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The linehaul optimization algorithm is a hybrid algorithm incorporating the basic structure of the Hungarian Assignment algorithm or equivalent and an improvement heuristic. However, in this particular case there is not a direct application of the existing, well-known Hungarian Assignment algorithm or equivalent in conjunction with a heuristic. The structure of the assignment model being used here is based on the Hungarian Assignment algorithm or equivalent but has been revised and enhanced to identify systematically (by using grouping) a number of equivalent optimal solutions (that give the same optimal, minimum cost for a particular iteration). A heuristic is then used to identify the ‘best’ optimal solution, of the many identified, that would contribute the most incremental cost reduction in future iterations of the heuristic. There is no method at present that finds all possible combinations using the Hungarian Assignment algorithm or equivalent because for most applications any optimal solution is sufficient. However, this optimization model uses an iterative procedure where the outcome of each iteration affects the next iteration significantly and a simple application of the original Hungarian Assignment algorithm or equivalent is not acceptable and does not provide the overall optimum. At each iteration, a leg assignment is made (where a trailer is moved over more than one leg) or a reassignment is made to move a trailer in a different time period by either an owner-operator (i.e. company) tractor or a broker (i.e. outside company) tractor. Furthermore, the original Hungarian Assignment algorithm or equivalent is not designed to solve a scheduling problem; it is designed to solve an assignment problem. In other words the algorithm has been revised and combined with a heuristic to solve a scheduling problem.