# American Institute of Mathematical Sciences

September  2021, 17(5): 2783-2804. 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  September 2021 Early access  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, 2021, 17 (5) : 2783-2804. doi: 10.3934/jimo.2020094
##### References:

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##### 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 $\mathscr{U}(500, 525)-h_1$ $\mathscr{U}(490, 515)-h_1$ $\mathscr{U}(445, 470)-h_1$ $\mathscr{U}(455, 480)-h_1$
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