STAR Co. provides paper to smaller companies with volumes that 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 de- mands for these widths vary from week to week. The following cutting patterns have been established: Pattern Number 12-ft 15-ft 30-ft Trim Loss (ft) 6. 10 3 10 3 8 4 2 5 7 ter 9 Integer Linear Optimization Models Trim loss is the leftover paper from a pattern (for example, for pattern 4, 2(12) + 1(15) + 2(30) = 99 feet used results in 100 – 99 = 1 foot of trim loss). Demands this week are 5670 12-foot rolls, 1680 15-foot rolls, and 3350 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). --

STAR Co. provides paper to smaller companies with volumes that 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 de- mands for these widths vary from week to week. The following cutting patterns have been established: Pattern Number 12-ft 15-ft 30-ft Trim Loss (ft) 6. 10 3 10 3 8 4 2 5 7 ter 9 Integer Linear Optimization Models Trim loss is the leftover paper from a pattern (for example, for pattern 4, 2(12) + 1(15) + 2(30) = 99 feet used results in 100 – 99 = 1 foot of trim loss). Demands this week are 5670 12-foot rolls, 1680 15-foot rolls, and 3350 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). --

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter4: Linear Programming Models

Section: Chapter Questions

Problem 91P

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STAR Co. provides paper to smaller companies with volumes that 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. Pattern Number 12‐ft 15‐ft 30‐ft Trim Loss (ft) 1 0 6 0 10 2 0 0 3 10 3 8 0 0 4 4 3 0 2 4 5 7 1 0 1 Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 3(12) + 0(15) + 2(30) = 96 feet used results in 100 − 96 = 4 foot of trim loss). Orders in hand for the coming week are 5,680 12-foot rolls, 1,670 15-foot rolls, and 3,340 30-foot rolls. Any of the three types of rolls produced in excess of the orders in hand will be sold on the open market at the selling price. No inventory is held. (a) Formulate an integer programming model that will determine how many 100-foot rolls to cut into each of the…
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 4 1 10 ft. 2 4 3 0 7 ft. 3 8 0 0 4 ft. 4 2 1 2 1 ft. 5 2 3 1 1 ft. Trim loss is the leftover paper from a pattern (e.g., for pattern 4, 2(12) + 1(15) + 2(30) = 99 feet used resulting in foot of trim loss). Orders in hand for the coming week are 5,670 12-foot rolls, 1,680 15-foot rolls, and 3,350 30-foot rolls. Any of the three types of rolls produced in excess of the orders in hand will be sold on the open market at the selling price. No inventory is held. (a) Formulate an integer programming model that will determine how many 100-foot rolls to cut into…
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