ler integer greater than X. The parameters Xxo and Xx1 are normalized cost con- stants typical of the OXC. The cost of LSR is given by where U is the number of bidirectional line ports of the LSR and is the number of bidirectional line ports supported by a single platform unit (e.g., a single rack). The parameters XLO and XL1 are constants typical of the LSR. The number Uj of bidirectional ports of the jth LSR can be calculated as the sum of the locally generated LSPs plus the number of transit LSPs that are sent to the LSR to perform grooming optimization. (8.14) Telecommunication Networks Similarly, the number qj of bidirectional ports of the jth OXC is given by Superscript(1) (8.15) Finally, neglecting the [x] operator to maintain the linearity of the cost function, the ILP target function writes (8.16) The target function is linear in the design variables as desired. In this condition the result- ing problem is an ILP problem if suitable constraints are set. Arriving at an ILP requires elimination from the cost function the lower integer part to the addenda representing the platform cost of the equipment. This is not a small approximation and it is worth a comment. Generally, deploying a new DWDM system or a new OXC is an expensive operation with respect to adding a new wavelength to an existing DWDM or a new card to an existing OXC. This is exactly due to the integer part operation that we have neglected in the cost function: that operator represents the fact that the whole platform cost is paid when the first equipment card is installed. Thus, while in practice the deployment of a new system is always avoided if possible, in our problem, this would not be true, since the first card will have the same cost of all the others. This approximation is important mainly in the case of DWDM systems whose platform has a high cost due to amplifiers and other line equipment. In specific cases, this approximation can cause the solution to be far from optimum. This situation is detected when there are a lot of DWDM syste