Abstract: A simple method was proposed to generate all minimal system states fulfilling the demand， time， and budget constraints (all lower boundary points). Inclusionexclusion formula with the lower boundary points was discussed. There are many cancelling terms in the direct expansion of the probability of a union of events， so an algorithm was proposed to determine the canceling terms. All data were supposed to be transmitted through k disjoint minimal paths simultaneously. It was pointed out that if all the pairs of canceling terms that unions of r1 terms and r terms(1<r≤k) were found out， the canceling terms of other unions in inclusionexclusion formula could be determined. The reliability formula was greatly simplified by using the proposed algorithm.

Key words: time constraint, cost constraint, stochasticflow network, inclusionexclusion formula, reliability