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Office Equipment Inc Case Problem

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Office Equipment Inc Case Problem
LP8 ASSIGNMENT
DISTRIBUTION SYSTEM DESIGN

By:
Jeffrey L. Blake
Course:
MT4210 Quantitative Analysis
Instructor:
Paul Larson
Distribution System Design

1. If the company does not change its current distribution strategy, what will its distribution costs be for the follow quarter?

Original shipping plan model

MIN 3.2x1+2.2x2+4.2x3+3.9x4+1.2x5+0.3x6+2.1x7+3.1x8+4.4x9+2.7x10+4.7x11+3.4x12+
2.1x13+2.5x14

DISTRIBUTION CONSTRAINTS 1. x1+x2+x3≤30,000 2. x4+x5≤20,000 3. –x1+x6+x7+x8+x9=0 4. –x2-x4+x10+x11+x12=0 5. –x3-x5+x13+x14=0 6. x6=3600 7. x7=4880 8. x8=2130 9. x9=1210 10. x10=6120 11. x11=4830 12. x12=2750 13. x13=8580 14. x14=4460

I used this distribution model because the question states that the company in not changing its current distribution strategy. Constraints 1-2 are the number of units that the two plants are able to produce. Constraints 3-5 are transshipment constraints; they guarantee that the number of units shipped into the distribution center is equal to the number shipped out. Constraints 6-14 are the number of units demanded at each customer zone and are in place to guarantee the demand is satisfied. Now to show how to calculate the totals we must set up the model to show no limitations as the problem is saying. To set that up I am going to list the new formulas without limitations.
MIN
3.2x1+2.2x2+4.2x3+3.9x4+1.2x5+0.3x6+2.1x7+3.1x8+4.4x9+2.7x10+4.7x11+
3.4x12+2.1x13+2.5x14+6.0x15+5.2x16+5.4x17+4.5x18+6.0x19+3.3x20+2.7x21+
5.4x22+3.3x23+2.4x24

S.T. (subject to):
1. x1+x2+x3≤30,000
2. x4+x5≤20,000
3. –x1+x6+x7+x8+x9+x15=0
4. –x2-x4+x10+x11+x12+x16+x17+x18+x19+x20+x21=0
5. –x3-x5+x13+x14+x22+x23+x24=0
6. x6+x16=3600
7. x7+x17=4880
8. x8+x18=2130
9. x9+x19=1210
10. x10+x15+x22=6120
11. x11+x23=4830
12. x12+x24=2750
13. x13+x20=8580
14. x14+x21=4460

If Darby keeps the current distribution plan, the total cost will be $620,770 for
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