Optimizing Operation of Water Supply Reservoir: The Role of Constraints

Table 2

Characteristics and properties of operation decisions in the six cases.

Case	Formulation	Characteristics	Properties
0	One-stage (Figures 2 and 3)	No binding release and storage capacity constraints (Figure 2)	Release decisions depend on total WA and follow the marginal value principle
1	One-stage (Figure 4)	Upper release capacity constraint binding in period 𝑡1 and also in other periods (Figure 4)	Increased total WA leads to spill
2	One-stage (Figure 5)	Lower release capacity constraint binding in period 𝑡2 (Figure 5)	Minimum requirement is satisfied in period 𝑡2, which remains with decreased total WA
3	Two-stage (Figure 6)	Upper storage capacity constraint binding in period 𝑡3 (29)	[𝑟^∗1,𝑟^∗2,…,𝑟^∗𝑡3] in stage 1 remain unchanged when WA in periods [𝑡3+1, 𝑡3+2,…,𝐻] (stage 2) decreases
4	Two-stage (Figure 7)	Lower storage capacity constraint binding in period 𝑡4 (31)	[𝑟^∗1,𝑟^∗2,…,𝑟^∗𝑡4] in stage 1 remain unchanged when WA in periods [𝑡4+1, 𝑡4+2,…,𝐻] (stage 2) increases
5	Three-stage (Figure 8)	Upper and lower storage capacity constraints binding in periods 𝑡3 and 𝑡4, respectively (33)	[𝑟^∗1,𝑟^∗2,…,𝑟^∗𝑡] (𝑡 = min(𝑡3,𝑡4)) in stage 1 are not affected by either the decrease or increase in WA in periods [𝑇+1,𝑇+2,…,𝐻] (𝑇=max(𝑡3,𝑡4)) (stage 3)