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October  2019, 15(4): 1733-1751. doi: 10.3934/jimo.2018120

A savings analysis of horizontal collaboration among VMI suppliers

Benedikt De Vos , , Birger Raa and  Stijn De Vuyst

Technologiepark 903, 9052 Zwijnaarde, Belgium

* Corresponding author

Received  June 2017 Revised  April 2018 Published  October 2019 Early access  August 2018

Fund Project: This research was supported by the Agency for Innovation by Science and Technology in Flanders (IWT).

This paper considers a logistics distribution network with multiple suppliers that each replenish a set of retailers having constant demand rates. The underlying optimization problem is the Cyclic Inventory Routing Problem (CIRP), for which a heuristic solution method is developed. Further, horizontal collaboration through a third party Logistics Service Provider (LSP) is considered and the collaborative savings potential is analyzed. A design of experiments is performed to evaluate the impact of some relevant cost and network structure factors on the collaborative savings potential. The results from the design of experiments show that for some factor combinations there is in fact no significant savings potential.

Keywords: Inventory-routing, collaborative logistics, inventory control, horizontal collaboration, savings analysis, design of experiments.
Mathematics Subject Classification: Primary: 90B06; Secondary: 90C59.
Citation: Benedikt De Vos, Birger Raa, Stijn De Vuyst. A savings analysis of horizontal collaboration among VMI suppliers. Journal of Industrial and Management Optimization, 2019, 15 (4) : 1733-1751. doi: 10.3934/jimo.2018120
References:
[1]

H. Andersson, Industrial aspects and literature survey: combined inventory management and routing, Computers & Operations Research, 37 (2010), 1515-1536.  doi: 10.1016/j.cor.2009.11.009.

[2]

J.-F. Audy and S. D'Amours, Impact of benefit sharing among companies in the implantation of a collaborative transportation system - an application in the furniture industry, in Pervasive Collaborative Networks, s. I. : Springer US, (2008), 519-532. doi: 10.1007/978-0-387-84837-2_54.

[3]

J.-F. Audy, S. D'Amours and L.-M. Rousseau, Cost allocation in the establishment of a collaborative transportation agreement - an application in the furniture industry, Journal of the Operational Research Society, 62 (2011), 960-970. 

[4]

J.-F. Audy, N. Lehoux, S. D'Amours and M. Rönnqvist, A framework for an efficient implementation of logistics collaborations, International Transactions in Operational Research, 19 (2012), 633-657.  doi: 10.1111/j.1475-3995.2010.00799.x.

[5]

T.-H Chen and J.-M Chen, Optimizing supply chain collaboration based on joint replenishment and channel coordination, Transportation Research Part E: Logistics and Transportation Review, 41 (2005), 261-285.  doi: 10.1016/j.tre.2004.06.003.

[6]

M. Chitsaz, A. Divsalar and P. Vansteenwegen, A two-phase algorithm for the cyclic inventory routing problem, European Journal of Operational Research, 254 (2016), 410-426.  doi: 10.1016/j.ejor.2016.03.056.

[7]

G. Clarke and J. W. Wright, Scheduling of vehicles from a central depot to a number of delivery points, Operations Research, 12 (1964), 568-581. 

[8]

L. C. Coelho, J.-F. Cordeau and G. Laporte, Thirty years of inventory routing, Transportation Science, 48 (2013), 1-19.  doi: 10.1287/trsc.2013.0472.

[9]

F. Cruijssen, M. Cools and W. Dullaert, Horizontal cooperation in logistics: Opportunities and impediments, Transportation Research Part E: Logistics and Transportation Review, 43 (2007), 129-142.  doi: 10.1016/j.tre.2005.09.007.

[10]

F. Cruijssen, P. Borm, H. Fleuren and H. Hamers, Supplier-initiated outsourcing: a methodology to exploit synergy in transportation, European Journal of Operational Research, 207 (2010), 763-774.  doi: 10.1016/j.ejor.2010.06.009.

[11]

Ö. Ergun, G. Kuyzu and M. Savelsbergh, Reducing truckload transportation costs through collaboration, Transportation Science, 41 (2007), 206-221.  doi: 10.1287/trsc.1060.0169.

[12]

M. Frisk, M. Göthe-Lundgren, K. Jörnsten and M. Rönnqvist, Cost allocation in collaborative forest transportation, European Journal of Operational Research, 205 (2010), 448-458. 

[13]

S. Lozano, P. Moreno, B. Adenso-Díaz and E. Algaba, Cooperative game theory approach to allocating benefits of horizontal cooperation, European Journal of Operational Research, 229 (2013), 444-452.  doi: 10.1016/j.ejor.2013.02.034.

[14]

R. Mason, C. Lalwani and R. Boughton, Combining vertical and horizontal collaboration for transport optimisation, Supply Chain Management: An International Journal, 12 (2007), 187-199.  doi: 10.1108/13598540710742509.

[15]

J. T. Mentzer, W. DeWitt, J. S. Keebler, S. Min, N. W. Nix, C. D. Smith and Z. G. Zacharia, Defining supply chain management, Journal of Business Logistics, 22 (2001), 1-25.  doi: 10.1002/j.2158-1592.2001.tb00001.x.

[16]

N. H. Moin and S. Salhi, Inventory routing problems: A logistical overview, Journal of the Operational Research Society, 58 (2007), 1185-1194.  doi: 10.1057/palgrave.jors.2602264.

[17]

O. Ö. Özener and Ö. Ergun, Allocating costs in a collaborative transportation procurement network, Transportation Science, 42 (2008), 146-165. 

[18]

D. Power, Supply chain management integration and implementation: A literature review, Supply Chain Management: An International Journal, 10 (2005), 252-263.  doi: 10.1108/13598540510612721.

[19]

B. Raa and E.-H Aghezzaf, A practical solution approach for the cyclic inventory routing problem, European Journal of Operational Research, 192 (2009), 429-441.  doi: 10.1016/j.ejor.2007.09.032.

[20]

B. Raa and W. Dullaert, Route and fleet design for cyclic inventory routing, European Journal of Operational Research, 256 (2017), 404-411.  doi: 10.1016/j.ejor.2016.06.009.

[21]

T. Simatupang and R. Sridharan, The collaborative supply chain, The International Journal of Logistics Management, 13 (2002), 15-30.  doi: 10.1108/09574090210806333.

[22]

G. Stefansson, Collaborative logistics management and the role of third-party service providers, International Journal of Physical Distribution & Logistics Management, 36 (2006), 76-92.  doi: 10.1108/09600030610656413.

[23]

C. Vanovermeire and K. Sörensen, Integration of the cost allocation in the optimization of collaborative bundling, Transportation Research Part E: Logistics and Transportation Review, 72 (2014), 125-143.  doi: 10.1016/j.tre.2014.09.009.

show all references

References:
[1]

H. Andersson, Industrial aspects and literature survey: combined inventory management and routing, Computers & Operations Research, 37 (2010), 1515-1536.  doi: 10.1016/j.cor.2009.11.009.

[2]

J.-F. Audy and S. D'Amours, Impact of benefit sharing among companies in the implantation of a collaborative transportation system - an application in the furniture industry, in Pervasive Collaborative Networks, s. I. : Springer US, (2008), 519-532. doi: 10.1007/978-0-387-84837-2_54.

[3]

J.-F. Audy, S. D'Amours and L.-M. Rousseau, Cost allocation in the establishment of a collaborative transportation agreement - an application in the furniture industry, Journal of the Operational Research Society, 62 (2011), 960-970. 

[4]

J.-F. Audy, N. Lehoux, S. D'Amours and M. Rönnqvist, A framework for an efficient implementation of logistics collaborations, International Transactions in Operational Research, 19 (2012), 633-657.  doi: 10.1111/j.1475-3995.2010.00799.x.

[5]

T.-H Chen and J.-M Chen, Optimizing supply chain collaboration based on joint replenishment and channel coordination, Transportation Research Part E: Logistics and Transportation Review, 41 (2005), 261-285.  doi: 10.1016/j.tre.2004.06.003.

[6]

M. Chitsaz, A. Divsalar and P. Vansteenwegen, A two-phase algorithm for the cyclic inventory routing problem, European Journal of Operational Research, 254 (2016), 410-426.  doi: 10.1016/j.ejor.2016.03.056.

[7]

G. Clarke and J. W. Wright, Scheduling of vehicles from a central depot to a number of delivery points, Operations Research, 12 (1964), 568-581. 

[8]

L. C. Coelho, J.-F. Cordeau and G. Laporte, Thirty years of inventory routing, Transportation Science, 48 (2013), 1-19.  doi: 10.1287/trsc.2013.0472.

[9]

F. Cruijssen, M. Cools and W. Dullaert, Horizontal cooperation in logistics: Opportunities and impediments, Transportation Research Part E: Logistics and Transportation Review, 43 (2007), 129-142.  doi: 10.1016/j.tre.2005.09.007.

[10]

F. Cruijssen, P. Borm, H. Fleuren and H. Hamers, Supplier-initiated outsourcing: a methodology to exploit synergy in transportation, European Journal of Operational Research, 207 (2010), 763-774.  doi: 10.1016/j.ejor.2010.06.009.

[11]

Ö. Ergun, G. Kuyzu and M. Savelsbergh, Reducing truckload transportation costs through collaboration, Transportation Science, 41 (2007), 206-221.  doi: 10.1287/trsc.1060.0169.

[12]

M. Frisk, M. Göthe-Lundgren, K. Jörnsten and M. Rönnqvist, Cost allocation in collaborative forest transportation, European Journal of Operational Research, 205 (2010), 448-458. 

[13]

S. Lozano, P. Moreno, B. Adenso-Díaz and E. Algaba, Cooperative game theory approach to allocating benefits of horizontal cooperation, European Journal of Operational Research, 229 (2013), 444-452.  doi: 10.1016/j.ejor.2013.02.034.

[14]

R. Mason, C. Lalwani and R. Boughton, Combining vertical and horizontal collaboration for transport optimisation, Supply Chain Management: An International Journal, 12 (2007), 187-199.  doi: 10.1108/13598540710742509.

[15]

J. T. Mentzer, W. DeWitt, J. S. Keebler, S. Min, N. W. Nix, C. D. Smith and Z. G. Zacharia, Defining supply chain management, Journal of Business Logistics, 22 (2001), 1-25.  doi: 10.1002/j.2158-1592.2001.tb00001.x.

[16]

N. H. Moin and S. Salhi, Inventory routing problems: A logistical overview, Journal of the Operational Research Society, 58 (2007), 1185-1194.  doi: 10.1057/palgrave.jors.2602264.

[17]

O. Ö. Özener and Ö. Ergun, Allocating costs in a collaborative transportation procurement network, Transportation Science, 42 (2008), 146-165. 

[18]

D. Power, Supply chain management integration and implementation: A literature review, Supply Chain Management: An International Journal, 10 (2005), 252-263.  doi: 10.1108/13598540510612721.

[19]

B. Raa and E.-H Aghezzaf, A practical solution approach for the cyclic inventory routing problem, European Journal of Operational Research, 192 (2009), 429-441.  doi: 10.1016/j.ejor.2007.09.032.

[20]

B. Raa and W. Dullaert, Route and fleet design for cyclic inventory routing, European Journal of Operational Research, 256 (2017), 404-411.  doi: 10.1016/j.ejor.2016.06.009.

[21]

T. Simatupang and R. Sridharan, The collaborative supply chain, The International Journal of Logistics Management, 13 (2002), 15-30.  doi: 10.1108/09574090210806333.

[22]

G. Stefansson, Collaborative logistics management and the role of third-party service providers, International Journal of Physical Distribution & Logistics Management, 36 (2006), 76-92.  doi: 10.1108/09600030610656413.

[23]

C. Vanovermeire and K. Sörensen, Integration of the cost allocation in the optimization of collaborative bundling, Transportation Research Part E: Logistics and Transportation Review, 72 (2014), 125-143.  doi: 10.1016/j.tre.2014.09.009.

Figure 1.  Location of LSP, suppliers and retailers in the illustrative example
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Figure 2.  Illustration of the factor $overlap$
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Figure 3.  Boxplots of percentage savings for different levels of $overlap$
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Figure 4.  Boxplots of percentage savings for different levels of $costlsp$
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Figure 5.  Boxplots of percentage savings for different levels of $nrs$
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Figure 6.  Interaction between the factors $overlap$ and $costlsp$
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Figure 7.  Interaction between the factors $overlap$ and $nr$
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Figure 8.  Interaction between the factors $costlsp$ and $nr$
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Table 1.  Input data for the illustrative example
LSP & SuppliersRetailers
$\tau$1.2/km $\eta_j$0.8/unit/day
$\varphi_0$20/tour $\varphi_j$10/visit
$\kappa$100 units $\kappa_j$100 units
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LSP & SuppliersRetailers
$\tau$1.2/km $\eta_j$0.8/unit/day
$\varphi_0$20/tour $\varphi_j$10/visit
$\kappa$100 units $\kappa_j$100 units
Table 2.  Routes for supplier 1 individually
$r$route $T_r$ $TC_r$
1 $S_1 - 6 - 5 - 1 - 2 - S_1$6152.41
2 $S_1 - 3 - 8 - S_1$572.62
3 $S_1 - 7 - 9 - 10 - 4 - S_1$7182.47
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$r$route $T_r$ $TC_r$
1 $S_1 - 6 - 5 - 1 - 2 - S_1$6152.41
2 $S_1 - 3 - 8 - S_1$572.62
3 $S_1 - 7 - 9 - 10 - 4 - S_1$7182.47
Table 3.  Routes for the LSP in the grand coalition {1, 2, 3}
$r$route $T_r$ $TC_r$
1 $LSP - 15 - 9 - 17 - 22 - 10 - 13 - 4 - LSP$4222.95
2 $LSP - 25 - 6 - 23 - 20 - 24 - LSP$3203.8
3 $LSP - 7 - 21 - 27 - LSP$6146.21
4 $LSP - 2 - 5 - 1 - 16 - 18 - 30 - LSP$5185.00
5 $LSP - 8 - 26 - 19 - 3 - 14 - 11 - LSP$3142.36
6 $LSP - 28 - 29 - 12 - LSP$5128.54
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$r$route $T_r$ $TC_r$
1 $LSP - 15 - 9 - 17 - 22 - 10 - 13 - 4 - LSP$4222.95
2 $LSP - 25 - 6 - 23 - 20 - 24 - LSP$3203.8
3 $LSP - 7 - 21 - 27 - LSP$6146.21
4 $LSP - 2 - 5 - 1 - 16 - 18 - 30 - LSP$5185.00
5 $LSP - 8 - 26 - 19 - 3 - 14 - 11 - LSP$3142.36
6 $LSP - 28 - 29 - 12 - LSP$5128.54
Table 4.  Costs and savings individual suppliers and coalitions
CoalitionCumulative individual costCoalition costSaving%Saving
1407.50---
2310.22---
3417.75---
{1}407.50410.20-2.70-0.66
{2}310.22310.010.210.07
{3}417.75428.84-11.09-2.65
{1, 2}717.72659.9657.768.05
{1, 3}825.25780.9644.295.3
{2, 3}727.97697.8630.114.14
{1, 2, 3}1135.471028.87106.69.39
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CoalitionCumulative individual costCoalition costSaving%Saving
1407.50---
2310.22---
3417.75---
{1}407.50410.20-2.70-0.66
{2}310.22310.010.210.07
{3}417.75428.84-11.09-2.65
{1, 2}717.72659.9657.768.05
{1, 3}825.25780.9644.295.3
{2, 3}727.97697.8630.114.14
{1, 2, 3}1135.471028.87106.69.39
Table 5.  Cost rates (in € per day) for the individual supplier instances
SuppliernrRetTotalDistributionHolding
S0 $32$ $620.7$ $447.7$ $173.0$
S1 $52$ $846.4$ $581.4$ $265.0$
S2 $44$ $751.4$ $516.3$ $235.1$
S3 $53$ $973.2$ $708.4$ $264.8$
S4 $46$ $779.8$ $552.7$ $227.0$
S5 $68$ $1255.6$ $904.3$ $351.4$
S6 $63$ $998.2$ $692.7$ $305.5$
S7 $31$ $521.5$ $368.3$ $153.2$
S8 $51$ $840.4$ $598.2$ $242.2$
S9 $56$ $1058.9$ $758.7$ $300.2$
L0 $84$ $1491.4$ $1061.3$ $430.1$
L1 $111$ $1886.6$ $1336.4$ $550.2$
L2 $118$ $1900.0$ $1279.1$ $620.9$
L3 $82$ $1257.8$ $843.9$ $413.8$
L4 $94$ $1662.8$ $1167.9$ $494.9$
L5 $120$ $1831.3$ $1249.8$ $581.5$
L6 $99$ $1639.2$ $1148.8$ $490.5$
L7 $109$ $1838.5$ $1296.7$ $541.8$
L8 $86$ $1546.4$ $1125.9$ $420.5$
L9 $87$ $1405.8$ $945.3$ $460.5$
Avg. $74.3$ $1255.3$ $879.2$ $376.1$
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SuppliernrRetTotalDistributionHolding
S0 $32$ $620.7$ $447.7$ $173.0$
S1 $52$ $846.4$ $581.4$ $265.0$
S2 $44$ $751.4$ $516.3$ $235.1$
S3 $53$ $973.2$ $708.4$ $264.8$
S4 $46$ $779.8$ $552.7$ $227.0$
S5 $68$ $1255.6$ $904.3$ $351.4$
S6 $63$ $998.2$ $692.7$ $305.5$
S7 $31$ $521.5$ $368.3$ $153.2$
S8 $51$ $840.4$ $598.2$ $242.2$
S9 $56$ $1058.9$ $758.7$ $300.2$
L0 $84$ $1491.4$ $1061.3$ $430.1$
L1 $111$ $1886.6$ $1336.4$ $550.2$
L2 $118$ $1900.0$ $1279.1$ $620.9$
L3 $82$ $1257.8$ $843.9$ $413.8$
L4 $94$ $1662.8$ $1167.9$ $494.9$
L5 $120$ $1831.3$ $1249.8$ $581.5$
L6 $99$ $1639.2$ $1148.8$ $490.5$
L7 $109$ $1838.5$ $1296.7$ $541.8$
L8 $86$ $1546.4$ $1125.9$ $420.5$
L9 $87$ $1405.8$ $945.3$ $460.5$
Avg. $74.3$ $1255.3$ $879.2$ $376.1$
Table 6.  Impact of $costLSP$ for the individual suppliers
$costLSP$TotalRelativeDistributionRelativeHoldingRelative
$90\%$ $1166.6$ $0.93$ $800.2$ $0.91$ $366.4$ $0.97$
$95\%$ $1211.2$ $0.96$ $839.3$ $0.95$ $371.9$ $0.99$
$100\%$ $1255.3$ $1$ $879.2$ $1$ $376.1$ $1$
$105\%$ $1300.0$ $1.04$ $913.1$ $1.04$ $386.9$ $1.03$
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$costLSP$TotalRelativeDistributionRelativeHoldingRelative
$90\%$ $1166.6$ $0.93$ $800.2$ $0.91$ $366.4$ $0.97$
$95\%$ $1211.2$ $0.96$ $839.3$ $0.95$ $371.9$ $0.99$
$100\%$ $1255.3$ $1$ $879.2$ $1$ $376.1$ $1$
$105\%$ $1300.0$ $1.04$ $913.1$ $1.04$ $386.9$ $1.03$
Table 7.  Impact of $overlap$ for the individual suppliers
$overlap$TotalRelativeDistributionRelativeHoldingRelative
1 $1255.3$ $1$ $879.2$ $1$ $376.1$ $1$
0 $1424.7$ $1.13$ $1041.3$ $1.18$ $383.5$ $1.02$
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$overlap$TotalRelativeDistributionRelativeHoldingRelative
1 $1255.3$ $1$ $879.2$ $1$ $376.1$ $1$
0 $1424.7$ $1.13$ $1041.3$ $1.18$ $383.5$ $1.02$
Table 8.  Illustration of the effect of $nr$
$nr$CoalitionTotalCumulativeSaving $\%$sav
1S3973.2973.200.00
2S3-L82409.62519.6110.14.37
3S3-L8-S23004.43271.0266.68.15
4S3-L8-S2-L64501.44910.2408.98.33
5S3-L8-S2-L6-L35620.96168.0547.18.87
6S3-L8-S2-L6-L3-L17248.38054.6806.410.01
7S3-L8-S2-L6-L3-L1-S58354.29310.2956.010.27
8S3-L8-S2-L6-L3-L1-S5-L49790.910973.11182.210.77
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$nr$CoalitionTotalCumulativeSaving $\%$sav
1S3973.2973.200.00
2S3-L82409.62519.6110.14.37
3S3-L8-S23004.43271.0266.68.15
4S3-L8-S2-L64501.44910.2408.98.33
5S3-L8-S2-L6-L35620.96168.0547.18.87
6S3-L8-S2-L6-L3-L17248.38054.6806.410.01
7S3-L8-S2-L6-L3-L1-S58354.29310.2956.010.27
8S3-L8-S2-L6-L3-L1-S5-L49790.910973.11182.210.77
Table 9.  Results of the ANOVA with main effects and two-way interactions
SourceType Ⅲ Sum of SquaresdfMean SquareFSig.
Corrected Model121661.580a215793.109918.9960.000
Intercept570.0291570.02990.4220.000
$overlap$91248.526191248.52614474.5610.000
$costLSP$20639.71136879.9041091.3450.000
$nr$8779.36371254.195198.9500.000
$overlap * costLSP$306.0543102.01816.1830.000
$overlap * nr$687.925798.27515.5890.000
Error7930.51012586.304
Total130162.1181280
Corrected Total129592.0891279
a R Squared = 0.939 (Adjusted R Squared = 0.938).
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SourceType Ⅲ Sum of SquaresdfMean SquareFSig.
Corrected Model121661.580a215793.109918.9960.000
Intercept570.0291570.02990.4220.000
$overlap$91248.526191248.52614474.5610.000
$costLSP$20639.71136879.9041091.3450.000
$nr$8779.36371254.195198.9500.000
$overlap * costLSP$306.0543102.01816.1830.000
$overlap * nr$687.925798.27515.5890.000
Error7930.51012586.304
Total130162.1181280
Corrected Total129592.0891279
a R Squared = 0.939 (Adjusted R Squared = 0.938).
Table 10.  Average percentage savings for the different $overlap$ levels
$overlap$01
Estimate $-7.8\%$ $9.1\%$
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$overlap$01
Estimate $-7.8\%$ $9.1\%$
Table 11.  Average percentage savings for the different $costlsp$ levels
$costLSP$ $90\%$ $95\%$ $100\%$ $105\%$
Estimate $6.1\%$ $2.3\%$ $-1.0\%$ $-4.8\%$
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$costLSP$ $90\%$ $95\%$ $100\%$ $105\%$
Estimate $6.1\%$ $2.3\%$ $-1.0\%$ $-4.8\%$
Table 12.  Average percentage savings for the different $nr$ levels
$nr$12345678
Estimate-4.8%-1.8%-0.1%1.0%1.9%2.5%3.0%3.5%
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$nr$12345678
Estimate-4.8%-1.8%-0.1%1.0%1.9%2.5%3.0%3.5%
Table 13.  Post-hoc Tukey test for $nr$
pctSava, b, c
Subset
$nr$N1234567
1160-4.7630
2160-1.7617
3160-0.1306
41601.0208
51601.87151.8715
61602.54442.5444
71603.04493.0449
81603.5125
Sig.1.0001.0001.0000.0510.2440.6320.710
a Means for groups in homogeneous subsets are displayed. Based on observed means. The error term is Mean Square(error) = 6.304
b Uses Harmonic Mean Sample Size = 160.000
c Alpha = 0.05
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pctSava, b, c
Subset
$nr$N1234567
1160-4.7630
2160-1.7617
3160-0.1306
41601.0208
51601.87151.8715
61602.54442.5444
71603.04493.0449
81603.5125
Sig.1.0001.0001.0000.0510.2440.6320.710
a Means for groups in homogeneous subsets are displayed. Based on observed means. The error term is Mean Square(error) = 6.304
b Uses Harmonic Mean Sample Size = 160.000
c Alpha = 0.05
[1]

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