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Bay Area Bakery. Group Members. Case study #1. Kevin Worrell, Asad Khan, Donavan Drewes, Harman Grewal, Sanju Dabi. Discussion Questions. Question 1 Agree/disagree with construction of new facility in San Jose Formulate and solve mathematical programming model(s)

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Bay area bakery

Bay Area Bakery

Group Members

Case study #1

Kevin Worrell, Asad Khan, Donavan Drewes, Harman Grewal, Sanju Dabi


Discussion questions
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


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


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
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

Santa Rosa

Santa Rosa

Sacramento

Scrmnto

Richmond

Rchmd

Brkly

San Francisco

Okld

Stockton

San Fran

Santa Cruz

San Jose

Santa Cruz

San Jose

Slns

Stckt

Mdst

Bakery of Origin

Major Market Areas

B1

D1

B2

D2

B3

D3

D4

B4

D5

B5

D6

B6

D7

D8

B7

D9

D10

D11

Mathematical Model

Let’s assume BN is the bakery plant of origin, and DN is the bakery destination for major market areas:


Mathematical model cont
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 Pin 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


Mathematical model cont1
Mathematical Model (Cont.)

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.


Mathematical model cont2
Mathematical Model (Cont.)

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 cont3
Mathematical Model (Cont.)

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

+ 22.2 B5D1 + 20.5 B5D2 + 20.6 B5D3 + 20.6 B5D4 + 20.6 B5D5 + 20.8 B5D6 + 20.9 B5D7 + 22 B5D8 + 22.6 B5D9 + 19.5 B5D10 + 20.6 B5D11

+ 25.8 B6D1 + 25.5 B6D2 + 23.6 B6D3 + 23.6 B6D4 + 23.4 B6D5 + 23.6 B6D6 + 23.1 B6D7 + 23 B6D8 + 23.8 B6D9 + 24.5 B6D10 + 25.2 B6D11

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

The LINDO equations for current year are as follows:

LP OPTIMUM FOUND AT STEP: 15

OBJECTIVE FUNCTION VALUE: $99,770


Mathematical model cont4
Mathematical Model (Cont.)

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

+ 22.2 B5D1 + 20.5 B5D2 + 20.6 B5D3 + 20.6 B5D4 + 20.6 B5D5 + 20.8 B5D6 + 20.9 B5D7 + 22 B5D8 + 22.6 B5D9 + 19.5 B5D10 + 20.6 B5D11

+ 25.8 B6D1 + 25.5 B6D2 + 23.6 B6D3 + 23.6 B6D4 + 23.4 B6D5 + 23.6 B6D6 + 23.1 B6D7 + 23 B6D8 + 23.8 B6D9 + 24.5 B6D10 + 25.2 B6D11

+ 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

The LINDO equation for current year with San Jose is:

LP OPTIMUM FOUND AT STEP: 12

OBJECTIVE FUNCTION VALUE: $99,090


Mathematical model cont5
Mathematical Model (Cont.)

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

+ 22.2 B5D1 + 20.5 B5D2 + 20.6 B5D3 + 20.6 B5D4 + 20.6 B5D5 + 20.8 B5D6 + 20.9 B5D7 + 22 B5D8 + 22.6 B5D9 + 19.5 B5D10 + 20.6 B5D11

+ 25.8 B6D1 + 25.5 B6D2 + 23.6 B6D3 + 23.6 B6D4 + 23.4 B6D5 + 23.6 B6D6 + 23.1 B6D7 + 23 B6D8 + 23.8 B6D9 + 24.5 B6D10 + 25.2 B6D11

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

The LINDO equation for year 1 without San Jose is:

LP OPTIMUM FOUND AT STEP: 16

OBJECTIVE FUNCTION VALUE:$103,457.4


Mathematical model cont6
Mathematical Model (Cont.)

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

+ 22.2 B5D1 + 20.5 B5D2 + 20.6 B5D3 + 20.6 B5D4 + 20.6 B5D5 + 20.8 B5D6 + 20.9 B5D7 + 22 B5D8 + 22.6 B5D9 + 19.5 B5D10 + 20.6 B5D11

+ 25.8 B6D1 + 25.5 B6D2 + 23.6 B6D3 + 23.6 B6D4 + 23.4 B6D5 + 23.6 B6D6 + 23.1 B6D7 + 23 B6D8 + 23.8 B6D9 + 24.5 B6D10 + 25.2 B6D11

+ 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

The LINDO equation for year 1 with San Jose is:

LP OPTIMUM FOUND AT STEP: 12

OBJECTIVE FUNCTION VALUE:$102,634.2


5 year analysis grid
5 Year Analysis Grid

Following is the analysis grid that contains up to 5 yrs with and without San Jose:


5 year analysis grid1
5 Year Analysis Grid

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
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


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


Table 1

Optimal Distribution for Current Scenario

Current Operation Cost (per day) : $103,270

Optimal Operation Cost (per day) : $99,770

Net savings: $3,500


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 temporary period is negligible)

  • For current year there is no need to run the Santa Rosa and Santa Cruz bakeries

SAVINGS!!


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 temporary period is negligible)

  • For current year there is no need to run the Santa Rosa and Santa Cruz bakeries


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 temporary period is negligible)

  • For current year there is no need to run the Santa Rosa and Santa Cruz bakeries


10 year capacity analysis
10 Year Capacity Analysis

  • 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 th year 2016 shipping analysis
10th Year (2016) Shipping Analysis

Cost Without San Jose Plant (per day) : $140,100.00

Cost with San Jose Plant (per day) : $135,700.00

Savings Differential with San Jose Plant (per day) : $4,400.00


Investment analysis
InvestmentAnalysis

  • 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


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


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


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


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


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


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


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


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




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