended. If the recommendation would be accepted, valuable time will be saved and the capacity for production will be increased as more circuit boards will be produced during the day.
Maximizing the number of holes that are drilled maximizes the number of circuit boards that can be produced. Each day, a limited amount of time is available for drilling, so that energy consumption of the production facility remains minimal. To increase the number of holes that can be drilled, the results of an evaluation could be implemented to minimize the time it takes to drill holes on each circuit board by minimizing the distance the drill travels per circuit board.
The following path is suggested to update the drill program, and as a result of the updated program, minimal time will be spent drilling holes, allowing more circuit board to be produced:
OrderHole Time
1 1 2.236
2 2 4.123
3 4 1.414
4 5 3.000
5 3 4.123
Total: 14.896
Therefore, the drilling of each circuit board will be completed in approximately 15 seconds.
As can be seen from the review of the current drilling program, each circuit board is drilled in approximately 23 seconds. .
OrderHole Time
1 1 7.071
2 5 5.385
3 2 2.282
4 3 2.236
5 4 6.000
Total: 22.974
With the drilling program update, 8 seconds can be saved per circuit board.
Given the four hours of time allotted for circuit board drilling, only 626 circuit boards per day are produced with the current program, but with the updated drilling program, 966 circuit boards per day can be produced. At a contribution of $100 of profit per board, the additional 340 circuit boards will contribute an additional $34,000 of profit per day.
The current drilling program was set up in haste by the drill distributor based on input from technicians so the drilling could begin immediately. With this study, communication channels can open between the engineers and technicians, and future such errors may be prevented.