Patent Document ID: 8949160
Application ID: 13414122
Patent Flag: 1

Claim One:
1. A system for providing scenario tree generation based at least in part upon scenario reduction, the system comprising one or more processor units configured for: receiving for at least a first time period a first forecast, wherein the first forecast comprises a first set of scenarios; reducing the first set of scenarios to a first subset of scenarios, wherein the first subset of scenarios comprises a subset of the first set of scenarios; receiving for at least a second time period a second forecast, wherein the second forecast comprises a second set of scenarios; reducing the second set of scenarios to a second subset of scenarios, wherein the second subset of scenarios comprises a subset of the second set of scenarios; and generating a scenario tree based at least in part upon the first subset of scenarios and the second subset of scenarios; wherein the scenario tree has interperiod independency; wherein the steps of reducing comprise applying an input Ξ to an algorithm to produce an output {tilde over (Ξ)}; and wherein the algorithm comprises: J * t ← argmin ⁢ n ( ξ ~ 1 t , … ⁢ , ξ ~ n t t ) ∈ ℝ n t ⁢ ∑ i = 1 s ⁢ min k = 1 ⁢ … ⁢ ⁢ n t ⁢ p i ⁢  ξ i t - ξ ~ k t  , ⁢ t = 1 , … ⁢ , T. ⁢ ( i. e. , J * t ⁢ ⁢ is ⁢ ⁢ the ⁢ ⁢ set ⁢ ⁢ of ⁢ ⁢ n t - medians ⁢ ⁢ of ⁢ ⁢ Ξ t. ) I t ⁡ ( j t ) ← { i t ∈ I t | j t ∈ argmin ⁢ n k t ⁢ ε ⁢ ⁢ J * t ⁢ ∑ t = 1 T ⁢  ξ i t - ξ ~ k t  } , ⁢ j t ∈ J * t , t = 1 , … ⁢ ⁢ T. ⁢ j ← 0 , ⁢ for ⁢ ⁢ all ⁢ ⁢ ( j 1 , … ⁢ , j T ) ∈ J * 1 × ⋯ × J * T ⁢ ⁢ do j ← j + 1 , ⁢ support ⁡ ( Ξ ~ ) ← support ⁡ ( Ξ ~ ) ⋃ { ξ ~ j } , ⁢ Pr ⁡ ( Ξ ~ = ξ ~ j ) = ⁢ q j = ⁢ ∑ i 1 ∈ I 1 ⁡ ( j 1 ) ⁢ ⁢ ⋯ ⁢ ⁢ ∑ i T ∈ I T ⁡ ( j T ) ⁢ Pr ⁢ ( Ξ = ( ξ i 1 , … ⁢ , ξ i T ) ) , end ⁢ ⁢ for S ~ ← j , ⁢ D K ⁡ ( Ξ , Ξ ~ ) = ⁢ ∑ i = 1 S ⁢ min j = 1 , … ⁢ , S ~ ⁢ ∑ t = 1 T ⁢ p i ⁢  ξ i t - ξ ~ j t  = ⁢ ∑ i = 1 S ⁢ ∑ t = 1 T ⁢ p i ⁢  ξ i t - ξ ~ j t ⁡ ( i )  = ⁢ ∑ t = 1 T ⁢ M t ⁡ ( n t ) .