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Investigation of Interior Point Algorithms for the Linear Transportation Problem

机译：线性运输问题的内点算法研究

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An efficient implementation of the Dual Affine (DA) interior-point algorithm forthe solution of linear transportation models with integer costs and right-hand side coefficients has recently been proposed. 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 efficient. 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 and PC algorithms are more appropriate for the solution of transportation problems with well scaled cost coefficients. On the other hand, the DA algorithm seems to be more efficient for assignment problems with well scaled cost coefficients and transportation problems whose costs and right-hand side coefficients are both badly scaled.

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