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發表於 2008-11-8 00:11:38
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Question 2: Fabrics and Fall Fashions [VeryDifficult]
From the 10th floor of her office building, Katherine Rallywatches the swarms of New Yorkers fight their way through the streets infestedwith yellow cabs and the sidewalks littered with hot dog stands. On thissweltering July day, she pays particular attention to the fashions worn by thevarious women and wonders what they will choose to wear in the fall. Herthoughts are not simply random musings; they are critical to her work since sheowns and manages TrendLines, an elite women's clothing company.
Today is an especially important day because she must meet withTed Lawson, the production manager, to decide upon next month's productionplan for the fall line. Specifically, she must determine the quantity of eachclothing item she should produce given the plant's production capacity, limitedresources, and demand forecasts. Accurate planning for next month's productionis critical to fall sales since the items produced next month will appear instores during September and women generally buy the majority of the fallfashions when they first appear in September.
She turns back to her sprawling glass desk and looks at thenumerous papers covering it. Her eyes roam across the clothing patternsdesigned almost six months ago, the lists of material requirements for eachpattern, and the lists of demand forecasts for each pattern determined bycustomer surveys at fashion shows. She remembers the hectic and sometimesnightmarish days of designing the fall line and presenting it at fashion showsin New York, Milan,and Paris.Ultimately, she paid her team of six designers a total of $2,000,000 for theirwork on her fall line. With the cost of hiring runway models, hair stylists,and make-up artists; sewing and fitting clothes; building the set;choreographing and rehearsing the show; and renting the conference hall, eachof the three fashion shows cost her an additional $2,500,000.
She studies the clothing patterns and material requirements. Herfall line consists of both professional and casual fashions. She determined theprice for each clothing item by taking into account the quality and cost ofmaterial, the cost of labour and machining, the demand for the item, and theprestige of the TrendLines brand name.
The fall professional fashions include:
Clothing Item
| Material Requirements
| Price
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Labour and Machine Cost
| Tailored wool slacks
| 2 yards of wool
3 yards of acetate for lining
| $200
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$60
| Cashmere sweater
| 1.5 yards of cashmere
| $350
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$150
| Silk blouse
| 2.5 yards of silk
| $250
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$150
| Silk camisole
| 0.5 yard of silk
| $175
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$100
| Tailored skirt
| 2 yards of rayon
1.5 yards of acetate of lining
| $370
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$180
| Wool blazer
| 2.5 yards of wool
1.5 yards of acetate of lining
| $420
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$240
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The fall casual fashions include:
Clothing Item
| Material Requirements
| Price
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Labour and Machine Cost
| Velvet pants
| 3 yards of velvet
3 yards of acetate of lining
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$350
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$150
| Cotton sweater
| 0.5 yards of cotton
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$130
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$70
| Cotton miniskirt
| 0.5 yards of cotton
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$175
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$90
| Velvet shirt
| 1.5 yards of velvet
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$300
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$160
| Button-down blouse
| 1.5 yards of rayon
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$120
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$90
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She knows that for the next month, she has ordered 55,000 yardsof wool, 30,000 yards of acetate, 10,000 yards of cashmere, 35,000 yards ofsilk, 30,000 yards of rayon, 20,000 yards of velvet, and 30,000 yards of cottonfor production. The prices of the materials are listed below.
Material
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Price per Yard
| Wool
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$10.00
| Acetate
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$2.0
| Cashmere
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$80.00
| Silk
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$15.00
| Rayon
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$2.5
| Velvet
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$10.00
| Cotton
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$3.0
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Any material that is not used in production can be sent back tothe textile wholesaler for a full refund, although scrap material cannot besent back to the wholesaler.
She knows that the production of the silk blouse leaves leftover scraps of material. Specifically, for the production of one silk blouse, 3 yards of silk and cotton are needed. From these 3 yards, 2.5 yards are used for the silk blouse and 0.5 yard is left as scrap material. She does not want to waste the material, so she plans to use the rectangular scrap of silk to produce a silk camisole. Therefore, whenever a silk blouse is produced, a silk camisole is also produced. Note that it is possible to produce a silk camisole without producing a silk blouse.
Similarly planning is for the production of cotton sweaters andcotton miniskirts.
Whenever a cottonsweater is produced, a cotton miniskirt is also produced and vice versa. Tohave a simple planning, assume the production units of the two are equal.
The demand forecasts indicate that some items have limiteddemand. Specifically, because the velvet pants and velvet shirts are fashionfads, TrendLines has forecasted that it can sell only 4,000 pairs of velvetpants and 5,000 velvet shirts. TrendLines does not want to produce more thanthe forecasted demand because once the pants and shirts go out of style, thecompany cannot sell them. TrendLines can produce less than the forecasteddemand, since the company is not required to meet the demand.
The cashmere sweater also has limited demand because it isquite expensive, and TrendLines knows it can sell at most 3,000 cashmeresweaters.
TrendLines predicts that the silk blouses and camisoles willbecome the hot fashion, and projects that it can sell at least 10,000 silkblouses and 12,000 silk camisoles.
The demand forecasts also indicate that the wool slacks andwool blazers have a great demand because they are basic items needed in everyprofessional wardrobe. Specifically, the demand is 7,000 pairs of wool slacksand 5,000 wool blazers at most. Katherine wants to meet at least 80 percent ofthe demand for these two items to maintain her loyal customer base and notlose business in the future.
Although the demand for tailored skirts could not beestimated, Katherine feels she should make at most 3,000 of them.
Formulate an Integer Linear Programming model for the aboveproblem to develop a production plan which satisfies all the production, resource,and demand (maximum and minimum) constraints to maximize the total profit.
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Youshould clearly define the decision variables used in your model
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Youshould clearly name the constraints
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Youshould use the Excel Solver to solve the problem, and clearly provide the finalrecommendation.
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發表於 2008-11-7 23:25:07
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