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Answers 1.- The annual inventory and distribution cost of the cur 2.- We would recommend setting up an NDC because doing so However, closing all regional DCs and handling all pr OPTION 1: Currentdistribution system (stockeach item ateveryDC). ANNUALCOST(Inventory+distribution)ofcurrentsystem w ith all H/M /LproductsatDC#. DC 1 DC2 DC 3 DC 4 DC 5 TOTAL High 123,154.52 $ 84,550.47 $ 66,633.24 $ 44,448.24 $ 23,099.34 $ 341, $ M edium 33,178.80 $ 60,969.50 $ 73,638.49 $ 75,906.40 $ 64,460.92 $ 308, $ Low 51,085.76 $ 44,423.59 $ 66,116.95 $ 117,770.79 $ 134,481.18 $ 413, $ TOTALANNUALCOSTOFCURRENTSYSTEM 1,063, $ TOTALANNUALCOSTOFOPTION 2 ρ=0 ρ=0.5 ρ=1 forpossible ρ values. 858,783.67 $ 949,123.92 $ 1,019,790.02 $ TOTALANNUALCOSTOFCURRENTSYSTEM 1,063,918.19 $ OPTION 2: Build aNational Distribution Center(NDC)and close 5regional DCs. 1892.1 Productshandled atNDC/day. Annual savings 690,616.50 Productshandled atNDC/year. 205,134.53 $ USD in best-case scenario. | 114,794.27 $ USD in m iddle-case scenario. V 44,128.17 $ USD in w orst-case scenario. 1,300,000.00 $ CostofNDC construction Tim e to recoverinvestm ent. 250,000.00 $ M oneyrecovered from DCs. 5.118592234 Yearsin best-case scenario. 1,050,000.00 $ Initial investm entrequired 9.14679808 Yearsin m iddle-case scenario.
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Page 1: ALKO Case Study

Answers1.- The annual inventory and distribution cost of the current distribution system (Option 1) is: $1,063,918.19 USD.

2.- We would recommend setting up an NDC because doing so can bring significant savings to the company in the long term.However, closing all regional DCs and handling all products at an NDC (Option 2) is not the best option.

OPTION 1: Current distribution system (stock each item at every DC).ANNUAL COST (Inventory + distribution) of current system with all H/M/L products at DC#.

DC 1 DC2 DC 3 DC 4 DC 5 TOTALHigh 123,154.52$ 84,550.47$ 66,633.24$ 44,448.24$ 23,099.34$ 341,885.80$

Medium 33,178.80$ 60,969.50$ 73,638.49$ 75,906.40$ 64,460.92$ 308,154.13$

Low 51,085.76$ 44,423.59$ 66,116.95$ 117,770.79$ 134,481.18$ 413,878.26$

TOTAL ANNUAL COST OF CURRENT SYSTEM1,063,918.19$

TOTAL ANNUAL COST OF OPTION 2 ρ=0 ρ=0.5 ρ=1for possible ρ values. 858,783.67$ 949,123.92$ 1,019,790.02$ TOTAL ANNUAL COST OF CURRENT SYSTEM

1,063,918.19$

OPTION 2: Build a National Distribution Center (NDC) and close 5 regional DCs.

1892.1 Products handled at NDC/day. Annual savings690,616.50 Products handled at NDC/year. 205,134.53$ USD in best-case scenario.

| 114,794.27$ USD in middle-case scenario.V 44,128.17$ USD in worst-case scenario.

1,300,000.00$ Cost of NDC construction Time to recover investment.250,000.00$ Money recovered from DCs. 5.118592234 Years in best-case scenario.

1,050,000.00$ Initial investment required 9.14679808 Years in middle-case scenario.23.79432481 Years in worst-case scenario.

best-case scenario: ρ=0 middle-case scenario: ρ=0.5 worst-case scenario: ρ=1

Page 2: ALKO Case Study

3.- If an NDC is built while keeping all regional DCs open, there are 2 more options:

Our recommendation would be option 3: To handle High demand products at regional DCs and build an NDC for Middle and Low demand products.Becasue:Option 4 requires the lowest initial investment and its recovery time is also the lowest. However, in the long term after investment recovery, option 3 implies higher annual savings.In both best and worst-case scenarios, annual savings are higher for option 3 than for option 4.

In the best-case scenario, annual savings are slightly higher for option 2 than for option 3. However, in middle and worst-case scenarios, annual savings are higher for option 3.The required initial investment and its recovery time are much higher for option 2 than for option 3.

TOTAL ANNUAL COST OF OPTION 2 ρ=0 ρ=0.5 ρ=1for possible ρ values. 858,783.67$ 949,123.92$ 1,019,790.02$ TOTAL ANNUAL COST OF CURRENT SYSTEM

1,063,918.19$

OPTION 2: Build a National Distribution Center (NDC) and close 5 regional DCs.

1892.1 Products handled at NDC/day. Annual savings690,616.50 Products handled at NDC/year. 205,134.53$ USD in best-case scenario.

| 114,794.27$ USD in middle-case scenario.V 44,128.17$ USD in worst-case scenario.

1,300,000.00$ Cost of NDC construction Time to recover investment.250,000.00$ Money recovered from DCs. 5.118592234 Years in best-case scenario.

1,050,000.00$ Initial investment required 9.14679808 Years in middle-case scenario.23.79432481 Years in worst-case scenario.

best-case scenario: ρ=0 middle-case scenario: ρ=0.5 worst-case scenario: ρ=1

TOTAL ANNUAL COST OF OPTION 3 ρ=0 ρ=0.5 ρ=1for possible ρ values. 868,656.00$ 944,698.30$ 1,004,278.26$ TOTAL ANNUAL COST OF CURRENT SYSTEM

1,063,918.19$

OPTION 3: Handle High products at regional DCs and build NDC for Middle and Low products.

982.9 Products handled at NDC/day. Annual savings358,758.50 Products handled at NDC/year. 195,262.20$ USD in best-case scenario.

| 119,219.89$ USD in middle-case scenario.V 59,639.93$ USD in worst-case scenario.

800,000.00$ Cost of NDC construction Time to recover investment.-$ Money recovered from DCs. 4.097055194 Years in best-case scenario.

800,000.00$ Initial investment required 6.710289682 Years in middle-case scenario.13.41383215 Years in worst-case scenario.

best-case scenario: ρ=0 middle-case scenario: ρ=0.5 worst-case scenario: ρ=1

Page 3: ALKO Case Study

The annual inventory and distribution cost of the current distribution system (Option 1) is: $1,063,918.19 USD.

We would recommend setting up an NDC because doing so can bring significant savings to the company in the long term.However, closing all regional DCs and handling all products at an NDC (Option 2) is not the best option.

OPTION 1: Current distribution system (stock each item at every DC).ANNUAL COST (Inventory + distribution) of current system with all H/M/L products at DC#.

DC 1 DC2 DC 3 DC 4 DC 5 TOTALHigh 123,154.52$ 84,550.47$ 66,633.24$ 44,448.24$ 23,099.34$ 341,885.80$

Medium 33,178.80$ 60,969.50$ 73,638.49$ 75,906.40$ 64,460.92$ 308,154.13$

Low 51,085.76$ 44,423.59$ 66,116.95$ 117,770.79$ 134,481.18$ 413,878.26$

TOTAL ANNUAL COST OF CURRENT SYSTEM1,063,918.19$

TOTAL ANNUAL COST OF OPTION 2 ρ=0 ρ=0.5 ρ=1for possible ρ values. 858,783.67$ 949,123.92$ 1,019,790.02$ TOTAL ANNUAL COST OF CURRENT SYSTEM

1,063,918.19$

OPTION 2: Build a National Distribution Center (NDC) and close 5 regional DCs.

1892.1 Products handled at NDC/day. Annual savings690,616.50 Products handled at NDC/year. 205,134.53$ USD in best-case scenario.

| 114,794.27$ USD in middle-case scenario.V 44,128.17$ USD in worst-case scenario.

1,300,000.00$ Cost of NDC construction Time to recover investment.250,000.00$ Money recovered from DCs. 5.118592234 Years in best-case scenario.

1,050,000.00$ Initial investment required 9.14679808 Years in middle-case scenario.23.79432481 Years in worst-case scenario.

best-case scenario: ρ=0 middle-case scenario: ρ=0.5 worst-case scenario: ρ=1

Page 4: ALKO Case Study

Our recommendation would be option 3: To handle High demand products at regional DCs and build an NDC for Middle and Low demand products.

Option 4 requires the lowest initial investment and its recovery time is also the lowest. However, in the long term after investment recovery, option 3 implies higher annual savings.In both best and worst-case scenarios, annual savings are higher for option 3 than for option 4.

In the best-case scenario, annual savings are slightly higher for option 2 than for option 3. However, in middle and worst-case scenarios, annual savings are higher for option 3.The required initial investment and its recovery time are much higher for option 2 than for option 3.

TOTAL ANNUAL COST OF OPTION 2 ρ=0 ρ=0.5 ρ=1for possible ρ values. 858,783.67$ 949,123.92$ 1,019,790.02$ TOTAL ANNUAL COST OF CURRENT SYSTEM

1,063,918.19$

OPTION 2: Build a National Distribution Center (NDC) and close 5 regional DCs.

1892.1 Products handled at NDC/day. Annual savings690,616.50 Products handled at NDC/year. 205,134.53$ USD in best-case scenario.

| 114,794.27$ USD in middle-case scenario.V 44,128.17$ USD in worst-case scenario.

1,300,000.00$ Cost of NDC construction Time to recover investment.250,000.00$ Money recovered from DCs. 5.118592234 Years in best-case scenario.

1,050,000.00$ Initial investment required 9.14679808 Years in middle-case scenario.23.79432481 Years in worst-case scenario.

best-case scenario: ρ=0 middle-case scenario: ρ=0.5 worst-case scenario: ρ=1

TOTAL ANNUAL COST OF OPTION 3 ρ=0 ρ=0.5 ρ=1for possible ρ values. 868,656.00$ 944,698.30$ 1,004,278.26$ TOTAL ANNUAL COST OF CURRENT SYSTEM

1,063,918.19$

OPTION 3: Handle High products at regional DCs and build NDC for Middle and Low products.

982.9 Products handled at NDC/day. Annual savings358,758.50 Products handled at NDC/year. 195,262.20$ USD in best-case scenario.

| 119,219.89$ USD in middle-case scenario.V 59,639.93$ USD in worst-case scenario.

800,000.00$ Cost of NDC construction Time to recover investment.-$ Money recovered from DCs. 4.097055194 Years in best-case scenario.

800,000.00$ Initial investment required 6.710289682 Years in middle-case scenario.13.41383215 Years in worst-case scenario.

best-case scenario: ρ=0 middle-case scenario: ρ=0.5 worst-case scenario: ρ=1

TOTAL ANNUAL COST OF OPTION 4 ρ=0 ρ=0.5 ρ=1for possible ρ values. 932,513.34$ 981,066.00$ 1,019,224.77$ TOTAL ANNUAL COST OF CURRENT SYSTEM

1,063,918.19$

OPTION 4: Handle High and Middle products at regional DCs and build NDC for Low products.

454.3 Products handled at NDC/day. Annual savings165,819.50 Products handled at NDC/year. 131,404.86$ USD in best-case scenario.

| 82,852.19$ USD in middle-case scenario.V 44,693.42$ USD in worst-case scenario.

400,000.00$ Cost of NDC construction Time to recover investment.-$ Money recovered from DCs. 3.044027533 Years in best-case scenario.

400,000.00$ Initial investment required 4.827874885 Years in middle-case scenario.8.94986342 Years in worst-case scenario.

best-case scenario: ρ=0 middle-case scenario: ρ=0.5 worst-case scenario: ρ=1

Page 5: ALKO Case Study

TOTAL ANNUAL COST OF OPTION 4 ρ=0 ρ=0.5 ρ=1for possible ρ values. 932,513.34$ 981,066.00$ 1,019,224.77$ TOTAL ANNUAL COST OF CURRENT SYSTEM

1,063,918.19$

OPTION 4: Handle High and Middle products at regional DCs and build NDC for Low products.

454.3 Products handled at NDC/day. Annual savings165,819.50 Products handled at NDC/year. 131,404.86$ USD in best-case scenario.

| 82,852.19$ USD in middle-case scenario.V 44,693.42$ USD in worst-case scenario.

400,000.00$ Cost of NDC construction Time to recover investment.-$ Money recovered from DCs. 3.044027533 Years in best-case scenario.

400,000.00$ Initial investment required 4.827874885 Years in middle-case scenario.8.94986342 Years in worst-case scenario.

best-case scenario: ρ=0 middle-case scenario: ρ=0.5 worst-case scenario: ρ=1

Page 6: ALKO Case Study

ALKO case studyOPTION 1: Current distribution system (stock each item at every DC).

Daily Demand for 1 product100 Products DC 1 DC 2 DC 3

Part 1 10 High Mean 35.48 22.61 17.66S. D. 6.98 6.48 5.26

Part 3 20 Medium Mean 2.48 4.15 6.15S. D. 3.16 6.2 6.39

Part 7 70 Low Mean 0.48 0.73 0.8S. D. 1.98 1.42 2.39

OPTION 1: Current distribution system (stock each item at every DC).ANNUAL COST (Inventory + distribution) of current system with all H/M/L products at DC#.

DC 1 DC2 DC 3 DC 4 DC 5High $ 123,154.52 $ 84,550.47 $ 66,633.24 $ 44,448.24 $ 23,099.34

Medium $ 33,178.80 $ 60,969.50 $ 73,638.49 $ 75,906.40 $ 64,460.92

Low $ 51,085.76 $ 44,423.59 $ 66,116.95 $ 117,770.79 $ 134,481.18

TOTAL ANNUAL COST OF CURRENT SYSTEM

TC = (Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to customer)(Avg Inv*Hday*365)+((Total units transported in a year)*Hday*(#days in transit))+((TL Trans. Cost)*D*365)+((LTL Trans. Cost)*D*365)

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Periodic review policy = OULDC 4 DC 5 Total Transport $/u Current NDC

11.81 3.36 Plant to DC TL 0.09 0.053.48 4.49 DC to cust. LTL 0.1 0.246.16 7.496.76 3.56 L+R R = T L1.94 2.54 11 6 5 days ---->3.76 3.98

Holding $/(u*day) 0.15 (transit or storage)

CSL 95%z = 1.6448536

TOTAL $ 341,885.80

$ 308,154.13

$ 413,878.26

$ 1,063,918.19

(Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to customer)(Avg Inv*Hday*365)+((Total units transported in a year)*Hday*(#days in transit))+((TL Trans. Cost)*D*365)+((LTL Trans. Cost)*D*365)

Page 8: ALKO Case Study

1.- Total annual cost (inventory + distribution) of current systemANNUAL COST (Inventory + distribution) of current system with 1 high product at DC1TC = (Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to customer)

(Avg Inv*Hday*365)+((Total units transported in a year)*Hday*(#days in transit))+((TL Trans. Cost)*D*365)+((LTL Trans. Cost)*D*365)

Avg Inv = Q/2 + SS Total units transported in a year = (lot size)*(# of orders in a year) = Q*(365/R)

4 days in production OUL = 428.358431 days in transit σ(l+r) = 23.150041

μ(l+r) = 390.28(transit or storage) SS = 38.078429 212.88

in OULThis estimated Q can be used in OUL when its value is not provided.

TC = (Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to Customer)

TC = 12315.452ANNUAL COST (Inventory + distribution) of current system with 1 high product at DC1* 10 high products = 123154.52

ANNUAL COST (Inventory + distribution) of current system with 10 high products at DC1

Q = μ*R

Page 9: ALKO Case Study

ANNUAL COST (Inventory + distribution) of current system with 1 high product at DC1(Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to customer)(Avg Inv*Hday*365)+((Total units transported in a year)*Hday*(#days in transit))+((TL Trans. Cost)*D*365)+((LTL Trans. Cost)*D*365)

Total units transported in a year = (lot size)*(# of orders in a year) = Q*(365/R)

This estimated Q can be used in OUL when its value is not provided.TC = (Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to Customer)

ANNUAL COST (Inventory + distribution) of current system with 1 high product at DC1

ANNUAL COST (Inventory + distribution) of current system with 10 high products at DC1

Page 10: ALKO Case Study

(Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to customer)

TC = (Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to Customer)

Page 11: ALKO Case Study

ALKO case studyOPTION 2: Build a National Distribution Center (NDC) and close 5 regional DCs.

100 Products Daily Demand for 1 productDC 1 DC 2 DC 3

Part 1 10 High Mean 35.48 22.61 17.66S. D. 6.98 6.48 5.26

Part 3 20 Medium Mean 2.48 4.15 6.15S. D. 3.16 6.2 6.39

Part 7 70 Low Mean 0.48 0.73 0.8S. D. 1.98 1.42 2.39

NDC Aggregation Daily Demand for 1 product100 Products Mean

10 High 90.92 12.273911357 17.06094077124720 Medium 26.43 12.150263372 16.75210136072570 Low 6.49 6.4518911956 8.7741324357454

ρ=0 ρ=0.5 ρ=1High $ 332,013.47 $ 346,311.42 $ 357,397.56 Medium $ 244,296.79 $ 271,786.43 $ 293,207.62 Low $ 282,473.41 $ 331,026.07 $ 369,184.84

TOTAL ANNUAL COST OF OPTION 2 ρ=0 ρ=0.5 ρ=1 $ 858,783.67 $ 949,123.92 $ 1,019,790.02

TOTAL ANNUAL COST OF CURRENT SYSTEM $ 1,063,918.19

OPTION 2: Build a National Distribution Center (NDC) and close 5 regional DCs.

1892.1 Products handled at NDC/day. Annual savings 690,616.50 Products handled at NDC/year. $ 205,134.53 USD in best-case scenario.

| $ 114,794.27 USD in middle-case scenario.V $ 44,128.17 USD in worst-case scenario.

$ 1,300,000.00 Cost of NDC construction Time to recover investment. $ 250,000.00 Money recovered from DCs. 5.118592234198 Years in best-case scenario. $ 1,050,000.00 Initial investment required 9.146798079766 Years in middle-case scenario.

23.79432480744 Years in worst-case scenario.

best-case scenario: ρ=0 middle-case scenario: ρ=0.5 worst-case scenario: ρ=1

S. D. ρ=0 S. D. ρ=0.5

ANNUAL COST (Inventory + distribution) of aggregated system with all H/M/L products at NDC for possible ρ values.

for possible ρ values.

Page 12: ALKO Case Study

handled per year.

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High DC 1 DC 2 DC 3 DC 4 DC 5DC 1 45.2304 36.7148 24.2904 31.3402DC 2 34.0848 22.5504 29.0952DC 3 18.3048 23.6174

DC 4 DC 5 DC 4 15.625211.81 3.36 DC 5

3.48 4.496.16 7.49 Medium DC 1 DC 2 DC 3 DC 4 DC 56.76 3.56 DC 1 19.592 20.1924 21.3616 11.24961.94 2.54 DC 2 39.618 41.912 22.0723.76 3.98 DC 3 43.1964 22.7484

DC 4 24.0656DC 5

20.772638 Low DC 1 DC 2 DC 3 DC 4 DC 520.338065 DC 1 2.8116 4.7322 7.4448 7.880410.599241 DC 2 3.3938 5.3392 5.6516

DC 3 8.9864 9.5122DC 4 14.9648DC 5

Periodic review policy = OULTransport $/u Current NDCPlant to DC TL 0.09 0.05DC to cust. LTL 0.1 0.24

L+R R = T L 411 6 5 days ----> 1

Holding $/(u*day) 0.15 (transit or storage)z = 1.6448536 CSL 95%

TC = (Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to customer)(Avg Inv*Hday*365)+((Total units transported in a year)*Hday*(#days in transit))+((TL Trans. Cost)*D*365)+((LTL Trans. Cost)*D*365)

Avg Inv = Q/2 + SS Total units transported in a year = (lot size)*(# of orders in a year) = Q*(365/R)

in OUL

S. D. ρ=1

ANNUAL COST (Inventory + distribution) of aggregated system with all H/M/L products at NDC for possible ρ values.

Q = μ*R

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High σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠jσ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j

ρ = 0 σ©^2 = 150.6489 150.6489 0ρ = 0.5 σ©^2 = 291.0757 150.6489 140.4268ρ = 1 σ©^2 = 431.5025 150.6489 280.8536

Medium σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠jσ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j

ρ = 0 σ©^2 = 147.6289 147.6289 0ρ = 0.5 σ©^2 = 280.6329 147.6289 133.004ρ = 1 σ©^2 = 413.6369 147.6289 266.008

Low σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠jσ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j

ρ = 0 σ©^2 = 41.6269 41.6269 0ρ = 0.5 σ©^2 = 76.9854 41.6269 35.3585ρ = 1 σ©^2 = 112.3439 41.6269 70.717

days in productiondays in transit

(transit or storage)

(Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to customer)(Avg Inv*Hday*365)+((Total units transported in a year)*Hday*(#days in transit))+((TL Trans. Cost)*D*365)+((LTL Trans. Cost)*D*365)

Total units transported in a year = (lot size)*(# of orders in a year) = Q*(365/R)

Page 16: ALKO Case Study

because ρ is the same for all combinations of regions in this case.

because ρ is the same for all combinations of regions in this case.

because ρ is the same for all combinations of regions in this case.

(Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to customer)

Page 17: ALKO Case Study

ALKO case studyOPTION 3: Use current distribution system for High products and build NDC for Middle and Low products.

100 Products Daily Demand for 1 productDC 1 DC 2 DC 3

Part 1 10 High Mean 35.48 22.61 17.66S. D. 6.98 6.48 5.26

Part 3 20 Medium Mean 2.48 4.15 6.15S. D. 3.16 6.2 6.39

Part 7 70 Low Mean 0.48 0.73 0.8S. D. 1.98 1.42 2.39

NDC Aggregation Daily Demand for 1 product100 Products Mean

10 High 90.92 12.273911357 17.06094077124720 Medium 26.43 12.1502633716 16.75210136072570 Low 6.49 6.45189119561 8.7741324357454

High $ 341,885.80 ρ=0 ρ=0.5 ρ=1

Medium $ 244,296.79 $ 271,786.43 $ 293,207.62 Low $ 282,473.41 $ 331,026.07 $ 369,184.84

TOTAL ANNUAL COST OF OPTION 3 ρ=0 ρ=0.5 ρ=1 $ 868,656.00 $ 944,698.30 $ 1,004,278.26

TOTAL ANNUAL COST OF CURRENT SYSTEM $ 1,063,918.19

OPTION 3: Handle High products at regional DCs and build NDC for Middle and Low products.

982.9 Products handled at NDC/day. Annual savings 358,758.50 Products handled at NDC/year. $ 195,262.20 USD in best-case scenario.

| $ 119,219.89 USD in middle-case scenario.V $ 59,639.93 USD in worst-case scenario.

$ 800,000.00 Cost of NDC construction Time to recover investment. $ - Money recovered from DCs. 4.097055194133 Years in best-case scenario. $ 800,000.00 Initial investment required 6.710289682254 Years in middle-case scenario.

13.41383215461 Years in worst-case scenario.

best-case scenario: ρ=0 middle-case scenario: ρ=0.5 worst-case scenario: ρ=1

S. D. ρ=0 S. D. ρ=0.5

ANNUAL COST (Inventory + distribution) of option 3 with with H products at 5 DCs and M/L products at NDC for possible ρ values.

for possible ρ values.

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handled per year.

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OPTION 3: Use current distribution system for High products and build NDC for Middle and Low products. High DC 1 DC 2 DC 3 DC 4 DC 5DC 1 45.2304 36.7148 24.2904 31.3402DC 2 34.0848 22.5504 29.0952DC 3 18.3048 23.6174

DC 4 DC 5 DC 4 15.625211.81 3.36 DC 5

3.48 4.496.16 7.49 Medium DC 1 DC 2 DC 3 DC 4 DC 56.76 3.56 DC 1 19.592 20.1924 21.3616 11.24961.94 2.54 DC 2 39.618 41.912 22.0723.76 3.98 DC 3 43.1964 22.7484

DC 4 24.0656DC 5

20.772638 Low DC 1 DC 2 DC 3 DC 4 DC 520.338065 DC 1 2.8116 4.7322 7.4448 7.880410.599241 DC 2 3.3938 5.3392 5.6516

DC 3 8.9864 9.5122DC 4 14.9648DC 5

Periodic review policy = OULTransport $/u Current NDCPlant to DC TL 0.09 0.05DC to cust. LTL 0.1 0.24

L+R R = T L 411 6 5 days ----> 1

Holding $/(u*day) 0.15 (transit or storage)z = 1.6448536 CSL 95%

TC = (Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to customer)(Avg Inv*Hday*365)+((Total units transported in a year)*Hday*(#days in transit))+((TL Trans. Cost)*D*365)+((LTL Trans. Cost)*D*365)

Avg Inv = Q/2 + SS Total units transported in a year = (lot size)*(# of orders in a year) = Q*(365/R)

in OUL

S. D. ρ=1

ANNUAL COST (Inventory + distribution) of option 3 with with H products at 5 DCs and M/L products at NDC for possible ρ values.

Q = μ*R

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High σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠jσ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j

ρ = 0 σ©^2 = 150.6489 150.6489 0ρ = 0.5 σ©^2 = 291.0757 150.6489 140.4268ρ = 1 σ©^2 = 431.5025 150.6489 280.8536

Medium σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠jσ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j

ρ = 0 σ©^2 = 147.6289 147.6289 0ρ = 0.5 σ©^2 = 280.6329 147.6289 133.004ρ = 1 σ©^2 = 413.6369 147.6289 266.008

Low σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠jσ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j

ρ = 0 σ©^2 = 41.6269 41.6269 0ρ = 0.5 σ©^2 = 76.9854 41.6269 35.3585ρ = 1 σ©^2 = 112.3439 41.6269 70.717

days in productiondays in transit

(transit or storage)

(Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to customer)(Avg Inv*Hday*365)+((Total units transported in a year)*Hday*(#days in transit))+((TL Trans. Cost)*D*365)+((LTL Trans. Cost)*D*365)

Total units transported in a year = (lot size)*(# of orders in a year) = Q*(365/R)

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because ρ is the same for all combinations of regions in this case.

because ρ is the same for all combinations of regions in this case.

because ρ is the same for all combinations of regions in this case.

(Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to customer)

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ALKO case studyOPTION 4: Use current distribution system for High and Middle products and build NDC for Low products.

100 Products Daily Demand for 1 productDC 1 DC 2 DC 3

Part 1 10 High Mean 35.48 22.61 17.66S. D. 6.98 6.48 5.26

Part 3 20 Medium Mean 2.48 4.15 6.15S. D. 3.16 6.2 6.39

Part 7 70 Low Mean 0.48 0.73 0.8S. D. 1.98 1.42 2.39

NDC Aggregation Daily Demand for 1 product100 Products Mean

10 High 90.92 12.273911357 17.06094077124720 Medium 26.43 12.1502633716 16.75210136072570 Low 6.49 6.45189119561 8.7741324357454

High $ 341,885.80 Medium $ 308,154.13

ρ=0 ρ=0.5 ρ=1Low $ 282,473.41 $ 331,026.07 $ 369,184.84

TOTAL ANNUAL COST OF OPTION 4 ρ=0 ρ=0.5 ρ=1 $ 932,513.34 $ 981,066.00 $ 1,019,224.77

TOTAL ANNUAL COST OF CURRENT SYSTEM $ 1,063,918.19

OPTION 4: Handle High and Middle products at regional DCs and build NDC for Low products.

454.3 Products handled at NDC/day. Annual savings 165,819.50 Products handled at NDC/year. $ 131,404.86 USD in best-case scenario.

| $ 82,852.19 USD in middle-case scenario.V $ 44,693.42 USD in worst-case scenario.

$ 400,000.00 Cost of NDC construction Time to recover investment. $ - Money recovered from DCs. 3.044027533378 Years in best-case scenario. $ 400,000.00 Initial investment required 4.827874885392 Years in middle-case scenario.

8.949863419925 Years in worst-case scenario.

best-case scenario: ρ=0 middle-case scenario: ρ=0.5 worst-case scenario: ρ=1

S. D. ρ=0 S. D. ρ=0.5

ANNUAL COST (Inventory + distribution) of option 4 with H/M products at 5 DCs and L products at NDC for possible ρ values.

for possible ρ values.

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handled per year.

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OPTION 4: Use current distribution system for High and Middle products and build NDC for Low products. High DC 1 DC 2 DC 3 DC 4 DC 5DC 1 45.2304 36.7148 24.2904 31.3402DC 2 34.0848 22.5504 29.0952DC 3 18.3048 23.6174

DC 4 DC 5 DC 4 15.625211.81 3.36 DC 5

3.48 4.496.16 7.49 Medium DC 1 DC 2 DC 3 DC 4 DC 56.76 3.56 DC 1 19.592 20.1924 21.3616 11.24961.94 2.54 DC 2 39.618 41.912 22.0723.76 3.98 DC 3 43.1964 22.7484

DC 4 24.0656DC 5

20.772638 Low DC 1 DC 2 DC 3 DC 4 DC 520.338065 DC 1 2.8116 4.7322 7.4448 7.880410.599241 DC 2 3.3938 5.3392 5.6516

DC 3 8.9864 9.5122DC 4 14.9648DC 5

Periodic review policy = OULTransport $/u Current NDCPlant to DC TL 0.09 0.05DC to cust. LTL 0.1 0.24

L+R R = T L 411 6 5 days ----> 1

Holding $/(u*day) 0.15 (transit or storage)z = 1.6448536 CSL 95%

TC = (Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to customer)(Avg Inv*Hday*365)+((Total units transported in a year)*Hday*(#days in transit))+((TL Trans. Cost)*D*365)+((LTL Trans. Cost)*D*365)

Avg Inv = Q/2 + SS Total units transported in a year = (lot size)*(# of orders in a year) = Q*(365/R)

in OUL

S. D. ρ=1

ANNUAL COST (Inventory + distribution) of option 4 with H/M products at 5 DCs and L products at NDC for possible ρ values.

Q = μ*R

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High σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠jσ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j

ρ = 0 σ©^2 = 150.6489 150.6489 0ρ = 0.5 σ©^2 = 291.0757 150.6489 140.4268ρ = 1 σ©^2 = 431.5025 150.6489 280.8536

Medium σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠jσ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j

ρ = 0 σ©^2 = 147.6289 147.6289 0ρ = 0.5 σ©^2 = 280.6329 147.6289 133.004ρ = 1 σ©^2 = 413.6369 147.6289 266.008

Low σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠jσ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j

ρ = 0 σ©^2 = 41.6269 41.6269 0ρ = 0.5 σ©^2 = 76.9854 41.6269 35.3585ρ = 1 σ©^2 = 112.3439 41.6269 70.717

days in productiondays in transit

(transit or storage)

(Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to customer)(Avg Inv*Hday*365)+((Total units transported in a year)*Hday*(#days in transit))+((TL Trans. Cost)*D*365)+((LTL Trans. Cost)*D*365)

Total units transported in a year = (lot size)*(# of orders in a year) = Q*(365/R)

Page 28: ALKO Case Study

because ρ is the same for all combinations of regions in this case.

because ρ is the same for all combinations of regions in this case.

because ρ is the same for all combinations of regions in this case.

(Holding cost of inventory in storage)+(Holding cost of inventory in transit)+(Transportation cost from plant to DC)+(Transportation cost from DC to customer)