We view a facility system as a kind of supply chain and model it as a connected graph in which the nodes represent suppliers, distribution centers or customers and the edges represent the paths of goods or information. The efficiency, and hence the reliability, of a facility system is to a large degree adversely affected by the edge failures in the network. In this paper, we consider facility systems' reliability analysis based on the classical p-median problem when subject to edge failures. We formulate two models based on deterministic case and stochastic case to measure the loss in efficiency due to edge failures and give computational results and reliability envelopes for a specific example.

An operational matrix of integration based on the linear Legendre multi-wavelets is established,and the procedure for applying the matrix to solve differential equation of a beam on elastic foundation problem which satisfies two-point boundary conditions is formulated.The fundamental idea of the linear Legendre multi-wavelets method is to convert the differential equation into a matrix equation which involves a finite number of variables.The examples are given to demonstrate the fast and flexible of the method,in the mean time, it is found that the trouble of Daubechies wavelets for solving the differential equation which need to calculate the correlation coefficients is avoided.

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