An investigation of the interior point algorithms for the linear transportation problem Report 93 - 100 L . Portugal

Recently, Resende and Veiga [31] have proposed an e cient implementation of the Dual A ne (DA) interior-pointalgorithm for the solution of linear transportationmodels with integer costs and right-hand side coe cients. This procedure incorporates a Preconditioned Conjugate Gradient (PCG) method for solving the linear system that is required in each iteration of the DA algorithm. In this paper, we introduce an Incomplete QR Decomposition (IQRD) preconditioning for the PCG algorithm. Computational experience shows that the IQRD preconditioning is quite appropriate in this instance and is more e cient than the preconditioning introduced by Resende and Veiga. We also show that the Primal Dual (PD) and the Predictor Corrector (PC) interior point algorithms can also be implemented by using the same type of technique. A comparison among these three algorithms is also included and indicates that the PD an PC algorithms are more appropriate for the solution of transportation problems with well scaled cost coe cients. On the other hand the DA algorithm seems to be more e cient for assignment problems with well scaled cost coe cients and transportation problems whose costs and right-hand side coe cients are both badly scaled.