Problem 12-1
STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established:
Number of: | ||||
Pattern | 12ft. | 15ft. | 30ft. | Trim Loss |
1 | 0 | 6 | 0 | 10 ft. |
2 | 5 | 2 | 0 | 10 ft. |
3 | 4 | 3 | 0 | 7 ft. |
4 | 3 | 0 | 2 | 4 ft. |
5 | 7 | 1 | 0 | 1 ft. |
Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 3(12) + 0(15) + 2(30) = 96 feet used resulting in 100-96 = 4 foot of trim loss). Demands this week are 5,680 12-foot rolls, 1,720 15-foot rolls, and 3,270 30-foot rolls. Develop an all-integer model that will determine how many 100-foot rolls to cut into each of the five patterns in order to meet demand and minimize trim loss (leftover paper from a pattern).
Optimal Solution:
Pattern | Number Rolls Used |
1 | |
2 | |
3 | |
4 | |
5 |
Trim Loss: feet
Rolls Used | |
Obj. Fun. | 0 |
0 | |
0 | |
1635 | |
1720 | |
Trim Loss | 8260 |
The calculations are:
Pattern | 12ft. | 15ft. | 30ft. | Trim Loss | |
1 | 0 | 6 | 0 | 10 | |
2 | 5 | 2 | 0 | 10 | |
3 | 4 | 3 | 0 | 7 | |
4 | 3 | 0 | 2 | 4 | |
5 | 7 | 1 | 0 | 1 | |
Rolls Used | |||||
Obj. Fun. | 0 | 16945 | 1720 | 3270 | |
0 | >= | >= | >= | ||
0 | 5680 | 1720 | 3270 | ||
1635 | |||||
1720 | |||||
Trim Loss | 8260 |
Problem 12-1 STAR Co. provides paper to smaller companies whose volumes are not large enough to...
0 STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established: Number of: Pattern 12ft. 15ft. 30ft. Trim Loss 1 0 0 3 10 ft. 2 0 6 0 10...
All I need is the Trim loss in part b STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established Number of: Pattern 12ft. 15ft. 30ft. Trim Loss 1 5...
STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established: Number of: Pattern 12ft. 15ft. 30ft. Trim Loss 1 0 6 0 10 ft. 2 0 0 3 10 ft....
STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mill. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established: Number of: Pattern 12ft. 15ft. 30ft. Trim Loss 1 0 6 0 10 ft. 2 0 0 3 10 ft....
****Solve the model formulated in part a. What is the minimal amount of trim loss?**** Trim Loss: ____ feet STAR Co. provides paper to smaller companies whose volumes are not large enough to warrant dealing directly with the paper mil. STAR receives 100-feet-wide paper rolls from the mill and cuts the rolls into smaller rolls of widths 12, 15, and 30 feet. The demands for these widths vary from week to week. The following cutting patterns have been established: Number...
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