An Inventory-Theory-Based Inexact Multistage Stochastic Programming Model for Water Resources Management

Table 6

Solution of the IB-IMSP model (period 3).

Water flow level	Probability	Joint flow	Optimized transferring water (10^6 m^3)	Optimized transferring batch (10^3 m^3)	Optimized transferring period (hour)
L	0.008	L-L-L	[7.30,9.70]	[2.40,2.64]	[11.77,13.85]
L	0.024	L-L-M	[4.00,5.70]	[1.73,2.02]	[15.35,18.71]
L	0.008	L-L-H	[0,1.40]	[0,1.03]	[0,30.98]
L	0.024	L-M-L	[4.90,6.50]	[1.92,2.16]	[14.38,16.90]
L	0.072	L-M-M	[1.60,2.50]	[1.10,1.34]	[23.18,29.58]
L	0.024	L-M-H	0	0	0
L	0.008	L-H-L	[0,2.60]	[0,1.37]	[0,22.73]
L	0.024	L-H-M	0	0	0
L	0.008	L-H-H	0	0	0
M	0.024	M-L-L	[3.50,5.90]	[1.62,2.06]	[15.09,20.00]
M	0.072	M-L-M	[0.20,1.90]	[0.39,1.17]	[26.59,83.66]
M	0.024	M-L-H	0	0	0
M	0.072	M-M-L	[1.10,2.70]	[0.91,1.39]	[24.17,27.89]
M	0.216	M-M-M	0	0	0
M	0.072	M-M-H	0	0	0
M	0.024	M-H-L	0	0	0
M	0.072	M-H-M	0	0	0
M	0.024	M-H-H	0	0	0
H	0.008	H-L-L	[0,1.60]	[0,1.07]	[0,28.98]
H	0.024	H-L-M	0	0	0
H	0.008	H-L-H	0	0	0
H	0.024	H-M-L	0	0	0
H	0.072	H-M-M	0	0	0
H	0.024	H-M-H	0	0	0
H	0.008	H-H-L	0	0	0
H	0.024	H-H-M	0	0	0
H	0.008	H-H-H	0	0	0

Total expected value of net benefit ($10⁹): 𝑓^±_opt = [3.53, 5.03].