The decision taken in stage 0 is called the initial decision, whereas decisions taken in succeeding stages are called recourse decisions. Recourse decisions are interpreted as corrective actions that are based on the actual values the random parameters realized so far, as well as the past decisions taken thus far.  Recourse decisions provide latitude for obtaining improved overall solutions by realigning the initial decision with possible realizations of uncertainties in the best possible way.

Restricting ourselves to linear multistage stochastic programs for illustration, we have the following form for a multistage stochastic program with (T+1) stages.

Minimize (or maximize):   c0x0 + E1[c1x1 + E2[c2x2 … + ET[cT­xT ] … ]]

such that:

where,

(ω1,...,ωt) represents random outcomes from event space (Ω1,...,Ωt) up to stage-t,

A(ω1,...,ωt)tp is the coefficient matrix generated by outcomes up to stage-t for all p=1…t, t=1…T,

c(ω1,...,ωt)t is the objective coefficients generated by outcomes up to stage-t for all t=1…T,  

b(ω1,...,ωt)t is the right-hand-side values generated by outcomes up to stage-t for all t=1…T,  

L(ω1,...,ωt)t and U(ω1,...,ωt)t  are the lower and upper bounds generated by outcomes up to stage-t for all t=1…T,

  ’~’ is one of the relational operators '≤', ‘=’, or ‘≥’ ; and

x0 and xt ≡ x(ω1,...,ωt)t are the decision variables (unknowns) for which optimal values are sought. The expression being optimized is called the cost due to initial-stage plus the expected cost of recourse.