# American Institute of Mathematical Sciences

doi: 10.3934/jimo.2020094

## Two-stage mean-risk stochastic mixed integer optimization model for location-allocation problems under uncertain environment

 1 School of Mathematics Science, Liaocheng University, Liaocheng, China 2 Business School, University of Shanghai for Science and Technology, Shanghai, China 3 Nanjing University of Information Science and Technology, Nanjing, China 4 National University of Singapore, Singapore

* Corresponding author: Shaojian Qu

Received  August 2019 Revised  February 2020 Published  May 2020

Fund Project: The first author is supported by National Social Science Foundation of China (No. 17BGL083)

The problem of the optimal location-allocation of processing factory and distribution center for supply chain networks under uncertain transportation cost and customer demand are studied. We establish a two-stage mean-risk stochastic 0-1 mixed integer optimization model, by considering the uncertainty and the risk measure of the supply chain. Given the complexity of the model this paper proposes a modified hybrid binary particle swarm optimization algorithm (MHB-PSO) to solve the resulting model, yielding the optimal location and maximal expected return of the supply chain simultaneously. A case study of a bread supply chain in Shanghai is then presented to investigate the specific influence of uncertainties on the food factory and distribution center location. Moreover, we compare the MHB-PSO with hybrid particle swarm optimization algorithm and hybrid genetic algorithm, to validate the proposed algorithm based on the computational time and the convergence rate.

Citation: Zhimin Liu, Shaojian Qu, Hassan Raza, Zhong Wu, Deqiang Qu, Jianhui Du. Two-stage mean-risk stochastic mixed integer optimization model for location-allocation problems under uncertain environment. Journal of Industrial & Management Optimization, doi: 10.3934/jimo.2020094
##### References:

show all references

##### References:
Network structure of location-allocation supply chain
Two-stage process of location-allocation problem
Location of flour factory, food factory, Rt-mart and bread demand area in Shanghai
Location-allocation supply chain network
Comparisons of different algorithms
Values of fitness functions and supply chain profit with different confidence
Gap analysis of various research focus of supply chain
 Reference Location type Random parameters Stochastic approach Risk approach Solving algorithm [27] Relief centers Demand, supply Two-stage Risk-neutral Heuristic [Irawan and Jones2019Formulation] Distribution center // Two-stage Risk-neutral Matheuristic [32] Emergency facility Demand Two-stage CVaR Bender decomposition [6] Warehouse // Two-stage Risk-neutral Branch-and-bound [21] Factory // Two-stage Risk-neutral Heuristic [24] Factory, warehouse // Two-stage Risk-neutral Heuristic [37] Facility Throughput costs One-stage Risk-neutral Heuristic [4] Factory Demand One-stage Risk-neutral Branch-and-bound [5] Facility Demand Two-stage Risk-neutral L-shaped [30] Distribution center // One-stage Risk-neutral Heuristic [50] Facility Lead time Two-stage CVaR Decomposition [19] Facility Demand One-stage Risk-neutral Combined simulated annealing
 Reference Location type Random parameters Stochastic approach Risk approach Solving algorithm [27] Relief centers Demand, supply Two-stage Risk-neutral Heuristic [Irawan and Jones2019Formulation] Distribution center // Two-stage Risk-neutral Matheuristic [32] Emergency facility Demand Two-stage CVaR Bender decomposition [6] Warehouse // Two-stage Risk-neutral Branch-and-bound [21] Factory // Two-stage Risk-neutral Heuristic [24] Factory, warehouse // Two-stage Risk-neutral Heuristic [37] Facility Throughput costs One-stage Risk-neutral Heuristic [4] Factory Demand One-stage Risk-neutral Branch-and-bound [5] Facility Demand Two-stage Risk-neutral L-shaped [30] Distribution center // One-stage Risk-neutral Heuristic [50] Facility Lead time Two-stage CVaR Decomposition [19] Facility Demand One-stage Risk-neutral Combined simulated annealing
Numerical optimal solution and value of the example
 $\mathbf{e}_{best}=(1, 1, 1, 0)$ $\mathbf{c}_{best}=(1, 0, 0,$ $0, 1, 0, 1, 0, 1, 0)$ $x_{111}^*=495.0740$ $x_{112}^*=935.0000$ $x^*_{113}=69.9260$ $x_{123}^*=382.7580$ $y_{111}^*=495.0740$ $y_{125}^*=424.7554$ $y_{127}^*=466.7951$ $y_{129}^*=43.4494$ $y_{135}^*=52.9868$ $y_{139}^*=399.6973$ $z_{111}^*=495.0740$ $z_{152}^*=477.7422$ $z_{171}^*=2.6723$ $z_{172}^*=7.1685$ $Pro=1.2952e+04$ $z_{174}^*=456.9543$ $z_{193}^*=443.1467$ Others=0 $Val=-1.2799e+04$
 $\mathbf{e}_{best}=(1, 1, 1, 0)$ $\mathbf{c}_{best}=(1, 0, 0,$ $0, 1, 0, 1, 0, 1, 0)$ $x_{111}^*=495.0740$ $x_{112}^*=935.0000$ $x^*_{113}=69.9260$ $x_{123}^*=382.7580$ $y_{111}^*=495.0740$ $y_{125}^*=424.7554$ $y_{127}^*=466.7951$ $y_{129}^*=43.4494$ $y_{135}^*=52.9868$ $y_{139}^*=399.6973$ $z_{111}^*=495.0740$ $z_{152}^*=477.7422$ $z_{171}^*=2.6723$ $z_{172}^*=7.1685$ $Pro=1.2952e+04$ $z_{174}^*=456.9543$ $z_{193}^*=443.1467$ Others=0 $Val=-1.2799e+04$
Comparisons of different algorithms
 Algorithm $\mathbf{e}_{best}$ $\mathbf{c}_{best}$ Pro Val TI MHB-PSO $(1, 1, 1, 0)$ $(1, 0, 0, 0, 1, 0, 1, 0, 1, 0)$ $1.2952e+04$ $-1.2799e+04$ $9849.4900$ Hybrid PSO $(0, 1, 1, 1)$ $(0, 0, 1, 0, 0, 1, 1, 0, 1, 0)$ $1.2861e+04$ $-1.2683e+04$ $11169.2300$ Hybrid GA $(0, 1, 0, 1)$ $(0, 0, 1, 0, 0, 1, 0, 0, 1, 1)$ $1.2855e+04$ $-1.2660e+04$ $12035.1647$
 Algorithm $\mathbf{e}_{best}$ $\mathbf{c}_{best}$ Pro Val TI MHB-PSO $(1, 1, 1, 0)$ $(1, 0, 0, 0, 1, 0, 1, 0, 1, 0)$ $1.2952e+04$ $-1.2799e+04$ $9849.4900$ Hybrid PSO $(0, 1, 1, 1)$ $(0, 0, 1, 0, 0, 1, 1, 0, 1, 0)$ $1.2861e+04$ $-1.2683e+04$ $11169.2300$ Hybrid GA $(0, 1, 0, 1)$ $(0, 0, 1, 0, 0, 1, 0, 0, 1, 1)$ $1.2855e+04$ $-1.2660e+04$ $12035.1647$
Results of MHB-PSO with different parameters
 System Parameters Results T N $c_{min}$ $c_{max}$ $\mathbf{e}_{best}$ $\mathbf{c}_{best}$ Val Error(%) 50 10 2.0 2.1 $(1, 1, 1, 0)$ $(1, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $-1.2690e+04$ 0.99 100 10 2.0 2.1 $(0, 1, 1, 1)$ $(0, 0, 1, 0, 0, 1, 1, 0, 1, 0)$ $-1.2712e+04$ 0.76 1000 10 2.0 2.1 $(1, 1, 1, 0)$ $(0, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $-1.2780e+04$ 0.23 2000 10 2.0 2.1 $(1, 1, 1, 0)$ $(0, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $-1.2780e+04$ 0.23 1000 100 2.0 2.1 $(1, 1, 1, 0)$ $(1, 0, 0, 0, 1, 0, 1, 0, 1, 0)$ $-1.2799e+04$ 0.08 1000 1000 2.0 2.1 $(1, 1, 1, 0)$ $(1, 0, 0, 0, 1, 0, 1, 0, 1, 0)$ $-1.2799e+04$ 0.08 1000 10 2.0 2.5 $(0, 1, 0, 1)$ $(0, 0, 1, 0, 1, 0, 0, 0, 1, 1)$ $-1.2801e+04$ 0.06 1000 10 2.0 3.0 $(1, 1, 0, 1)$ $(0, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $-1.2809e+04$ 0.00 1000 10 2.0 4.0 $(1, 1, 1, 0)$ $(0, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $-1.2780e+04$ 0.23 1000 10 2.5 3.0 $(1, 1, 0, 1)$ $(0, 0, 0, 1, 1, 0, 1, 0, 1, 0)$ $-1.2721e+04$ 0.69 1000 10 2.5 4.0 $(1, 1, 1, 0)$ $(0, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $-1.2760e+04$ 0.38
 System Parameters Results T N $c_{min}$ $c_{max}$ $\mathbf{e}_{best}$ $\mathbf{c}_{best}$ Val Error(%) 50 10 2.0 2.1 $(1, 1, 1, 0)$ $(1, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $-1.2690e+04$ 0.99 100 10 2.0 2.1 $(0, 1, 1, 1)$ $(0, 0, 1, 0, 0, 1, 1, 0, 1, 0)$ $-1.2712e+04$ 0.76 1000 10 2.0 2.1 $(1, 1, 1, 0)$ $(0, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $-1.2780e+04$ 0.23 2000 10 2.0 2.1 $(1, 1, 1, 0)$ $(0, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $-1.2780e+04$ 0.23 1000 100 2.0 2.1 $(1, 1, 1, 0)$ $(1, 0, 0, 0, 1, 0, 1, 0, 1, 0)$ $-1.2799e+04$ 0.08 1000 1000 2.0 2.1 $(1, 1, 1, 0)$ $(1, 0, 0, 0, 1, 0, 1, 0, 1, 0)$ $-1.2799e+04$ 0.08 1000 10 2.0 2.5 $(0, 1, 0, 1)$ $(0, 0, 1, 0, 1, 0, 0, 0, 1, 1)$ $-1.2801e+04$ 0.06 1000 10 2.0 3.0 $(1, 1, 0, 1)$ $(0, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $-1.2809e+04$ 0.00 1000 10 2.0 4.0 $(1, 1, 1, 0)$ $(0, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $-1.2780e+04$ 0.23 1000 10 2.5 3.0 $(1, 1, 0, 1)$ $(0, 0, 0, 1, 1, 0, 1, 0, 1, 0)$ $-1.2721e+04$ 0.69 1000 10 2.5 4.0 $(1, 1, 1, 0)$ $(0, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $-1.2760e+04$ 0.38
Supply chain profit with random and expected transportation cost and demand
 $\xi(\omega)$ $\mathbf{e}_{best}$ $\mathbf{c}_{best}$ Pro Random $(1, 1, 1, 0)$ $(1, 0, 0, 0, 1, 0, 1, 0, 1, 0)$ $1.2952e+04$ Expected $(0, 1, 0, 1)$ $(0, 0, 0, 1, 0, 1, 0, 0, 1, 1)$ $1.2819e+04$
 $\xi(\omega)$ $\mathbf{e}_{best}$ $\mathbf{c}_{best}$ Pro Random $(1, 1, 1, 0)$ $(1, 0, 0, 0, 1, 0, 1, 0, 1, 0)$ $1.2952e+04$ Expected $(0, 1, 0, 1)$ $(0, 0, 0, 1, 0, 1, 0, 0, 1, 1)$ $1.2819e+04$
Comparison of supply chain profit of model with $\lambda = 0.1$ and $\lambda = 0$
 $\lambda$ $\mathbf{e}_{best}$ $\mathbf{c}_{best}$ Pro $\lambda=0$ $(1, 1, 1, 0)$ $(0, 0, 1, 1, 0, 1, 1, 0, 1, 0)$ $1.3007e+04$ $\lambda=0.1$ $(1, 1, 1, 0)$ $(1, 0, 0, 0, 1, 0, 1, 0, 1, 0)$ $1.2952e+04$
 $\lambda$ $\mathbf{e}_{best}$ $\mathbf{c}_{best}$ Pro $\lambda=0$ $(1, 1, 1, 0)$ $(0, 0, 1, 1, 0, 1, 1, 0, 1, 0)$ $1.3007e+04$ $\lambda=0.1$ $(1, 1, 1, 0)$ $(1, 0, 0, 0, 1, 0, 1, 0, 1, 0)$ $1.2952e+04$
Effect of raw material cost and retail price on supply chain profit
 $(r_{11}, r_{12})$ $h_1$ ${\mathbf e}_{best}$ ${\mathbf c}_{best}$ Pro (4.6, 4.8) 14.0 $(1, 1, 1, 0)$ $(0, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $1.1989e+04$ (4.6, 4.8) 14.5 $(1, 1, 1, 0)$ $(1, 0, 0, 0, 1, 0, 1, 0, 1, 0)$ $1.2952e+04$ (4.6, 4.8) 15.0 $(1, 1, 1, 0)$ $(1, 0, 0, 0, 1, 0, 1, 0, 1, 0)$ $1.3809e+04$ (4.3, 4.8) 14.5 $(0, 1, 1, 1)$ $(0, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $1.3233e+04$ (4.9, 4.8) 14.5 $(0, 1, 0, 1)$ $(0, 0, 0, 1, 0, 1, 0, 0, 1, 1)$ $1.2500e+04$ (4.6, 4.5) 14.5 $(0, 1, 0, 1)$ $(0, 0, 0, 1, 0, 1, 0, 0, 1, 1)$ $1.3063e+04$ (4.6, 5.0) 14.5 $(1, 1, 1, 0)$ $(0, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $1.2914e+04$ (4.3, 4.5) 14.5 $(0, 1, 1, 1)$ $(0, 0, 0, 1, 0, 0, 1, 1, 1, 0)$ $1.3424e+04$ (4.9, 5.0) 14.5 $(0, 1, 0, 1)$ $(0, 0, 0, 1, 0, 1, 0, 0, 1, 1)$ $1.2361e+04$
 $(r_{11}, r_{12})$ $h_1$ ${\mathbf e}_{best}$ ${\mathbf c}_{best}$ Pro (4.6, 4.8) 14.0 $(1, 1, 1, 0)$ $(0, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $1.1989e+04$ (4.6, 4.8) 14.5 $(1, 1, 1, 0)$ $(1, 0, 0, 0, 1, 0, 1, 0, 1, 0)$ $1.2952e+04$ (4.6, 4.8) 15.0 $(1, 1, 1, 0)$ $(1, 0, 0, 0, 1, 0, 1, 0, 1, 0)$ $1.3809e+04$ (4.3, 4.8) 14.5 $(0, 1, 1, 1)$ $(0, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $1.3233e+04$ (4.9, 4.8) 14.5 $(0, 1, 0, 1)$ $(0, 0, 0, 1, 0, 1, 0, 0, 1, 1)$ $1.2500e+04$ (4.6, 4.5) 14.5 $(0, 1, 0, 1)$ $(0, 0, 0, 1, 0, 1, 0, 0, 1, 1)$ $1.3063e+04$ (4.6, 5.0) 14.5 $(1, 1, 1, 0)$ $(0, 0, 0, 1, 0, 1, 1, 0, 1, 0)$ $1.2914e+04$ (4.3, 4.5) 14.5 $(0, 1, 1, 1)$ $(0, 0, 0, 1, 0, 0, 1, 1, 1, 0)$ $1.3424e+04$ (4.9, 5.0) 14.5 $(0, 1, 0, 1)$ $(0, 0, 0, 1, 0, 1, 0, 0, 1, 1)$ $1.2361e+04$
Parameters for suppliers, processing factories, and distribution centers
 Index Suppliers Processing plants Distribution centers $s, i, j$ $a_{1s}$ $r_{1s}$ $b_{i1}$ $q_{i1}$ $f_i$ $\tau_{1j}$ $w_{1j}$ $g_j$ 1 1500 4.6 850 0.80 185 500 0.25 135 2 1200 4.8 935 0.75 180 480 0.25 130 3 $/$ $/$ 845 0.81 200 450 0.25 120 4 $/$ $/$ 950 0.76 160 470 0.25 125 5 $/$ $/$ $/$ $/$ $/$ 510 0.25 140 6 $/$ $/$ $/$ $/$ $/$ 490 0.25 130 7 $/$ $/$ $/$ $/$ $/$ 520 0.25 145 8 $/$ $/$ $/$ $/$ $/$ 505 0.25 143 9 $/$ $/$ $/$ $/$ $/$ 460 0.25 123 10 $/$ $/$ $/$ $/$ $/$ 485 0.25 133
 Index Suppliers Processing plants Distribution centers $s, i, j$ $a_{1s}$ $r_{1s}$ $b_{i1}$ $q_{i1}$ $f_i$ $\tau_{1j}$ $w_{1j}$ $g_j$ 1 1500 4.6 850 0.80 185 500 0.25 135 2 1200 4.8 935 0.75 180 480 0.25 130 3 $/$ $/$ 845 0.81 200 450 0.25 120 4 $/$ $/$ 950 0.76 160 470 0.25 125 5 $/$ $/$ $/$ $/$ $/$ 510 0.25 140 6 $/$ $/$ $/$ $/$ $/$ 490 0.25 130 7 $/$ $/$ $/$ $/$ $/$ 520 0.25 145 8 $/$ $/$ $/$ $/$ $/$ 505 0.25 143 9 $/$ $/$ $/$ $/$ $/$ 460 0.25 123 10 $/$ $/$ $/$ $/$ $/$ 485 0.25 133
Random transportation cost from flour factory to food factory
 Flour factory Yingyuan food factory Changli food factory Ziyan food factory Sunhong food factory Fuxin third $\mathscr{U}(0.18, 0.21)$ $\mathscr{U}(0.12, 0.16)$ $\mathscr{U}(0.25, 0.28)$ $\mathscr{U}(0.40, 0.43)$ Fuxin $\mathscr{U}(0.45, 0.49)$ $\mathscr{U}(0.25, 0.28)$ $\mathscr{U}(0.11, 0.15)$ $\mathscr{U}(0.27, 0.30)$
 Flour factory Yingyuan food factory Changli food factory Ziyan food factory Sunhong food factory Fuxin third $\mathscr{U}(0.18, 0.21)$ $\mathscr{U}(0.12, 0.16)$ $\mathscr{U}(0.25, 0.28)$ $\mathscr{U}(0.40, 0.43)$ Fuxin $\mathscr{U}(0.45, 0.49)$ $\mathscr{U}(0.25, 0.28)$ $\mathscr{U}(0.11, 0.15)$ $\mathscr{U}(0.27, 0.30)$
Random transportation cost of food factory transporting product to Rt-mart supermarket
 Rt-mart Yingyuan food factory Changli food factory Ziyan food factory Sunhong food factory Meilanhu $\mathscr{U}(0.26, 0.30)$ $\mathscr{U}(0.37, 0.40)$ $\mathscr{U}(0.46, 0.49)$ $\mathscr{U}(0.65, 0.68)$ Anting $\mathscr{U}(0.46, 0.49)$ $\mathscr{U}(0.41, 0.45)$ $\mathscr{U}(0.40, 0.44)$ $\mathscr{U}(0.68, 0.72)$ Nanxiang $\mathscr{U}(0.31, 0.34)$ $\mathscr{U}(0.27, 0.31)$ $\mathscr{U}(0.33, 0.36)$ $\mathscr{U}(0.56, 0.60)$ Yangpu $\mathscr{U}(0.08, 0.11)$ $\mathscr{U}(0.17, 0.20)$ $\mathscr{U}(0.34, 0.37)$ $\mathscr{U}(0.41, 0.44)$ Sijing $\mathscr{U}(0.45, 0.49)$ $\mathscr{U}(0.27, 0.31)$ $\mathscr{U}(0.18, 0.21)$ $\mathscr{U}(0.48, 0.52)$ Chunshen $\mathscr{U}(0.36, 0.39)$ $\mathscr{U}(0.12, 0.16)$ $\mathscr{U}(0.06, 0.09)$ $\mathscr{U}(0.33, 0.37)$ Kangqiao $\mathscr{U}(0.26, 0.29)$ $\mathscr{U}(0.11, 0.15)$ $\mathscr{U}(0.24, 0.28)$ $\mathscr{U}(0.19, 0.23)$ Songjiang $\mathscr{U}(0.58, 0.62)$ $\mathscr{U}(0.37, 0.41)$ $\mathscr{U}(0.21, 0.25)$ $\mathscr{U}(0.51, 0.55)$ Fengxian $\mathscr{U}(0.58, 0.62)$ $\mathscr{U}(0.36, 0.40)$ $\mathscr{U}(0.24, 0.27)$ $\mathscr{U}(0.30, 0.34)$ Nicheng $\mathscr{U}(0.63, 0.67)$ $\mathscr{U}(0.52, 0.55)$ $\mathscr{U}(0.54, 0.57)$ $\mathscr{U}(0.22, 0.25)$
 Rt-mart Yingyuan food factory Changli food factory Ziyan food factory Sunhong food factory Meilanhu $\mathscr{U}(0.26, 0.30)$ $\mathscr{U}(0.37, 0.40)$ $\mathscr{U}(0.46, 0.49)$ $\mathscr{U}(0.65, 0.68)$ Anting $\mathscr{U}(0.46, 0.49)$ $\mathscr{U}(0.41, 0.45)$ $\mathscr{U}(0.40, 0.44)$ $\mathscr{U}(0.68, 0.72)$ Nanxiang $\mathscr{U}(0.31, 0.34)$ $\mathscr{U}(0.27, 0.31)$ $\mathscr{U}(0.33, 0.36)$ $\mathscr{U}(0.56, 0.60)$ Yangpu $\mathscr{U}(0.08, 0.11)$ $\mathscr{U}(0.17, 0.20)$ $\mathscr{U}(0.34, 0.37)$ $\mathscr{U}(0.41, 0.44)$ Sijing $\mathscr{U}(0.45, 0.49)$ $\mathscr{U}(0.27, 0.31)$ $\mathscr{U}(0.18, 0.21)$ $\mathscr{U}(0.48, 0.52)$ Chunshen $\mathscr{U}(0.36, 0.39)$ $\mathscr{U}(0.12, 0.16)$ $\mathscr{U}(0.06, 0.09)$ $\mathscr{U}(0.33, 0.37)$ Kangqiao $\mathscr{U}(0.26, 0.29)$ $\mathscr{U}(0.11, 0.15)$ $\mathscr{U}(0.24, 0.28)$ $\mathscr{U}(0.19, 0.23)$ Songjiang $\mathscr{U}(0.58, 0.62)$ $\mathscr{U}(0.37, 0.41)$ $\mathscr{U}(0.21, 0.25)$ $\mathscr{U}(0.51, 0.55)$ Fengxian $\mathscr{U}(0.58, 0.62)$ $\mathscr{U}(0.36, 0.40)$ $\mathscr{U}(0.24, 0.27)$ $\mathscr{U}(0.30, 0.34)$ Nicheng $\mathscr{U}(0.63, 0.67)$ $\mathscr{U}(0.52, 0.55)$ $\mathscr{U}(0.54, 0.57)$ $\mathscr{U}(0.22, 0.25)$
Random distribution cost of distribution center transporting product to consumer
 Rt-mart Demand area 1 Demand area 2 Demand area 3 Demand area 4 Meilanhu $\mathscr{U}(1.00, 1.50)$ $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(2.00, 2.50)$ $\mathscr{U}(1.70, 2.20)$ Anting $\mathscr{U}(1.00, 1.50)$ $\mathscr{U}(1.40, 1.90)$ $\mathscr{U}(1.90, 2.40)$ $\mathscr{U}(1.80, 2.30)$ Nanxiang $\mathscr{U}(1.00, 1.50)$ $\mathscr{U}(1.40, 1.90)$ $\mathscr{U}(1.90, 2.40)$ $\mathscr{U}(1.70, 2.20)$ Yangpu $\mathscr{U}(1.10, 1.60)$ $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(2.00, 2.50)$ $\mathscr{U}(1.20, 1.70)$ Sijing $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(1.00, 1.50)$ $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(1.50, 2.00)$ Chunshen $\mathscr{U}(1.40, 1.90)$ $\mathscr{U}(1.10, 1.60)$ $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(1.40, 1.90)$ Kangqiao $\mathscr{U}(1.40, 1.90)$ $\mathscr{U}(1.40, 1.90)$ $\mathscr{U}(1.60, 2.10)$ $\mathscr{U}(1.10, 1.60)$ Songjiang $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(1.00, 1.50)$ $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(1.60, 2.10)$ Fengxian $\mathscr{U}(1.70, 2.20)$ $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(1.00, 1.50)$ $\mathscr{U}(1.60, 2.10)$ Nicheng $\mathscr{U}(1.70, 2.20)$ $\mathscr{U}(1.70, 2.20)$ $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(1.00, 1.50)$
 Rt-mart Demand area 1 Demand area 2 Demand area 3 Demand area 4 Meilanhu $\mathscr{U}(1.00, 1.50)$ $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(2.00, 2.50)$ $\mathscr{U}(1.70, 2.20)$ Anting $\mathscr{U}(1.00, 1.50)$ $\mathscr{U}(1.40, 1.90)$ $\mathscr{U}(1.90, 2.40)$ $\mathscr{U}(1.80, 2.30)$ Nanxiang $\mathscr{U}(1.00, 1.50)$ $\mathscr{U}(1.40, 1.90)$ $\mathscr{U}(1.90, 2.40)$ $\mathscr{U}(1.70, 2.20)$ Yangpu $\mathscr{U}(1.10, 1.60)$ $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(2.00, 2.50)$ $\mathscr{U}(1.20, 1.70)$ Sijing $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(1.00, 1.50)$ $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(1.50, 2.00)$ Chunshen $\mathscr{U}(1.40, 1.90)$ $\mathscr{U}(1.10, 1.60)$ $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(1.40, 1.90)$ Kangqiao $\mathscr{U}(1.40, 1.90)$ $\mathscr{U}(1.40, 1.90)$ $\mathscr{U}(1.60, 2.10)$ $\mathscr{U}(1.10, 1.60)$ Songjiang $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(1.00, 1.50)$ $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(1.60, 2.10)$ Fengxian $\mathscr{U}(1.70, 2.20)$ $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(1.00, 1.50)$ $\mathscr{U}(1.60, 2.10)$ Nicheng $\mathscr{U}(1.70, 2.20)$ $\mathscr{U}(1.70, 2.20)$ $\mathscr{U}(1.50, 2.00)$ $\mathscr{U}(1.00, 1.50)$
Random demand of consumer
 Demand area 1 Demand area 2 Demand area 3 Demand area 4 $\mathscr{U}(500, 525)-h_1$ $\mathscr{U}(490, 515)-h_1$ $\mathscr{U}(445, 470)-h_1$ $\mathscr{U}(455, 480)-h_1$
 Demand area 1 Demand area 2 Demand area 3 Demand area 4 $\mathscr{U}(500, 525)-h_1$ $\mathscr{U}(490, 515)-h_1$ $\mathscr{U}(445, 470)-h_1$ $\mathscr{U}(455, 480)-h_1$
 [1] Ripeng Huang, Shaojian Qu, Xiaoguang Yang, Zhimin Liu. Multi-stage distributionally robust optimization with risk aversion. Journal of Industrial & Management Optimization, 2021, 17 (1) : 233-259. doi: 10.3934/jimo.2019109 [2] Haodong Yu, Jie Sun. Robust stochastic optimization with convex risk measures: A discretized subgradient scheme. Journal of Industrial & Management Optimization, 2021, 17 (1) : 81-99. doi: 10.3934/jimo.2019100 [3] Yasmine Cherfaoui, Mustapha Moulaï. Biobjective optimization over the efficient set of multiobjective integer programming problem. Journal of Industrial & Management Optimization, 2021, 17 (1) : 117-131. doi: 10.3934/jimo.2019102 [4] Hongguang Ma, Xiang Li. Multi-period hazardous waste collection planning with consideration of risk stability. Journal of Industrial & Management Optimization, 2021, 17 (1) : 393-408. doi: 10.3934/jimo.2019117 [5] Marek Macák, Róbert Čunderlík, Karol Mikula, Zuzana Minarechová. Computational optimization in solving the geodetic boundary value problems. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 987-999. doi: 10.3934/dcdss.2020381 [6] Haixiang Yao, Ping Chen, Miao Zhang, Xun Li. Dynamic discrete-time portfolio selection for defined contribution pension funds with inflation risk. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020166 [7] Youming Guo, Tingting Li. Optimal control strategies for an online game addiction model with low and high risk exposure. Discrete & Continuous Dynamical Systems - B, 2020  doi: 10.3934/dcdsb.2020347 [8] Wenyuan Wang, Ran Xu. General drawdown based dividend control with fixed transaction costs for spectrally negative Lévy risk processes. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2020179 [9] Vadim Azhmyakov, Juan P. Fernández-Gutiérrez, Erik I. Verriest, Stefan W. Pickl. A separation based optimization approach to Dynamic Maximal Covering Location Problems with switched structure. Journal of Industrial & Management Optimization, 2021, 17 (2) : 669-686. doi: 10.3934/jimo.2019128 [10] 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 [11] Bixiang Wang. Mean-square random invariant manifolds for stochastic differential equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1449-1468. doi: 10.3934/dcds.2020324 [12] Jingrui Sun, Hanxiao Wang. Mean-field stochastic linear-quadratic optimal control problems: Weak closed-loop solvability. Mathematical Control & Related Fields, 2021, 11 (1) : 47-71. doi: 10.3934/mcrf.2020026 [13] Ahmad Z. Fino, Wenhui Chen. A global existence result for two-dimensional semilinear strongly damped wave equation with mixed nonlinearity in an exterior domain. Communications on Pure & Applied Analysis, 2020, 19 (12) : 5387-5411. doi: 10.3934/cpaa.2020243 [14] Ying Liu, Yanping Chen, Yunqing Huang, Yang Wang. Two-grid method for semiconductor device problem by mixed finite element method and characteristics finite element method. Electronic Research Archive, 2021, 29 (1) : 1859-1880. doi: 10.3934/era.2020095 [15] Tong Peng. Designing prorated lifetime warranty strategy for high-value and durable products under two-dimensional warranty. Journal of Industrial & Management Optimization, 2021, 17 (2) : 953-970. doi: 10.3934/jimo.2020006 [16] Nguyen Thi Kim Son, Nguyen Phuong Dong, Le Hoang Son, Alireza Khastan, Hoang Viet Long. Complete controllability for a class of fractional evolution equations with uncertainty. Evolution Equations & Control Theory, 2020  doi: 10.3934/eect.2020104 [17] Jie Li, Xiangdong Ye, Tao Yu. Mean equicontinuity, complexity and applications. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 359-393. doi: 10.3934/dcds.2020167 [18] Mugen Huang, Moxun Tang, Jianshe Yu, Bo Zheng. A stage structured model of delay differential equations for Aedes mosquito population suppression. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3467-3484. doi: 10.3934/dcds.2020042 [19] Shahede Omidi, Jafar Fathali. Inverse single facility location problem on a tree with balancing on the distance of server to clients. Journal of Industrial & Management Optimization, 2020  doi: 10.3934/jimo.2021017 [20] Russell Ricks. The unique measure of maximal entropy for a compact rank one locally CAT(0) space. Discrete & Continuous Dynamical Systems - A, 2021, 41 (2) : 507-523. doi: 10.3934/dcds.2020266

2019 Impact Factor: 1.366

## Tools

Article outline

Figures and Tables