The Darby Company Case

(1)

LAXMI PRASANNA KEESARA

ANUJ SHARMA

(2)

Background

Darby Company manufactures and distributes meters used to measure electric power consumption. The company has production plants in El Paso, Texas and San Bernardino,

California. The company also has three distribution centers in Fort Worth, Texas; Santa Fe, New Mexico; and Las Vegas, Nevada. The company has nine customer zones that its product is shipped to from the three distribution centers and they are; Dallas, San Antonio, Wichita, Kansas City, Denver, Salt Lake City, Phoenix, Los Angeles, and San Diego.

objective

Due to the rapid growth that Darby Company has experienced, the overall efficiency of our distribution system is being assessed to verify that Darby Company is maximizing its distribution resources.

Results obtained Table 1

Master Summary Table

Unit Cost

#

Units Version 1 Version 2 Version 3 TOTAL COST $ 620,770 $ 600,942 $ 553,534

Manufacturing Cost

* Units ( El Paso) $10.50 28,220 21,260 21,260

* Units ( San Bernardino) $10.00 13,040 20,000 20,000

Total Units 41,260 41,260 41,260

TOTAL MANUFACTURING $426,710 $423,230 $423,230

TOTAL TRANSPORTATION $194,060 $177,712 $130,304

$/Units $15 $15 $13

Recommendation

After a thorough analysis of the Darby Company distribution system, Version 3 of the

distribution methods analyzed is the distribution network that Darby Company should pursue to

Version 3 costs $2 less per meter to ship than Version 1 or Version 2

(3)

Should Darby choose to include some shipping directly from the manufacturer in its schedule, it will save $3480.00 in manufacturing costs as well as $67,236 in transportation costs at its current demand schedule. Darby also has the potential in save $2.00 in transportation costs per unit and, therefore, could face an additional potential savings of $17,480 as its demand

increases, totaling a potential cost savings of $88,196.

Further, Darby has the ability to meet an increase of demand up to 8740 units before it is forced to expand its manufacturing operations. If the cost of opening a new plant is an average near $2 million, and the costs of shipping up to 8740 additional units is approximately $120,000, Darby can save, $1.8 million by waiting to increase production.

Managerial Report

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

Table 2

#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?

UNITS UNIT COST DALLAS

SALT

LAKE WICHITA

KANSAS

CITY DENVER PHOENIX

SALT LAKE LOS ANGELES SAN DIEGO

FORT WORTH DIST PLT 14,520 6300 4880 2130 1210

SANTE FE DIST PLT 13,700 6120 2750 4830

LAS VEGAS DIST PLT 13,040 8580 4460

TOTAL UNITS (EL PASO) 28,220 $ 10.50 $ 296,310.00

TOTAL UNITS (SAN BERNADION) 13,040 $ 10.00 $ 130,400.00

TOTAL UNITS 41,260

TOTAL MANUFACTURING $ 426,710.00

TOTAL TRANSPORTATION $ 194,060.00

TOTAL COST $ 620,770.00

ElPaso Production Plant

San Bernardino Production Plant

(4)

Table 3

Transportation costs will be reduced from version 1 to version 2 by $16,348. This is largely due to the lower production cost in San Bernardino passed on to the distribution center then onto the transportation cost.

#3. The company wants to explore the possibility of satisfying some of the customer demand directly from the production plants. In particular, the shipping cost is $0.30 per unit from San Bernardino to Los Angeles and $0.70 from San Bernardino to San Diego. The cost for direct shipments from El Paso to San Antonio is $3.50 per unit. Can distribution costs be further reduced by considering these direct plant to customer shipments?

UNITS UNIT COST DALLAS SALT LAKE WICHITA KANSAS CITY DENVER SAN DIEGO SALT LAKE PHOENIX LOS ANGELES SAN DIEGO

SANTE FE DIST PLT 6,740 6120 620

LAS VEGAS DIST PLT 20,000 4830 2750 8580 3840

TOTAL UNITS (EL PASO) 21,260 $ 10.50 $ 223,230.00 TOTAL UNITS (SAN BERNADION) 20,000 $ 10.00 $ 200,000.00

TOTAL MANUFACTURING $ 423,230.00 TOTAL TRANSPORTATION $ 177,712.00

TOTAL COST $ 600,942.00

ElPaso Production Plant

(5)

Table 4

#4. Over the next five years, Darby is anticipating moderate growth (5000 meters) to the North and West. Would you recommend that they consider plant expansion at this time?

Due to the fact that Darby is currently under-selling its current supply of 50,000 meters, it is not practical for Darby to expand its plant operations at this time. If the company grows by

approximately 5000 meters, there will still be a remaining portion of 3,740 of the supply remaining.

Table5

SALT LAKE WICHITA

KANSAS

CITY DENVER PHOENIX SALT LAKE SAN ANTONIO LOS ANGELES SAN DIEGO LOS ANGELES SAN DIEGO

SANTE FE DIST PLT 6,740 6120 2750 4830

El PASO (Direct Line) 4,880 4880

SAN BERNARDINO (Direct Line) 13,040 8580 4460

TOTAL UNITS (EL PASO) 21,260 10.50$ $ 223,230.00

TOTAL UNITS (SAN BERNADION) 20,000 10.00$ $ 200,000.00

TOTAL COST $ 553,534.00

ElPaso Production Plants

Distribution Network Version 3

San Bernardino Production Plants

Total Units Available 50,000

Total Units Shipped 41,260

Units Remaining 8,740

Growth Expectancy 5,000

Total Units After Growth 3,740

Delivery System Growth Analysis

Version 3 costs

$67,236 less than Version 1

(6)

Appendix Table 1

Master Summary Table

Unit Cost

#

Units Version 1 Version 2 Version 3 TOTAL COST $ 620,770 $ 600,942 $ 553,534

Manufacturing Cost

* Units ( El Paso) $10.50 28,220 21,260 21,260

* Units ( San Bernardino) $10.00 13,040 20,000 20,000

Total Units 41,260 41,260 41,260

TOTAL MANUFACTURING $426,710 $423,230 $423,230

TOTAL TRANSPORTATION $194,060 $177,712 $130,304

$/Units $15 $15 $13

Version 3 costs $2 less per meter to ship than Version 1 or Version 2

Version 3 has a savings of $67,236 compared to Version 1

(7)

Warehouse Expansion

Unit Cost # Units Version 1 Version 2 Version 3

TOTAL COST $ 620,770 $ 600,942 $ 553,534

Manufacturing Cost

* Units ( El Paso) $10.50 28220 21260 21260

* Units ( San Bernadino) $10.00 13040 20000 20000

TOTAL MANUFACTURING $426,710 $423,230 $423,230

TOTAL TRANSPORTATION $194,060 $177,712 $130,304

Variable Case 3-1 Case 3-2 Case 3-3a

EPFW X13 14520 14520 9640 EPSF X14 13700 6740 6740 EPLV X15 0 0 0 EPSA X17 - - 4880 SBSF X24 0 0 0 SBLV X25 13040 20000 6960 SBLA X213 - - 8580 SBSD X214 - - 4460 FWDA X36 6300 6300 6300 FWSA X37 4880 4880 0 FWWI X38 2130 2130 2130 FWKC X39 1210 1210 1210 FWDE X310 - 0 0 SFDA X46 - 0 0 SFSA X47 - 0 0 SFWI X48 - 0 0 SFKC X49 - 0 0 SFDE X410 6120 6120 6120 SFSL X411 4830 0 0 SFPH X412 2750 0 620 SFLA X413 - 0 0 SFSD X414 - 620 0 LVDE X510 - 0 0 LVSL X511 - 4830 4830 LVPH X512 - 2750 2130 LVLA X513 8580 8580 0 LVSD X514 4460 3840 0

(8)

Shipping Cost Per Unit from Production Plants to Distribution Centers (in $) Distribution Center Fort Worth Santa Fe Las Vegas Plant El Paso 3.2 2.2 4.2 San Bernardino * 3.9 1.2

Quarterly Demand Forecast

Customer Zone Demand (meters)

Dallas 6300 San Antonio 4880 Wichita 2130 Kansas City 1210 Denver 6120

Salt Lake City 4830

Phoenix 2750

Los Angeles 8580

San Diego 4460

Shipping Cost from the Distribution Centers to the Customer Zones

Distribution Center Customer Zone Fort Worth Santa Fe Las Vegas Dallas 0.3 5.2 * San Antonio 2.1 5.4 * Wichita 3.1 4.5 * Kansas City 4.4 6 * Denver 6 2.7 5.4

Salt Lake City * 4.7 3.3

Phoenix * 3.4 2.4

(9)

Version 1 Network 6300 6 x36 ` 4880 x37 7 x13 x38 30000 2130 3 x39 8 x14 1 1210 9 x15 x410 6120 x24 x411 10 4 x412 20000 x25 4830 11 2 2750 12 x513 5 8580 x514 13 4460 14 Dallas San Antonio Wichita Kansas City Denver Salt Lake Phoenix Los Angeles San Diego Las Vegas El Paso San Bernadino Fort Worth Sante Fe 13.70 12.70 13.90 .30 4.40 2.70 2.10 3.10 4.70 3.40 2.10 2.50 14.70 11.20

SALT

LAKE WICHITA KANSAS

CITY DENVER PHOENIX SALT LAKE LOS ANGELES SAN DIEGO

SANTE FE DIST PLT 13,700 6120 2750 4830

TOTAL COST $ 620,770.00

ElPaso Production Plant

(10)

Linear Model Objective Function Model MIN 13.7x13+12.7x14+14.7x15+13.9x24+11.2x25+.3x36+2.1x37+3.1x38+4.4x39+2.7x410+4.7x411+3.4x412+2.1x513+2.5x514 s.t. x13+x14+x15 < 30000 x24+x25 < 20000 x13-x36-x37-x38-x39 = 0 x14+x24-x410-x411-x412 = 0 x15+x25-x513-x514 = 0 x36 = 6300 x37 = 4880 x38 = 2130 x39 = 1210 x410 = 6120 x411 = 4830 x412 = 2750 x513 = 8580 x514 = 4460 Xij > 0 Layout x13 14520 x14 13700 x15 0 x24 0 x25 13040 x36 6300 x37 4880 x38 2130 x39 1210 x410 6120 x411 4830 x412 2750 x513 8580 x514 4460 13.7x13+12.7x14+14.7x15+13.9x24+11.2x25+.3x36+2.1x37+3.1x38+4.4x39+2.7x410+4.7x411+3.4x412+2.1x513+2.5x514 620770 x13+x14+x15 28220 x24+x25 13040 x13-x36-x37-x38-x39 0 x14+x24-x410-x411-x412 0 x15+x25-x513-x514 0 x36 6300 x37 4880 x38 2130 x39 1210 x410 6120 x411 4830 x412 2750

(11)

Microsoft Excel 12.0 Answer Report Worksheet: [DARBY.xlsx]V1

Report Created: 7/23/2010 11:21:22 PM

Target Cell (Min)

Cell Name Original Value Final Value

$C$44 > 0 620770

Adjustable Cells

$C$28 x13 > 0 14520 $C$29 x14 > 0 13700 $C$30 x15 > 0 0 $C$31 x24 > 0 0 $C$32 x25 > 0 13040 $C$33 x36 > 0 6300 $C$34 x37 > 0 4880 $C$35 x38 > 0 2130 $C$36 x39 > 0 1210 $C$37 x410 > 0 6120 $C$38 x411 > 0 4830 $C$39 x412 > 0 2750 $C$40 x513 > 0 8580 $C$41 x514 > 0 4460 Constraints

Cell Name Cell Value Formula Status Slack

$C$46 x13+x14+x15 > 28220 $C$46<=30000 Not Binding 1780 $C$47 x24+x25 > 13040 $C$47<=20000 Not Binding 6960 $C$48 x13-x36-x37-x38-x39 > 0 $C$48=0 Not Binding 0 $C$49 x14+x24-x410-x411-x412 > 0 $C$49=0 Not Binding 0 $C$50 x15+x25-x513-x514 > 0 $C$50=0 Not Binding 0 $C$51 x36 > 6300 $C$51=6300 Not Binding 0 $C$52 x37 > 4880 $C$52=4880 Not Binding 0 $C$53 x38 > 2130 $C$53=2130 Not Binding 0 $C$54 x39 > 1210 $C$54=1210 Not Binding 0 $C$55 x410 > 6120 $C$55=6120 Not Binding 0 $C$56 x411 > 4830 $C$56=4830 Not Binding 0 $C$57 x412 > 2750 $C$57=2750 Not Binding 0 $C$58 x513 > 8580 $C$58=8580 Not Binding 0 $C$59 x514 > 4460 $C$59=4460 Not Binding 0

(12)

Version 2 Network 6300 6 x36 4880 x37 7 x13 x38 30000 x39 2130 x14 3 x310 x46 8 x47 1 x48 1210 x49 9 x15 x410 6120 x24 x411 10 4 x412 20000 x25 x414 4830 x413 11 2 x510 x511 2750 x512 12 x513 5 8580 x514 13 4460 14 Dallas San Antonio Wichita Kansas City Denver Salt Lake Phoenix Los Angeles San Diego Las Vegas El Paso San Bernadino Fort Worth Sante Fe 13.70 12.70 14.70 13.90 11.20 2.10 2.50 3.30 3.40 4.70 6.00 6.00 4.50 5.40 4.40 .30 5.20 2.10 5.40 3.30 2.40 2.70 3.10 2.70

UNITS UNIT COST DALLAS SALT LAKE WICHITA KANSAS CITY DENVER SAN DIEGO SALT LAKE PHOENIX LOS ANGELES SAN DIEGO

SANTE FE DIST PLT 6,740 6120 620

LAS VEGAS DIST PLT 20,000 4830 2750 8580 3840

ElPaso Production Plant

(13)

Objective Function Model MIN 13.7x13+12.7x14+14.7x15+13.9x24+11.2x25+.3x36+2.1x37+3.1x38+4.4x39+6x310+5.2x46+5.4x47+4.5x48+6x49+2.7x410+4.7x411+3.4x412+3.3x413+2.7x414+5.4x510+3.3x511+2.4x512+2.1x513+2.5x514 s.t. x13+x14+x15 < 30000 x24+x25 < 20000 x13-x36-x37-x38-x39-x310 = 0 x14+x24-x46-x47-x48-x49-x410-x411-x412-x413-x414 = 0 x15+x25-x510-x511-x512-x513-x514 = 0 x36+x46 = 6300 x37+x47 = 4880 x38+x48 = 2130 x39+x49 = 1210 x310+x410+x510 = 6120 x411+x511 = 4830 x412+x512 = 2750 x413+x513 = 8580 x414+x514 = 4460 Layout x13 14520 x14 6740 x15 0 x24 0 x25 20000 x36 6300 x37 4880 x38 2130 x39 1210 x310 0 x46 0 x47 0 x48 0 x49 0 x410 6120 x411 0 x412 0 x413 0 x414 620 x510 0 x511 4830 x512 2750 x513 8580 x514 3840 13.7x13+12.7x14+14.7x15+13.9x24+11.2x25+.3x36+2.1x37+3.1x38+4.4x39+6x310+5.2x46+5.4x47+4.5x48+6x49+2.7x410+4.7x411+3.4x412+3.3x413+2.7x414+5.4x510+3.3x511+2.4x512+2.1x513+2.5x514 600942 x13+x14+x15 21260 x24+x25 20000 x13-x36-x37-x38-x39-x310 0 x14+x24-x46-x47-x48-x49-x410-x411-x412-x413-x414 0 x15+x25-x510-x511-x512-x513-x514 0 x36+x46 6300 x37+x47 4880 x38+x48 2130 x39+x49 1210 x310+x410+x510 6120 x411+x511 4830 x412+x512 2750 x413+x513 8580 x414+x514 4460

(14)

Microsoft Excel 12.0 Answer Report Worksheet: [DARBY.xlsx]Sheet2 Report Created: 7/24/2010 12:33:40 AM

Target Cell (Min)

$C$54 > 0 600942

Adjustable Cells

$C$28 x13 > 0 14520 $C$29 x14 > 0 6740 $C$30 x15 > 0 0 $C$31 x24 > 0 0 $C$32 x25 > 0 20000 $C$33 x36 > 0 6300 $C$34 x37 > 0 4880 $C$35 x38 > 0 2130 $C$36 x39 > 0 1210 $C$37 x310 > 0 0 $C$38 x46 > 0 0 $C$39 x47 > 0 0 $C$40 x48 > 0 0 $C$41 x49 > 0 0 $C$42 x410 > 0 6120 $C$43 x411 > 0 0 $C$44 x412 > 0 0 $C$45 x413 > 0 0 $C$46 x414 > 0 620 $C$47 x510 > 0 0 $C$48 x511 > 0 4830 $C$49 x512 > 0 2750 $C$50 x513 > 0 8580 $C$51 x514 > 0 3840 Constraints

$C$56 x13+x14+x15 > 21260 $C$56<=30000 Not Binding 8740 $C$57 x24+x25 > 20000 $C$57<=20000 Binding 0 $C$58 x13-x36-x37-x38-x39-x310 > 0 $C$58=0 Not Binding 0 $C$59 x14+x24-x46-x47-x48-x49-x410-x411-x412-x413-x414 > 0 $C$59=0 Not Binding 0 $C$60 x15+x25-x510-x511-x512-x513-x514 > 0 $C$60=0 Not Binding 0 $C$61 x36+x46 > 6300 $C$61=6300 Not Binding 0 $C$62 x37+x47 > 4880 $C$62=4880 Not Binding 0 $C$63 x38+x48 > 2130 $C$63=2130 Not Binding 0 $C$64 x39+x49 > 1210 $C$64=1210 Not Binding 0 $C$65 x310+x410+x510 > 6120 $C$65=6120 Not Binding 0 $C$66 x411+x511 > 4830 $C$66=4830 Not Binding 0

(15)

Version 3 Network 6300 x17 6 x36 4880 x37 7 x13 x38 30000 x39 2130 x14 3 x310 x46 8 x47 1 x48 1210 x49 9 x15 x410 6120 x24 x411 10 4 x412 20000 x25 x414 4830 x413 11 2 x510 x511 2750 x512 12 x513 5 8580 x514 13 x213 4460 x214 14 Dallas San Antonio Wichita Kansas City Denver Salt Lake Phoenix Los Angeles San Diego Las Vegas El Paso San Bernadino Fort Worth Sante Fe 13.70 12.70 14.70 13.90 11.20 2.10 2.50 3.30 3.40 4.70 6.00 6.00 4.50 5.40 4.40 .30 5.20 2.10 5.40 3.30 2.40 2.70 3.10 2.70 14.00 10.30 10.70

UNITS UNIT COST DALLAS SALT LAKE WICHITA

KANSAS

CITY DENVER PHOENIX SALT LAKE SAN ANTONIO LOS ANGELES SAN DIEGO LOS ANGELES SAN DIEGO FORT WORTH DIST PLT 9,640 6300 4880 2130 1210

SANTE FE DIST PLT 6,740 6120 2750 4830

El PASO (Direct Line) 4,880 4880

SAN BERNARDINO (Direct Line) 13,040 8580 4460

TOTAL UNITS (EL PASO) 21,260 10.50$ $ 223,230.00

TOTAL UNITS (SAN BERNADION) 20,000 10.00$ $ 200,000.00

TOTAL COST $ 553,534.00

ElPaso Production Plants

Distribution Network Version 3

San Bernardino Production Plants

(16)

Objective Function Model MIN 13.7x13+12.7x14+14.7x15+14x17+13.9x24+11.2x25+10.3x213+10.70x214+.3x36+2.1x37+3.1x38+4.4x39+6x310+5.2x46+5.4x47+4.5x48+6x49+2.7x410+4.7x411+3.4x412+3.3x413+2.7x414+5.4x510+3.3x511+2.4x512+2.1x513+2.5x514 s.t. x13+x14+x15+x17 < 30000 x24+x25+x213+x214 < 20000 x13-x36-x37-x38-x39-x310 = 0 x14+x24-x46-x47-x48-x49-x410-x411-x412-x413-x414 = 0 x15+x25-x510-x511-x512-x513-x514 = 0 x36+x46 = 6300 x37+x47+x17 = 4880 x38+x48 = 2130 x39+x49 = 1210 x310+x410+x510 = 6120 x411+x511 = 4830 x412+x512 = 2750 x213+x413+x513 = 8580 x214+x414+x514 = 4460 Xij > 0 Layout x13 9640 x14 6740 x15 0 x17 4880 x24 0 x25 6960 x213 8580 x214 4460 x36 6300 x37 0 x38 2130 x39 1210 x310 0 x46 0 x47 0 x48 0 x49 0 x410 6120 x411 0 x412 620 x413 0 x414 0 x510 0 x511 4830 x512 2130 x513 0 x514 0 13.7x13+12.7x14+14.7x15+14x17+13.9x24+11.2x25+10.3x213+10.70x214+.3x36+2.1x37+3.1x38+4.4x39+6x310+5.2x46+5.4x47+4.5x48+6x49+2.7x410+4.7x411+3.4x412+3.3x413+2.7x414+5.4x510+3.3x511+2.4x512+2.1x513+2.5x514 553534 x13+x14+x15+x17 21260 x24+x25+x213+x214 20000 x13-x36-x37-x38-x39-x310 0 x14+x24-x46-x47-x48-x49-x410-x411-x412-x413-x414 0 x15+x25-x510-x511-x512-x513-x514 0 x36+x46 6300

(17)

Microsoft Excel 12.0 Answer Report Worksheet: [DARBY.xlsx]V3

Report Created: 7/24/2010 12:52:11 AM

Target Cell (Min)

$C$57 > 0 553534

Adjustable Cells

$C$28 x13 > 0 9640 $C$29 x14 > 0 6740 $C$30 x15 > 0 0 $C$31 x17 > 0 4880 $C$32 x24 > 0 0 $C$33 x25 > 0 6960 $C$34 x213 > 0 8580 $C$35 x214 > 0 4460 $C$36 x36 > 0 6300 $C$37 x37 > 0 0 $C$38 x38 > 0 2130 $C$39 x39 > 0 1210 $C$40 x310 > 0 0 $C$41 x46 > 0 0 $C$42 x47 > 0 0 $C$43 x48 > 0 0 $C$44 x49 > 0 0 $C$45 x410 > 0 6120 $C$46 x411 > 0 0 $C$47 x412 > 0 620 $C$48 x413 > 0 0 $C$49 x414 > 0 0 $C$50 x510 > 0 0 $C$51 x511 > 0 4830 $C$52 x512 > 0 2130 $C$53 x513 > 0 0 $C$54 x514 > 0 0 Constraints

$C$59 x13+x14+x15+x17 > 21260 $C$59<=30000 Not Binding 8740 $C$60 x24+x25+x213+x214 > 20000 $C$60<=20000 Binding 0 $C$61 x13-x36-x37-x38-x39-x310 > 0 $C$61=0 Not Binding 0 $C$62 x14+x24-x46-x47-x48-x49-x410-x411-x412-x413-x414 > 0 $C$62=0 Not Binding 0 $C$63 x15+x25-x510-x511-x512-x513-x514 > 0 $C$63=0 Not Binding 0 $C$64 x36+x46 > 6300 $C$64=6300 Not Binding 0 $C$65 x17+x37+x47 > 4880 $C$65=4880 Not Binding 0 $C$66 x38+x48 > 2130 $C$66=2130 Not Binding 0 $C$67 x39+x49 > 1210 $C$67=1210 Not Binding 0 $C$68 x310+x410+x510 > 6120 $C$68=6120 Not Binding 0 $C$69 x411+x511 > 4830 $C$69=4830 Not Binding 0 $C$70 x412+x512 > 2750 $C$70=2750 Not Binding 0 $C$71 x213+x413+x513 > 8580 $C$71=8580 Not Binding 0 $C$72 x214+x414+x514 > 4460 $C$72=4460 Not Binding 0

(18)