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 the following quarter. This is computed by taking the information from above and putting it into the objective function which shows the minimized shipping cost to be $194,060. To find the manufacturing cost, we take the values for x1 through x6 and multiple by their respective costs per unit. For example, the values x1, x2 and x3 are the number of items shipped from the El Paso plant, where the manufacturing cost is $10.50 per unit. These values are 14,520 units to ship to the Ft. Worth distribution center, 13,700 units to ship to the Santa Fe plant and 0 to ship to the Las Vegas distribution plant. In order to ship the meters, they must produce them, therefore the manufacturing cost at the El Paso plant is $152,460 (14520x10.50) + $148,850 (13,700x10.50) = $296,310. The San Bernardino plant only has a value for shipping to the Las Vegas distribution center and this value is 13,040 units. Since the cost of manufacturing at that plant is only $10 per unit, their cost is $130,400. When the cost of manufacturing at each plant is added to the cost of shipping throughout the system the total is $296,310 + $130,400 + $194,060 = $620,770. If the company does not change its current distribution strategy the following quarter the distribution cost for the following quarter will be $620,060.

2. Suppose that the company is willing to consider dropping the distribution center limitations: that is, customers could be served by any of the distribution centers for which costs are available. Can costs be reduced? By how much?

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 + 0.3x25 +0.7x26 + 3.5x27

s.t.:

1. x1 + x2 + x3 + x27 ≤ 30,000

2. x4 + x5 + x25 + x26 ≤ 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...