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

## A savings analysis of horizontal collaboration among VMI suppliers

 Technologiepark 903, 9052 Zwijnaarde, Belgium

* Corresponding author

Received  June 2017 Revised  April 2018 Published  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.

Citation: Benedikt De Vos, Birger Raa, Stijn De Vuyst. A savings analysis of horizontal collaboration among VMI suppliers. Journal of Industrial & Management Optimization, 2019, 15 (4) : 1733-1751. doi: 10.3934/jimo.2018120
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##### References:
Location of LSP, suppliers and retailers in the illustrative example
Illustration of the factor $overlap$
Boxplots of percentage savings for different levels of $overlap$
Boxplots of percentage savings for different levels of $costlsp$
Boxplots of percentage savings for different levels of $nrs$
Interaction between the factors $overlap$ and $costlsp$
Interaction between the factors $overlap$ and $nr$
Interaction between the factors $costlsp$ and $nr$
Input data for the illustrative example
 LSP & Suppliers Retailers $\tau$ 1.2/km $\eta_j$ 0.8/unit/day $\varphi_0$ 20/tour $\varphi_j$ 10/visit $\kappa$ 100 units $\kappa_j$ 100 units
 LSP & Suppliers Retailers $\tau$ 1.2/km $\eta_j$ 0.8/unit/day $\varphi_0$ 20/tour $\varphi_j$ 10/visit $\kappa$ 100 units $\kappa_j$ 100 units
Routes for supplier 1 individually
 $r$ route $T_r$ $TC_r$ 1 $S_1 - 6 - 5 - 1 - 2 - S_1$ 6 152.41 2 $S_1 - 3 - 8 - S_1$ 5 72.62 3 $S_1 - 7 - 9 - 10 - 4 - S_1$ 7 182.47
 $r$ route $T_r$ $TC_r$ 1 $S_1 - 6 - 5 - 1 - 2 - S_1$ 6 152.41 2 $S_1 - 3 - 8 - S_1$ 5 72.62 3 $S_1 - 7 - 9 - 10 - 4 - S_1$ 7 182.47
Routes for the LSP in the grand coalition {1, 2, 3}
 $r$ route $T_r$ $TC_r$ 1 $LSP - 15 - 9 - 17 - 22 - 10 - 13 - 4 - LSP$ 4 222.95 2 $LSP - 25 - 6 - 23 - 20 - 24 - LSP$ 3 203.8 3 $LSP - 7 - 21 - 27 - LSP$ 6 146.21 4 $LSP - 2 - 5 - 1 - 16 - 18 - 30 - LSP$ 5 185.00 5 $LSP - 8 - 26 - 19 - 3 - 14 - 11 - LSP$ 3 142.36 6 $LSP - 28 - 29 - 12 - LSP$ 5 128.54
 $r$ route $T_r$ $TC_r$ 1 $LSP - 15 - 9 - 17 - 22 - 10 - 13 - 4 - LSP$ 4 222.95 2 $LSP - 25 - 6 - 23 - 20 - 24 - LSP$ 3 203.8 3 $LSP - 7 - 21 - 27 - LSP$ 6 146.21 4 $LSP - 2 - 5 - 1 - 16 - 18 - 30 - LSP$ 5 185.00 5 $LSP - 8 - 26 - 19 - 3 - 14 - 11 - LSP$ 3 142.36 6 $LSP - 28 - 29 - 12 - LSP$ 5 128.54
Costs and savings individual suppliers and coalitions
 Coalition Cumulative individual cost Coalition cost Saving %Saving 1 407.50 - - - 2 310.22 - - - 3 417.75 - - - {1} 407.50 410.20 -2.70 -0.66 {2} 310.22 310.01 0.21 0.07 {3} 417.75 428.84 -11.09 -2.65 {1, 2} 717.72 659.96 57.76 8.05 {1, 3} 825.25 780.96 44.29 5.3 {2, 3} 727.97 697.86 30.11 4.14 {1, 2, 3} 1135.47 1028.87 106.6 9.39
 Coalition Cumulative individual cost Coalition cost Saving %Saving 1 407.50 - - - 2 310.22 - - - 3 417.75 - - - {1} 407.50 410.20 -2.70 -0.66 {2} 310.22 310.01 0.21 0.07 {3} 417.75 428.84 -11.09 -2.65 {1, 2} 717.72 659.96 57.76 8.05 {1, 3} 825.25 780.96 44.29 5.3 {2, 3} 727.97 697.86 30.11 4.14 {1, 2, 3} 1135.47 1028.87 106.6 9.39
Cost rates (in € per day) for the individual supplier instances
 Supplier nrRet Total Distribution Holding 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. $74.3$ $1255.3$ $879.2$ $376.1$
 Supplier nrRet Total Distribution Holding 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. $74.3$ $1255.3$ $879.2$ $376.1$
Impact of $costLSP$ for the individual suppliers
 $costLSP$ Total Relative Distribution Relative Holding Relative $90\%$ $1166.6$ $0.93$ $800.2$ $0.91$ $366.4$ $0.97$ $95\%$ $1211.2$ $0.96$ $839.3$ $0.95$ $371.9$ $0.99$ $100\%$ $1255.3$ $1$ $879.2$ $1$ $376.1$ $1$ $105\%$ $1300.0$ $1.04$ $913.1$ $1.04$ $386.9$ $1.03$
 $costLSP$ Total Relative Distribution Relative Holding Relative $90\%$ $1166.6$ $0.93$ $800.2$ $0.91$ $366.4$ $0.97$ $95\%$ $1211.2$ $0.96$ $839.3$ $0.95$ $371.9$ $0.99$ $100\%$ $1255.3$ $1$ $879.2$ $1$ $376.1$ $1$ $105\%$ $1300.0$ $1.04$ $913.1$ $1.04$ $386.9$ $1.03$
Impact of $overlap$ for the individual suppliers
 $overlap$ Total Relative Distribution Relative Holding Relative 1 $1255.3$ $1$ $879.2$ $1$ $376.1$ $1$ 0 $1424.7$ $1.13$ $1041.3$ $1.18$ $383.5$ $1.02$
 $overlap$ Total Relative Distribution Relative Holding Relative 1 $1255.3$ $1$ $879.2$ $1$ $376.1$ $1$ 0 $1424.7$ $1.13$ $1041.3$ $1.18$ $383.5$ $1.02$
Illustration of the effect of $nr$
 $nr$ Coalition Total Cumulative Saving $\%$sav 1 S3 973.2 973.2 0 0.00 2 S3-L8 2409.6 2519.6 110.1 4.37 3 S3-L8-S2 3004.4 3271.0 266.6 8.15 4 S3-L8-S2-L6 4501.4 4910.2 408.9 8.33 5 S3-L8-S2-L6-L3 5620.9 6168.0 547.1 8.87 6 S3-L8-S2-L6-L3-L1 7248.3 8054.6 806.4 10.01 7 S3-L8-S2-L6-L3-L1-S5 8354.2 9310.2 956.0 10.27 8 S3-L8-S2-L6-L3-L1-S5-L4 9790.9 10973.1 1182.2 10.77
 $nr$ Coalition Total Cumulative Saving $\%$sav 1 S3 973.2 973.2 0 0.00 2 S3-L8 2409.6 2519.6 110.1 4.37 3 S3-L8-S2 3004.4 3271.0 266.6 8.15 4 S3-L8-S2-L6 4501.4 4910.2 408.9 8.33 5 S3-L8-S2-L6-L3 5620.9 6168.0 547.1 8.87 6 S3-L8-S2-L6-L3-L1 7248.3 8054.6 806.4 10.01 7 S3-L8-S2-L6-L3-L1-S5 8354.2 9310.2 956.0 10.27 8 S3-L8-S2-L6-L3-L1-S5-L4 9790.9 10973.1 1182.2 10.77
Results of the ANOVA with main effects and two-way interactions
 Source Type Ⅲ Sum of Squares df Mean Square F Sig. Corrected Model 121661.580a 21 5793.109 918.996 0.000 Intercept 570.029 1 570.029 90.422 0.000 $overlap$ 91248.526 1 91248.526 14474.561 0.000 $costLSP$ 20639.711 3 6879.904 1091.345 0.000 $nr$ 8779.363 7 1254.195 198.950 0.000 $overlap * costLSP$ 306.054 3 102.018 16.183 0.000 $overlap * nr$ 687.925 7 98.275 15.589 0.000 Error 7930.510 1258 6.304 Total 130162.118 1280 Corrected Total 129592.089 1279 a R Squared = 0.939 (Adjusted R Squared = 0.938).
 Source Type Ⅲ Sum of Squares df Mean Square F Sig. Corrected Model 121661.580a 21 5793.109 918.996 0.000 Intercept 570.029 1 570.029 90.422 0.000 $overlap$ 91248.526 1 91248.526 14474.561 0.000 $costLSP$ 20639.711 3 6879.904 1091.345 0.000 $nr$ 8779.363 7 1254.195 198.950 0.000 $overlap * costLSP$ 306.054 3 102.018 16.183 0.000 $overlap * nr$ 687.925 7 98.275 15.589 0.000 Error 7930.510 1258 6.304 Total 130162.118 1280 Corrected Total 129592.089 1279 a R Squared = 0.939 (Adjusted R Squared = 0.938).
Average percentage savings for the different $overlap$ levels
 $overlap$ 0 1 Estimate $-7.8\%$ $9.1\%$
 $overlap$ 0 1 Estimate $-7.8\%$ $9.1\%$
Average percentage savings for the different $costlsp$ levels
 $costLSP$ $90\%$ $95\%$ $100\%$ $105\%$ Estimate $6.1\%$ $2.3\%$ $-1.0\%$ $-4.8\%$
 $costLSP$ $90\%$ $95\%$ $100\%$ $105\%$ Estimate $6.1\%$ $2.3\%$ $-1.0\%$ $-4.8\%$
Average percentage savings for the different $nr$ levels
 $nr$ 1 2 3 4 5 6 7 8 Estimate -4.8% -1.8% -0.1% 1.0% 1.9% 2.5% 3.0% 3.5%
 $nr$ 1 2 3 4 5 6 7 8 Estimate -4.8% -1.8% -0.1% 1.0% 1.9% 2.5% 3.0% 3.5%
Post-hoc Tukey test for $nr$
 pctSava, b, c Subset $nr$ N 1 2 3 4 5 6 7 1 160 -4.7630 2 160 -1.7617 3 160 -0.1306 4 160 1.0208 5 160 1.8715 1.8715 6 160 2.5444 2.5444 7 160 3.0449 3.0449 8 160 3.5125 Sig. 1.000 1.000 1.000 0.051 0.244 0.632 0.710 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
 pctSava, b, c Subset $nr$ N 1 2 3 4 5 6 7 1 160 -4.7630 2 160 -1.7617 3 160 -0.1306 4 160 1.0208 5 160 1.8715 1.8715 6 160 2.5444 2.5444 7 160 3.0449 3.0449 8 160 3.5125 Sig. 1.000 1.000 1.000 0.051 0.244 0.632 0.710 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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