Bay Area Bakery Case study #1 Group Members Kevin Worrell, Asad Khan, Donavan Drewes, Harman Grewal, Sanju Dabi Discussion Questions Question 1 Agree/disagree with construction of new facility in San Jose Question 2 If we disagree - what actions are necessary Is the current distribution optimal Question 3 Formulate and solve mathematical programming model(s) Make all necessary assumptions 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 Question 2 If we disagree - what actions are necessary Is the current distribution optimal Question 3 Formulate and solve a mathematical programming model(s) Make all necessary assumptions 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 Question 2 If we disagree - what actions are necessary Is the current distribution optimal Question 3 Formulate and solve a mathematical programming model(s) Make all necessary assumptions 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 Question 2 If we disagree - what actions are necessary Is the current distribution optimal Question 3 Formulate and solve a mathematical programming model(s) Make all necessary assumptions 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 B1 B2 B3 B4 B5 B6 B7 Bakery of Origin Major Market Areas Santa Rosa Scrmnto Rchmd Brkly Okld San Fran San Jose Santa Cruz Slns Stckt Mdst 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 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 (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 (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 (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 + 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 LP OPTIMUM FOUND AT STEP: 15 OBJECTIVE FUNCTION VALUE: $99,770 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 Mathematical Model (Cont.) The LINDO equation for current year with San Jose is: 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 LP OPTIMUM FOUND AT STEP: 12 OBJECTIVE FUNCTION VALUE: $99,090 Mathematical Model (Cont.) The LINDO equation for year 1 without San Jose is: 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 LP OPTIMUM FOUND AT STEP: 16 OBJECTIVE FUNCTION VALUE: $103,457.4 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 Mathematical Model (Cont.) The LINDO equation for year 1 with San Jose is: 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 LP OPTIMUM FOUND AT STEP: 12 OBJECTIVE FUNCTION VALUE: $102,634.2 5 Year Analysis Grid Following 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 5 Santa Rosa QTY 300 306 312 318 324 330 Sacram ento QTY 500 510 520 530 540 550 Richm ond QTY 600 612 624 636 648 660 Berkeley QTY 400 408 416 424 432 440 Oakland QTY 1100 1122 1144 1166 1188 1210 San Francisco QTY 1300 1300 1300 1300 1300 1300 San Jose QTY 600 720 840 960 1080 1200 Santa Cruz QTY 100 102 104 106 108 110 Salinas QTY 100 102 104 106 108 110 Stockton QTY 400 408 416 424 432 440 Modesto QTY 100 102 104 106 108 110 Total QTY 5500 5692 5884 6076 6268 6460 w /o San Jose $99,770.00 $103,457.00 $111,085.00 $118,933.00 w ith Jose Jose $99,090.00 $102,634.00 $109,723.00 $117,007.00 $680.00 $823.00 $1,092.50 $1,362.00 $1,644.00 $1,926.00 $248,200.00 $300,395.00 $398,762.50 $497,130.00 $600,060.00 $702,990.00 $300,395.00 $699,157.50 $1,196,287.50 $1,796,347.50 $2,499,337.50 Savings (Day) Savings (Year) Savings (Cum ) 5 Year Analysis Grid Bakery Start Year Bakery Starts on Jan 1 2007 2008 1 Year Recovery 2007 END $300,395.00 2008 END $398,762.50 2009 END 2 Year Recovery 2008 END $699,157.50 2009 END $895,892.50 2010 END 3 Year Recovery 2009 END $1,196,287.50 2010 END $1,495,952.50 2011 END 4 Year Recovery 2010 END $1,796,347.50 2011 END $2,198,942.50 2009 $497,130.00 2010 END 2010 $600,060.00 2011 END $1,097,190.00 2011 END $1,303,050.00 $1,800,180.00 5 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. 2011 $702,990.00 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 To Major Market Areas From Bakery Plant Locations (Quantity in cwt) Santa Rosa Sacramento Santa Rosa Sacramento Richmond San Francisco 300 500 Richmond 600 Berkeley 400 Oakland 1100 San Francisco 1300 San Jose 200 Santa Cruz 400 100 Salinas 100 Stockton Modesto Stockton 400 100 Current Operation Cost (per day) : $103,270 Optimal Operation Cost (per day) : $99,770 Net savings: $3,500 Santa Cruz 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 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 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 10th Year (2016) Shipping Analysis To Major Market Areas Santa Rosa (D1) From Bakery Plant Locations (Quantity in cwt) (w/o San Jose / with San Jose) Santa Rosa (B1) Sacramento (B2) 360 / 320 Sacramento (D2) San Fran (B4) Stockton (B5) Santa Cruz (B6) San Jose (B7) 0 / 40 Berkeley (D4) 280 / 0 140 / 0 600 720 / 720 720 200 / 480 480 1180 / 1320 1320 San Fran (D6) 1300 / 1300 San Jose (D7) TOTALS 360 600 / 600 Richmond (D3) Oakland (D5) Richmond (B3) 600 / 140 480 / 0 0 / 960 1800 Santa Cruz (D8) 120 / 0 0 / 120 120 Salinas (D9) 120 / 0 0 /120 120 Stockton (D10) 0 / 280 Modesto (D11) 120 / 120 TOTALS 500 / 320 740 / 1000 700 / 700 1300 20 / 0 480 / 200 480 120 2700 / 2700 2000 / 2000 Cost Without San Jose Plant (per day) Cost with San Jose Plant (per day) Savings Differential with San Jose Plant (per day) 500 / 200 720 / 0 : $140,100.00 : $135,700.00 : $4,400.00 0 / 1200 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 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 Any Questions?? Any Questions??