A savings analysis of horizontal collaboration among VMI suppliers

Benedikt De Vos; Birger Raa; Stijn De Vuyst

doi:10.3934/jimo.2018120

Article Contents

2019, Volume 15, Issue 4: 1733-1751. Doi: 10.3934/jimo.2018120

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A savings analysis of horizontal collaboration among VMI suppliers

Technologiepark 903, 9052 Zwijnaarde, Belgium

* Corresponding author
* Corresponding author

Received: June 2017

Revised: April 2018

Early access: August 2018

Published: July 2019

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

Abstract / Introduction Full Text(HTML) Figure(8) / Table(13) Related Papers Cited by

Abstract

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:

Mathematics Subject Classification: Primary: 90B06; Secondary: 90C59.

Citation:

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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 & 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

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Table 2. 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

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Table 3. Routes for the LSP in the grand coalition {1, 2, 3}

$r$	route	$T_r$	$TC_r$
1	$LSP - 15 - 9 - 17 - 22 - 10 - 13 - 4 - LSP$	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

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Table 4. 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

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Table 5. 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.	$74.3$	$1255.3$	$879.2$	$376.1$

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Table 6. Impact of $costLSP$ for the individual suppliers

$costLSP$	Total	Relative	Distribution	Relative	Holding	Relative
$90\%$	$1166.6$	$0.93$	$800.2$	$0.91$	$366.4$	$0.97$
$95\%$	$1211.2$	$0.96$	$839.3$	$0.95$	$371.9$	$0.99$
$100\%$	$1255.3$	$1$	$879.2$	$1$	$376.1$	$1$
$105\%$	$1300.0$	$1.04$	$913.1$	$1.04$	$386.9$	$1.03$

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Table 7. 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	$1424.7$	$1.13$	$1041.3$	$1.18$	$383.5$	$1.02$

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Table 8. 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

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Table 9. Results of the ANOVA with main effects and two-way interactions

Source	Type Ⅲ Sum of Squares	df	Mean Square	F	Sig.
Corrected Model	121661.580^a	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).

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Table 10. Average percentage savings for the different $overlap$ levels

$overlap$	0	1
Estimate	$-7.8\%$	$9.1\%$

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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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Table 12. 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%

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Table 13. Post-hoc Tukey test for $nr$

pctSav^{a, 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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References

[1]	H. Andersson, et al., 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.