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 five patterns in order to minimize trim loss. (Let Pi = number of rolls cut into pattern i, for i = 1, 2, 3, 4, 5.) Min s.t.12-ft 15-ft 30-ft P1, P2, P3, P4, P5 ≥ 0 (b) Solve the model formulated in part (a). What is the minimal amount of trim loss (in ft)? ft How many of each pattern should be used? Pattern 1 rollsPattern 2 rollsPattern 3 rollsPattern 4 rollsPattern 5 rolls How many of each type of roll will be sold on the open market? 12-ft rolls15-ft rolls30-ft rolls

Practical Management Science

6th Edition

ISBN:9781337406659

Author:WINSTON, Wayne L.

Publisher:WINSTON, Wayne L.

Chapter2: Introduction To Spreadsheet Modeling

Section: Chapter Questions

Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...

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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 five patterns in order to minimize trim loss. (Let P_i = number of rolls cut into pattern i, for i = 1, 2, 3, 4, 5.)

Min

s.t.12-ft

15-ft

30-ft

P₁, P₂, P₃, P₄, P₅ ≥ 0

(b)

Solve the model formulated in part (a). What is the minimal amount of trim loss (in ft)?

How many of each pattern should be used?

Pattern 1 rollsPattern 2 rollsPattern 3 rollsPattern 4 rollsPattern 5 rolls

How many of each type of roll will be sold on the open market?

12-ft rolls15-ft rolls30-ft rolls

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