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srpchase.gms : Scenario Tree Construction Example

SCENRED2 - Scenario Tree Construction Example
3-stage stochastic purchase example problem

Analytical solution:
    OPT  = 4.167 (Optimal value)
    VOPI = 3.667 (Value of perfect information)

H. Heitsch, W. Roemisch, and C. Strugarek
Stability of Multistage Stochastic Programs
SIAM Journal on Optimization 17 (2006), 511-525
Reference:
Small Model of Type: LP
$Title Scenario Tree Construction Example (SRPCHASE,SEQ=344) $Ontext SCENRED2 - Scenario Tree Construction Example 3-stage stochastic purchase example problem Analytical solution: OPT = 4.167 (Optimal value) VOPI = 3.667 (Value of perfect information) H. Heitsch, W. Roemisch, and C. Strugarek Stability of Multistage Stochastic Programs SIAM Journal on Optimization 17 (2006), 511-525 $Offtext * Dimension (even number) $if not set DIM $set DIM 1000 $ife mod(%DIM%,2)=1 $eval DIM %DIM%+1 Sets n nodes / n0*n%DIM% / t time periods / t1*t3 / stage(n,t) stage mapping ancestor(n,n) ancestor matrix leaf(n) leaf nodes; * Build a fan * Assign stage mapping and leaf nodes stage('n0','t1') = yes; stage( n ,'t2') = ord(n)>1 and ord(n)<=%DIM%/2+1; stage( n ,'t3') = ord(n)>%DIM%/2+1; leaf(n) = stage(n,'t3'); * Build ancenstor relations to represent the fan ancestor(n,'n0')$stage(n,'t2') = yes; ancestor(n,n-card(leaf))$stage(n,'t3') = yes; * Random variables (price) and probabilities Parameters price(n) node prices prob(n) node probabilities; prob(n) = 1/card(leaf); * First stage price('n0') = 1; prob('n0') = 1; * Second stage - price is uniformly distributed in [0,1] price(n)$stage(n,'t2') = uniform(0,1); * Third stage - price is conditional linearly distributed Scalar alpha, beta; loop(stage(n,'t3'), alpha = 1-price(n-card(leaf)); beta = 1-2*price(n-card(leaf)); price(n) = uniform(0,1); price(n)$beta = alpha/beta - sign(beta)*sqrt(sqr(alpha/beta) - price(n)/beta); ); * Initialize ScenRed2 $set sr2prefix srpchase $libinclude scenred2 file fopts Scenred option file / 'sr2%sr2prefix%.opt' /; putclose fopts 'order 1' / 'section epsilon' / ' 2 0.05' / ' 3 0.05' / 'end'; * Scenred2 method choice ScenRedParms('construction_method') = 2; ScenRedParms('reduction_method' ) = 2; ScenRedParms('sroption' ) = 1; * Scenred2 call $libinclude runscenred2 %sr2prefix% tree_con n ancestor prob ancestor prob price Variables x(n) amount of purchase y(n) slack variable cost objective value; Positive variables x,y; Equations objective expected cost slack(n) slack equation demand(n) demand inequality; Set srn(n) subset of nodes after tree construction; srn(n) = prob(n); objective.. cost =e= sum(srn, prob(srn)*price(srn)*x(srn)); slack(srn)$(not leaf(srn)).. y(srn) =e= x(srn) + sum(ancestor(srn,n), y(n)); demand(leaf(srn)).. x(srn) + sum(ancestor(srn,n), y(n)) =g= 1; Model purchase / all /; Solve purchase minimizing cost using lp;