Suchergebnisse

A variety of pivot column selection rules based upon the gradient criteria
(including the steepest edge) have been explored to improve the efficiency of the primal
simplex method. Simplex-like algorithms have been proposed imbedding the gradient
direction (GD) which includes all variables whose increase or decrease leads to an improvement
in the objective function. Recently a frame work has been developed in the
simplex method to incorporate the reduced-gradient direction (RGD) consisting of only
variables whose increase leads to an improvement in the objective function. In this paper,
the results are extended to embed GD in the simplex method based on the concept
of combining directions. Also mathematical properties related to combining directions
as well as deleting a variable from all basic directions are presented.

ABSTRACTThis paper presents network models to determine the optimal replacement policy for a fleet of vehicles over a finite planning horizon. First, a minimum cost‐flow model is developed to determine the optimal replacement schedule for a fleet of fixed size consisting of a single type of vehicle of various ages. The model is then extended to allow for restrictions on capital expenditures that limit the purchase of new vehicles in any time period and to allow for fluctuations in the fleet size due to planned expansion or retrenchment. Finally, a multi‐commodity network model is developed for a fleet consisting of multiple vehicle types and ages.