Answers
1.- 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 TOTAL
High $ 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 SYSTEM
1,063,918.19 $
TOTAL ANNUAL COST OF OPTION 2 ρ=0 ρ=0.5 ρ=1
for 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 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. 5.118592234 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
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=1
for 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 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. 5.118592234 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=1
for 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 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. 4.097055194 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
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 TOTAL
High $ 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 SYSTEM
1,063,918.19 $
TOTAL ANNUAL COST OF OPTION 2 ρ=0 ρ=0.5 ρ=1
for 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 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. 5.118592234 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
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=1
for 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 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. 5.118592234 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=1
for 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 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. 4.097055194 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=1
for 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 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. 3.044027533 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
TOTAL ANNUAL COST OF OPTION 4 ρ=0 ρ=0.5 ρ=1
for 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 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. 3.044027533 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
ALKO case study
OPTION 1: Current distribution system (stock each item at every DC). Daily Demand for 1 product
100 Products DC 1 DC 2 DC 3
Part 1 10 High Mean 35.48 22.61 17.66
S. D. 6.98 6.48 5.26
Part 3 20 Medium Mean 2.48 4.15 6.15
S. D. 3.16 6.2 6.39
Part 7 70 Low Mean 0.48 0.73 0.8
S. 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 5
High $ 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)
Periodic review policy = OUL
DC 4 DC 5 Total Transport $/u Current NDC
11.81 3.36 Plant to DC TL 0.09 0.05 3.48 4.49 DC to cust. LTL 0.1 0.24 6.16 7.49 6.76 3.56 L+R R = T L 1.94 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)
1.- Total annual cost (inventory + distribution) of current system
ANNUAL COST (Inventory + distribution) of current system with 1 high product at DC1
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) 4 days in production OUL = 428.3584
1 days in transit σ(l+r) = 23.15004
μ(l+r) = 390.28
(transit or storage) SS = 38.07843 Q = μ*R 212.88
in OUL
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) TC = 12315.45
ANNUAL COST (Inventory + distribution) of current system with 1 high product at DC1 * 10 high products = 123154.5
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
ALKO case study
OPTION 2: Build a National Distribution Center (NDC) and close 5 regional DCs.
100 Products Daily Demand for 1 product
DC 1 DC 2 DC 3
Part 1 10 High Mean 35.48 22.61 17.66
S. D. 6.98 6.48 5.26
Part 3 20 Medium Mean 2.48 4.15 6.15
S. D. 3.16 6.2 6.39
Part 7 70 Low Mean 0.48 0.73 0.8
S. D. 1.98 1.42 2.39
NDC Aggregation Daily Demand for 1 product
100 Products Mean S. D. ρ=0 S. D. ρ=0.5
10 High 90.92 12.27391136 17.06094077
20 Medium 26.43 12.15026337 16.75210136
70 Low 6.49 6.451891196 8.774132436
ANNUAL COST (Inventory + distribution) of aggregated system with all H/M/L products at NDC for possible ρ values.
ρ=0 ρ=0.5 ρ=1
High $ 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
for 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 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. 5.118592234 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
High DC 1 DC 2 DC 3 DC 4 DC 5 DC 1 45.2304 36.7148 24.2904 31.3402 DC 2 34.0848 22.5504 29.0952 DC 3 18.3048 23.6174 DC 4 DC 5 DC 4 15.6252 11.81 3.36 DC 5 3.48 4.49 6.16 7.49 Medium DC 1 DC 2 DC 3 DC 4 DC 5 6.76 3.56 DC 1 19.592 20.1924 21.3616 11.2496 1.94 2.54 DC 2 39.618 41.912 22.072 3.76 3.98 DC 3 43.1964 22.7484 DC 4 24.0656 DC 5 S. D. ρ=1 20.77264 Low DC 1 DC 2 DC 3 DC 4 DC 5 20.33807 DC 1 2.8116 4.7322 7.4448 7.8804 10.59924 DC 2 3.3938 5.3392 5.6516 DC 3 8.9864 9.5122
ANNUAL COST (Inventory + distribution) of aggregated system with all H/M/L products at NDC for possible ρ values. DC 4 14.9648 DC 5
Periodic review policy = OUL
Transport $/u Current NDC
Plant to DC TL 0.09 0.05
DC to cust. LTL 0.1 0.24
L+R R = T L 4
11 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) Q = μ*R
High σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠j σ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j
ρ = 0 σ©^2 = 150.6489 150.6489 0
ρ = 0.5 σ©^2 = 291.0757 150.6489 140.4268 ρ = 1 σ©^2 = 431.5025 150.6489 280.8536
Medium σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠j σ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j
ρ = 0 σ©^2 = 147.6289 147.6289 0
ρ = 0.5 σ©^2 = 280.6329 147.6289 133.004 ρ = 1 σ©^2 = 413.6369 147.6289 266.008
Low σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠j
σ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j ρ = 0 σ©^2 = 41.6269 41.6269 0 ρ = 0.5 σ©^2 = 76.9854 41.6269 35.3585 ρ = 1 σ©^2 = 112.3439 41.6269 70.717 days in production days 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)
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.
ALKO case study
OPTION 3: Use current distribution system for High products and build NDC for Middle and Low products.
100 Products Daily Demand for 1 product
DC 1 DC 2 DC 3
Part 1 10 High Mean 35.48 22.61 17.66
S. D. 6.98 6.48 5.26
Part 3 20 Medium Mean 2.48 4.15 6.15
S. D. 3.16 6.2 6.39
Part 7 70 Low Mean 0.48 0.73 0.8
S. D. 1.98 1.42 2.39
NDC Aggregation Daily Demand for 1 product
100 Products Mean S. D. ρ=0 S. D. ρ=0.5
10 High 90.92 12.27391136 17.06094077
20 Medium 26.43 12.15026337 16.75210136
70 Low 6.49 6.451891196 8.774132436
ANNUAL COST (Inventory + distribution) of option 3 with with H products at 5 DCs and M/L products at NDC for possible ρ values. 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
for 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 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. 4.097055194 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
High DC 1 DC 2 DC 3 DC 4 DC 5 DC 1 45.2304 36.7148 24.2904 31.3402 DC 2 34.0848 22.5504 29.0952 DC 3 18.3048 23.6174 DC 4 DC 5 DC 4 15.6252 11.81 3.36 DC 5 3.48 4.49 6.16 7.49 Medium DC 1 DC 2 DC 3 DC 4 DC 5 6.76 3.56 DC 1 19.592 20.1924 21.3616 11.2496 1.94 2.54 DC 2 39.618 41.912 22.072 3.76 3.98 DC 3 43.1964 22.7484 DC 4 24.0656 DC 5 S. D. ρ=1 20.77264 Low DC 1 DC 2 DC 3 DC 4 DC 5 20.33807 DC 1 2.8116 4.7322 7.4448 7.8804 10.59924 DC 2 3.3938 5.3392 5.6516 DC 3 8.9864 9.5122
ANNUAL COST (Inventory + distribution) of option 3 with with H products at 5 DCs and M/L products at NDC for possible ρ values. DC 4 14.9648 DC 5
Periodic review policy = OUL
Transport $/u Current NDC
Plant to DC TL 0.09 0.05
DC to cust. LTL 0.1 0.24
L+R R = T L 4
11 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) Q = μ*R
High σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠j σ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j
ρ = 0 σ©^2 = 150.6489 150.6489 0
ρ = 0.5 σ©^2 = 291.0757 150.6489 140.4268 ρ = 1 σ©^2 = 431.5025 150.6489 280.8536
Medium σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠j σ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j
ρ = 0 σ©^2 = 147.6289 147.6289 0
ρ = 0.5 σ©^2 = 280.6329 147.6289 133.004 ρ = 1 σ©^2 = 413.6369 147.6289 266.008
Low σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠j
σ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j ρ = 0 σ©^2 = 41.6269 41.6269 0 ρ = 0.5 σ©^2 = 76.9854 41.6269 35.3585 ρ = 1 σ©^2 = 112.3439 41.6269 70.717 days in production days 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)
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.
ALKO case study
OPTION 4: Use current distribution system for High and Middle products and build NDC for Low products.
100 Products Daily Demand for 1 product
DC 1 DC 2 DC 3
Part 1 10 High Mean 35.48 22.61 17.66
S. D. 6.98 6.48 5.26
Part 3 20 Medium Mean 2.48 4.15 6.15
S. D. 3.16 6.2 6.39
Part 7 70 Low Mean 0.48 0.73 0.8
S. D. 1.98 1.42 2.39
NDC Aggregation Daily Demand for 1 product
100 Products Mean S. D. ρ=0 S. D. ρ=0.5
10 High 90.92 12.27391136 17.06094077
20 Medium 26.43 12.15026337 16.75210136
70 Low 6.49 6.451891196 8.774132436
ANNUAL COST (Inventory + distribution) of option 4 with H/M products at 5 DCs and L products at NDC for possible ρ values. High $ 341,885.80
Medium $ 308,154.13
ρ=0 ρ=0.5 ρ=1
Low $ 282,473.41 $ 331,026.07 $ 369,184.84
TOTAL ANNUAL COST OF OPTION 4 ρ=0 ρ=0.5 ρ=1
for 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 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. 3.044027533 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
High DC 1 DC 2 DC 3 DC 4 DC 5 DC 1 45.2304 36.7148 24.2904 31.3402 DC 2 34.0848 22.5504 29.0952 DC 3 18.3048 23.6174 DC 4 DC 5 DC 4 15.6252 11.81 3.36 DC 5 3.48 4.49 6.16 7.49 Medium DC 1 DC 2 DC 3 DC 4 DC 5 6.76 3.56 DC 1 19.592 20.1924 21.3616 11.2496 1.94 2.54 DC 2 39.618 41.912 22.072 3.76 3.98 DC 3 43.1964 22.7484 DC 4 24.0656 DC 5 S. D. ρ=1 20.77264 Low DC 1 DC 2 DC 3 DC 4 DC 5 20.33807 DC 1 2.8116 4.7322 7.4448 7.8804 10.59924 DC 2 3.3938 5.3392 5.6516 DC 3 8.9864 9.5122
ANNUAL COST (Inventory + distribution) of option 4 with H/M products at 5 DCs and L products at NDC for possible ρ values. DC 4 14.9648 DC 5
Periodic review policy = OUL
Transport $/u Current NDC
Plant to DC TL 0.09 0.05
DC to cust. LTL 0.1 0.24
L+R R = T L 4
11 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) Q = μ*R
High σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠j σ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j
ρ = 0 σ©^2 = 150.6489 150.6489 0
ρ = 0.5 σ©^2 = 291.0757 150.6489 140.4268 ρ = 1 σ©^2 = 431.5025 150.6489 280.8536
Medium σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠j σ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j
ρ = 0 σ©^2 = 147.6289 147.6289 0
ρ = 0.5 σ©^2 = 280.6329 147.6289 133.004 ρ = 1 σ©^2 = 413.6369 147.6289 266.008
Low σ©^2 = Σσi ^2 + Σ (ρij*σi*σj) if i ≠j
σ©^2 = Σσi ^2 + ρij*Σ(σi*σj) if i ≠j ρ = 0 σ©^2 = 41.6269 41.6269 0 ρ = 0.5 σ©^2 = 76.9854 41.6269 35.3585 ρ = 1 σ©^2 = 112.3439 41.6269 70.717 days in production days 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)
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.
