# Darby Case Study

1977 Words Apr 19th, 2008 8 Pages
I. Problem Description

The Darby Company is re-evaluating its current production and distribution system in order to determine whether it is cost-effective or if a different approach should be considered. The company produces meters that measure the consumption of electrical power. Currently, they produce these meters are two locations – El Paso, Texas and San Bernardino, California. The San Bernardino plant is newer, and therefore the technology is more effective, meaning that their cost per unit is \$10.00, while the El Paso plant produces at \$10.50. However, the El Paso plant has a higher capacity at 30,000 to San Bernardino’s 20,000. Once manufactured, the meters are sent to one of three distribution centers – Ft. Worth, Texas, Santa
Without distribution 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

Without distribution limitations and supplying direct to Los Angeles, San Diego and San Antonio:
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 + x23 + x24 = 0
6. x6 + x16 =3600
7. x7 + x17 + x27 = 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 + x25 =8580
14. x14 + x21 + x26 = 4460