• Previous Article
    Coordination of VMI supply chain with a loss-averse manufacturer under quality-dependency and marketing-dependency
  • JIMO Home
  • This Issue
  • Next Article
    A note on network repair crew scheduling and routing for emergency relief distribution problem
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
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.  Google Scholar

[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.  Google Scholar

[3]

J.-F. AudyS. 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.   Google Scholar

[4]

J.-F. AudyN. LehouxS. 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.  Google Scholar

[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.  Google Scholar

[6]

M. ChitsazA. 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.  Google Scholar

[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.   Google Scholar

[8]

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

[9]

F. CruijssenM. 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.  Google Scholar

[10]

F. CruijssenP. BormH. 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.  Google Scholar

[11]

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

[12]

M. FriskM. Göthe-LundgrenK. Jörnsten and M. Rönnqvist, Cost allocation in collaborative forest transportation, European Journal of Operational Research, 205 (2010), 448-458.   Google Scholar

[13]

S. LozanoP. MorenoB. 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.  Google Scholar

[14]

R. MasonC. 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.  Google Scholar

[15]

J. T. MentzerW. DeWittJ. S. KeeblerS. MinN. W. NixC. 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.  Google Scholar

[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.  Google Scholar

[17]

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

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[21]

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

[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.  Google Scholar

[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.  Google Scholar

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.  Google Scholar

[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.  Google Scholar

[3]

J.-F. AudyS. 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.   Google Scholar

[4]

J.-F. AudyN. LehouxS. 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.  Google Scholar

[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.  Google Scholar

[6]

M. ChitsazA. 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.  Google Scholar

[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.   Google Scholar

[8]

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

[9]

F. CruijssenM. 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.  Google Scholar

[10]

F. CruijssenP. BormH. 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.  Google Scholar

[11]

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

[12]

M. FriskM. Göthe-LundgrenK. Jörnsten and M. Rönnqvist, Cost allocation in collaborative forest transportation, European Journal of Operational Research, 205 (2010), 448-458.   Google Scholar

[13]

S. LozanoP. MorenoB. 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.  Google Scholar

[14]

R. MasonC. 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.  Google Scholar

[15]

J. T. MentzerW. DeWittJ. S. KeeblerS. MinN. W. NixC. 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.  Google Scholar

[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.  Google Scholar

[17]

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

[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.  Google Scholar

[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.  Google Scholar

[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.  Google Scholar

[21]

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

[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.  Google Scholar

[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.  Google Scholar

Figure 1.  Location of LSP, suppliers and retailers in the illustrative example
Figure 2.  Illustration of the factor $overlap$
Figure 3.  Boxplots of percentage savings for different levels of $overlap$
Figure 4.  Boxplots of percentage savings for different levels of $costlsp$
Figure 5.  Boxplots of percentage savings for different levels of $nrs$
Figure 6.  Interaction between the factors $overlap$ and $costlsp$
Figure 7.  Interaction between the factors $overlap$ and $nr$
Figure 8.  Interaction between the factors $costlsp$ and $nr$
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
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
$r$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
$r$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
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. $74.3$ $1255.3$ $879.2$ $376.1$
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
$90\%$ $1166.6$ $0.93$ $800.2$ $0.91$ $366.4$ $0.97$
$95\%$ $1211.2$ $0.96$ $839.3$ $0.95$ $371.9$ $0.99$
$100\%$ $1255.3$ $1$ $879.2$ $1$ $376.1$ $1$
$105\%$ $1300.0$ $1.04$ $913.1$ $1.04$ $386.9$ $1.03$
$costLSP$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 $1424.7$ $1.13$ $1041.3$ $1.18$ $383.5$ $1.02$
$overlap$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
$nr$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).
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 $-7.8\%$ $9.1\%$
$overlap$01
Estimate $-7.8\%$ $9.1\%$
Table 11.  Average percentage savings for the different $costlsp$ levels
$costLSP$ $90\%$ $95\%$ $100\%$ $105\%$
Estimate $6.1\%$ $2.3\%$ $-1.0\%$ $-4.8\%$
$costLSP$ $90\%$ $95\%$ $100\%$ $105\%$
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%
$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
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]

Ömer Arslan, Selçuk Kürşat İşleyen. A model and two heuristic methods for The Multi-Product Inventory-Location-Routing Problem with heterogeneous fleet. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021002

[2]

Mahdi Karimi, Seyed Jafar Sadjadi. Optimization of a Multi-Item Inventory model for deteriorating items with capacity constraint using dynamic programming. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021013

[3]

Arthur Fleig, Lars Grüne. Strict dissipativity analysis for classes of optimal control problems involving probability density functions. Mathematical Control & Related Fields, 2020  doi: 10.3934/mcrf.2020053

[4]

David W. K. Yeung, Yingxuan Zhang, Hongtao Bai, Sardar M. N. Islam. Collaborative environmental management for transboundary air pollution problems: A differential levies game. Journal of Industrial & Management Optimization, 2021, 17 (2) : 517-531. doi: 10.3934/jimo.2019121

[5]

Xi Zhao, Teng Niu. Impacts of horizontal mergers on dual-channel supply chain. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020173

[6]

Guangbin CAI, Yang Zhao, Wanzhen Quan, Xiusheng Zhang. Design of LPV fault-tolerant controller for hypersonic vehicle based on state observer. Journal of Industrial & Management Optimization, 2021, 17 (1) : 447-465. doi: 10.3934/jimo.2019120

[7]

Fuensanta Andrés, Julio Muñoz, Jesús Rosado. Optimal design problems governed by the nonlocal $ p $-Laplacian equation. Mathematical Control & Related Fields, 2021, 11 (1) : 119-141. doi: 10.3934/mcrf.2020030

[8]

Amru Hussein, Martin Saal, Marc Wrona. Primitive equations with horizontal viscosity: The initial value and The time-periodic problem for physical boundary conditions. Discrete & Continuous Dynamical Systems - A, 2020  doi: 10.3934/dcds.2020398

[9]

Xiao-Xu Chen, Peng Xu, Jiao-Jiao Li, Thomas Walker, Guo-Qiang Yang. Decision-making in a retailer-led closed-loop supply chain involving a third-party logistics provider. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021014

[10]

Hong Niu, Zhijiang Feng, Qijin Xiao, Yajun Zhang. A PID control method based on optimal control strategy. Numerical Algebra, Control & Optimization, 2021, 11 (1) : 117-126. doi: 10.3934/naco.2020019

[11]

George W. Patrick. The geometry of convergence in numerical analysis. Journal of Computational Dynamics, 2021, 8 (1) : 33-58. doi: 10.3934/jcd.2021003

[12]

Min Chen, Olivier Goubet, Shenghao Li. Mathematical analysis of bump to bucket problem. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5567-5580. doi: 10.3934/cpaa.2020251

[13]

Jian-Xin Guo, Xing-Long Qu. Robust control in green production management. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021011

[14]

Qianqian Han, Xiao-Song Yang. Qualitative analysis of a generalized Nosé-Hoover oscillator. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020346

[15]

Laurence Cherfils, Stefania Gatti, Alain Miranville, Rémy Guillevin. Analysis of a model for tumor growth and lactate exchanges in a glioma. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020457

[16]

Vieri Benci, Sunra Mosconi, Marco Squassina. Preface: Applications of mathematical analysis to problems in theoretical physics. Discrete & Continuous Dynamical Systems - S, 2020  doi: 10.3934/dcdss.2020446

[17]

Thomas Y. Hou, Dong Liang. Multiscale analysis for convection dominated transport equations. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 281-298. doi: 10.3934/dcds.2009.23.281

[18]

Nahed Naceur, Nour Eddine Alaa, Moez Khenissi, Jean R. Roche. Theoretical and numerical analysis of a class of quasilinear elliptic equations. Discrete & Continuous Dynamical Systems - S, 2021, 14 (2) : 723-743. doi: 10.3934/dcdss.2020354

[19]

Mohamed Dellal, Bachir Bar. Global analysis of a model of competition in the chemostat with internal inhibitor. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 1129-1148. doi: 10.3934/dcdsb.2020156

[20]

Xu Zhang, Chuang Zheng, Enrique Zuazua. Time discrete wave equations: Boundary observability and control. Discrete & Continuous Dynamical Systems - A, 2009, 23 (1&2) : 571-604. doi: 10.3934/dcds.2009.23.571

2019 Impact Factor: 1.366

Metrics

  • PDF downloads (219)
  • HTML views (1033)
  • Cited by (0)

Other articles
by authors

[Back to Top]