bay area bakery

Bay Area Bay Area BakeryBakery

Group MembersKevin Worrell, Asad Khan, Donavan Drewes,

Harman Grewal, Sanju Dabi

Case study #1

Discussion Questions Question 1

Agree/disagree with construction of new facility in San Jose Formulate and solve mathematical programming model(s) Make all necessary assumptions

Question 2 If we disagree - what actions are necessary Is the current distribution optimal

Question 3 10 year growth projections Effects on need for new San Jose facility

Question 4 Additional factors to consider

Discussion Questions Question 1

Agree/disagree with new facility in San Jose Formulate and solve a mathematical programming model(s) Make all necessary assumptions

Question 2 If we disagree - what actions are necessary Is the current distribution optimal

Question 3 10 year growth projections Effects on need for new San Jose facility

Question 4 Additional factors to consider

Project Assumptions

Jan 1, 2006 to Dec 31, 2006 is current operating year with current operating QTY and is the baseline position of the Bakery operation.

Assume Jan 1, 2007 is the first day the San Jose Plant can come online. Recognize San Jose plant savings on December 31st of the year Builder has San Jose plant ready for operation and gets paid the $4,000,000 on

January 1 of that year. Bakery corporation has $4,000,000 in liquid asset reserves therefore the

money is interest free. Current operation cost is flat and production cost includes all the overhead

production costs (e.g. equipment maintenance, facilities, wages etc). Roadmap approach with an intention to operate up and beyond 10yrs Products are priced in market such that we make same profit always despite of

inflation and increased taxes

Mathematical Model Let’s assume BN is the bakery plant of origin, and DN is the bakery destination

for major market areas:

Santa Rosa

Sacramento Richmond San Francisco

Stockton Santa Cruz San Jose

Bakery of Origin B1 B2 B3 B4 B5 B6 B7

Santa Rosa

Scrmnto Rchmd Brkly Okld San Fran San Jose

Santa Cruz

Slns Stckt Mdst

Major Market Areas

D1 D2 D3 D4 D5 D6 D7 D8 D9 D10 D11

Mathematical Model (Cont.)

Based on the data from Table 3 and Table 1 the minimization equation for LINDO comes out to be as follows:

MIN Pa1 B1D1 +…+ Pa11 B1D11 + Pb1 B2D1 + …+ Pb11 B2D11 + Pc1 B3D1 +…+ Pc11 B3D11 + Pd1 B4D1 + … + Pd11 B4D11 + Pe1 B5D1 +…+ Pe11 B5D11 + Pf1 B6D1 +…+ Pf11 B6D11 + {Pin B7Dnn}

The above equation is shown with San Jose (in bold). Where P in is the total cost associated for delivering products from bakery of origin to major market areas. This total cost is calculated as the

sum of baking cost and delivery cost as follows:

Pin = Baking cost from the bakery of origin + Delivery cost to the major market areas


The constraint equations for LINDO are as follows:

The following equations are derived from the fact that a particular bakery can supply to major market areas with the consideration of capacity (Table 1 and Table 3):

•B1D1 + …+ B1D11 <= 500•B2D1 + …+ B2D11 <= 1000•B3D1 +…+ B3D11 <= 2700•B4D1 +…+ B4D11 <= 2000•B5D1 +…+ B5D11 <= 500•B6D1 +…+ B6D11 <= 800•{B7D1 +…+ B7D11 <= 1200}

The bold equation is added for the construction of San Jose bakery.


Second set of constraint equations for LINDO are:

Following equations are derived by the fact that the bakeries are supplying a major market area with the consideration of demand over N years. Where Gx is the demand over N years based on the 10% increase for a particular bakery of origin.

•B1D1 +…+ B6D1 {+B7D1} >= Ga

•B1D2 +…+ B6D2 {+B7D1} >= Gb

•B1D3 +…+ B6D3 {+B7D1} >= Gc

•B1D4 +…+ B6D4 {+B7D1} >= Gd

•B1D5 +…+ B6D5 {+B7D1} >= Ge

•B1D6 +…+ B6D6 {+B7D1} >= Gf

•B1D7 +…+ B6D7 {+B7D1} >= Gg

•B1D8 +…+ B6D8 {+B7D1} >= Gh

•B1D9 +…+ B6D9 {+B7D1} >= Gi

•B1D10 +…+ B6D10 {+B7D1} >= Gj

•B1D11 +…+ B6D11 {+B7D1} >= Gk

The bold equation is added for the construction of San Jose bakery.

Mathematical Model (Cont.)The LINDO equations for current year are as follows:

MIN 21 B1D1 + 22.9 B1D2 + 21 B1D3 + 21 B1D4 + 21.2 B1D5 + 21.2 B1D6 + 22.7 B1D7 + 23.8 B1D8 + 24.6 B1D9 + 22.7 B1D10 + 23.8 B1D11

+ 21.4 B2D1 + 18.5 B2D2 + 19.4 B2D3 + 19.4 B2D4 + 19.6 B2D5 + 19.8 B2D6 + 20.9 B2D7 + 22 B2D8 + 22.6 B2D9 + 19.5 B2D10 + 20.6 B2D11

+ 19.2 B3D1 + 18.9 B3D2 + 17 B3D3 + 17 B3D4 + 17.2 B3D5 + 17.4 B3D6 + 18.5 B3D7 + 19.6 B3D8 + 20.2 B3D9 + 19.1 B3D10 + 20 B3D11

+ 20.2 B4D1 + 20.6 B4D2 + 18.4 B4D3 + 18.4 B4D4 + 18.2 B4D5 + 18 B4D6 + 19.5 B4D7 + 20.6 B4D8 + 21.4 B4D9 + 20.1 B4D10 + 21 B4D11



SUBJECT TO

B1D1 +…+ B1D11 <= 500

B2D1 +…+ B2D11 <= 1000

B3D1 +…+ B3D11 <= 2700

B4D1 +…+ B4D11 <= 2000

B5D1 +…+ B5D11 <= 500

B6D1 +…+ B6D11 <= 800

B1D1 +…+ B6D1 >= 300

B1D2 +…+ B6D2 >= 500

B1D3 +…+ B6D3 >= 600

B1D4 +…+ B6D4 >= 400

B1D5 +…+ B6D5 >= 1100

B1D6 +…+ B6D6 >= 1300

B1D7 +…+ B6D7 >= 600

B1D8 +…+ B6D8 >= 100

B1D9 +…+ B6D9 >= 100

B1D10 +…+ B6D10 >= 400

B1D11 +…+ B6D11 >= 100

END

LP OPTIMUM FOUND AT STEP: 15

OBJECTIVE FUNCTION VALUE: $99,770

Mathematical Model (Cont.)The LINDO equation for current year with San Jose is:







+ 21.2 B7D1 + 20.9 B7D2 + 19 B7D3 + 19.0 B7D4 + 18.8 B7D5 + 19.0 B7D6 + 18.5 B7D7 + 19.6 B7D8 + 20.2 B7D9 + 19.9 B7D10 + 20.6 B7D11

SUBJECT TO

B1D1 +…+ B1D11 <= 500

B2D1 +…+ B2D11 <= 1000

B3D1 +…+ B3D11 <= 2700

B4D1 +…+ B4D11 <= 2000

B5D1 +…+ B5D11 <= 500

B6D1 +…+ B6D11 <= 800

B7D1 +…+ B7D11 <= 1200

B1D1 +…+ B7D1 >= 300

B1D2 +…+ B7D2 >= 500

B1D3 +…+ B7D3 >= 600

B1D4 +…+ B7D4 >= 400

B1D5 +…+ B7D5 >= 1100

B1D6 +…+ B7D6 >= 1300

B1D7 +...+ B7D7 >= 600

B1D8 +...+ B7D8 >= 100

B1D9 +…+ B7D9 >= 100

B1D10 +…+ B7D10 >= 400

B1D11 +…+ B7D11 >= 100

END


OBJECTIVE FUNCTION VALUE: $99,090

Mathematical Model (Cont.)The LINDO equation for year 1 without San Jose is:







SUBJECT TO

B1D1 +…+ B1D11 <= 500

B2D1 +…+ B2D11 <= 1000

B3D1 +…+ B3D11 <= 2700

B4D1 +…+ B4D11 <= 2000

B5D1 +…+ B5D11 <= 500

B6D1 +…+ B6D11 <= 800

B1D1 +…+ B6D1 >= 306

B1D2 +…+ B6D2 >= 510

B1D3 +…+ B6D3 >= 612

B1D4 +…+ B6D4 >= 408

B1D5 +…+ B6D5 >= 1122

B1D6 +…+ B6D6 >= 1300

B1D7 +…+ B6D7 >= 720

B1D8 +…+ B6D8 >= 102

B1D9 +…+ B6D9 >= 102

B1D10 +…+ B6D10 >= 408

B1D11 +…+ B6D11 >= 102

END


OBJECTIVE FUNCTION VALUE: $103,457.4

Mathematical Model (Cont.)The LINDO equation for year 1 with San Jose is:







+ 21.2 B7D1 + 20.9 B7D2 + 19 B7D3 + 19.0 B7D4 + 18.8 B7D5 + 19.0 B7D6 + 18.5 B7D7 + 19.6 B7D8 + 20.2 B7D9 + 19.9 B7D10 + 20.6 B7D11

SUBJECT TO

B1D1 +…+ B1D11 <= 500

B2D1 +…+ B2D11 <= 1000

B3D1 +…+ B3D11 <= 2700

B4D1 +…+ B4D11 <= 2000

B5D1 +…+ B5D11 <= 500

B6D1 +…+ B6D11 <= 800

B7D1 +…+ B7D11 <= 1200

B1D1 +…+ B7D1 >= 306

B1D2 +…+ B7D2 >= 510

B1D3 +…+ B7D3 >= 612

B1D4 +…+ B7D4 >= 408

B1D5 +…+ B7D5 >= 1122

B1D6 +…+ B7D6 >= 1300

B1D7 +…+ B7D7 >= 720

B1D8 +…+ B7D8 >= 102

B1D9 +…+ B7D9 >= 102

B1D10 +…+ B7D10 >= 408

B1D11 +…+ B7D11 >= 102

END


OBJECTIVE FUNCTION VALUE: $102,634.2

5 Year Analysis GridFollowing is the analysis grid that contains up to 5 yrs with and

without San Jose:2006 2007 2008 2009 2010 2011

Year from 2006 0 1 2 3 4 5Santa Rosa QTY 300 306 312 318 324 330Sacramento QTY 500 510 520 530 540 550Richmond QTY 600 612 624 636 648 660Berkeley QTY 400 408 416 424 432 440Oakland QTY 1100 1122 1144 1166 1188 1210San Francisco QTY 1300 1300 1300 1300 1300 1300San Jose QTY 600 720 840 960 1080 1200Santa Cruz QTY 100 102 104 106 108 110Salinas QTY 100 102 104 106 108 110Stockton QTY 400 408 416 424 432 440Modesto QTY 100 102 104 106 108 110

Total QTY 5500 5692 5884 6076 6268 6460w/o San Jose $99,770.00 $103,457.00 $111,085.00 $118,933.00with Jose Jose $99,090.00 $102,634.00 $109,723.00 $117,007.00Savings (Day) $680.00 $823.00 $1,092.50 $1,362.00 $1,644.00 $1,926.00Savings (Year) $248,200.00 $300,395.00 $398,762.50 $497,130.00 $600,060.00 $702,990.00Savings (Cum) $300,395.00 $699,157.50 $1,196,287.50 $1,796,347.50 $2,499,337.50

5 Year Analysis Grid

Bakery Start Year Bakery

Starts on Jan 12007 2008 2009 2010 2011

1 Year Recovery 2007 END $300,395.00 2008 END $398,762.50 2009 END $497,130.00 2010 END $600,060.00 2011 END $702,990.002 Year Recovery 2008 END $699,157.50 2009 END $895,892.50 2010 END $1,097,190.00 2011 END $1,303,050.003 Year Recovery 2009 END $1,196,287.50 2010 END $1,495,952.50 2011 END $1,800,180.004 Year Recovery 2010 END $1,796,347.50 2011 END $2,198,942.505 Year Recovery 2011 END $2,499,337.50

At our projected 5 year term we are unable to recover the $4,000,000 cost of starting a new bakery.

5 Year Analysis Conclusions

Current distribution is not optimal It can be improved further as shown in table 1 $3500/day savings Assumption: Cost of keeping a plant non-operational for

temporary period is negligible) For current year there is no need to run the Santa Rosa and

Santa Cruz bakeries

Optimal Distribution for Current Scenario

To Major Market Areas

From Bakery Plant Locations (Quantity in cwt)Santa Rosa

Sacramento

Richmond

San Francisco

Stockton Santa Cruz

Santa Rosa 300

Sacramento 500

Richmond 600

Berkeley 400

Oakland 1100

San Francisco 1300

San Jose 200 400

Santa Cruz 100

Salinas 100

Stockton 400

Modesto 100

Current Operation Cost (per day) : $103,270Optimal Operation Cost (per day) : $99,770 Net savings: $3,500

Table 1

Optimizing Current Operation

Current distribution is not optimal It can be improved further as shown in table 1 $3500/day Assumption: Cost of keeping a plant non-operational for


Santa Cruz bakeriesSAVINGS!!

Optimizing Current Operation

Current distribution is not optimal It can be improved further as shown in table 1 $3500/day savings Assumption: Cost of keeping a plant non-operational for


Santa Cruz bakeries

Will the Bay Area Bakery have the capacity to meet the growth projections for the next 10 years?

Bay Area Bakery will reach maximum production limit (7500 units per day) with current bakery plant capacity starting Jan 1, 2017 (11th year).

Lack of increasing capacity by constructing San Jose plant could realize a 112 cwt loss of market sales potential per day yielding a $122,640.00 loss in profits for fiscal year 2017 ($3.00 per cwt).

Growth of San Jose market (200%) by 2016 (10th year) is main driver.

Capacity Analysis

10 Year Capacity Analysis

10th Year (2016) Shipping AnalysisTo Major Market Areas

From Bakery Plant Locations (Quantity in cwt) (w/o San Jose / with San Jose)

Santa Rosa (B1)

Sacramento (B2)

Richmond (B3)

San Fran (B4)

Stockton (B5)

Santa Cruz(B6)

San Jose (B7)

TOTALS

Santa Rosa (D1) 360 / 320 0 / 40 360

Sacramento (D2) 600 / 600 600

Richmond (D3) 720 / 720 720

Berkeley (D4) 280 / 0 200 / 480 480

Oakland (D5) 140 / 0 1180 / 1320 1320

San Fran (D6) 1300 / 1300 1300

San Jose (D7) 600 / 140 700 / 700 20 / 0 480 / 0 0 / 960 1800

Santa Cruz (D8) 120 / 0 0 / 120 120

Salinas (D9) 120 / 0 0 /120 120

Stockton (D10) 0 / 280 480 / 200 480

Modesto (D11) 120 / 120 120

TOTALS 500 / 320 740 / 1000 2700 / 2700 2000 / 2000 500 / 200 720 / 0 0 / 1200

Cost Without San Jose Plant (per day) : $140,100.00Cost with San Jose Plant (per day) : $135,700.00Savings Differential with San Jose Plant (per day) : $4,400.00

Investment Analysis There can be many considerations to when the San Jose Bakery

should be opened depending on management and investor goals:

Minimize time to recuperate $4,000,000 investment Maximize additional savings after investment recuperated Latest deployment time and still recuperate investment Effect on other bakery operations

Investment Analysis

Additional Factors

Construction cost growth (Materials, Labor etc) Pure money inflation cost Current and future maintenance Operation cost for current plants Land cost due to growth in cities Analysis considering other location than San Jose Enhance the product line Competition from other bakeries Decrease in demand

Any Questions??

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