Exact and Approximation Algorithms for the Loader Problem

The paper considers the loader problem that is commonly faced by a 3PL company. Based on the linear programming relaxation of the integer linear programming model for the problem, an approximation algorithm is first present for the loader problem using the random rounding techniques, and then its performance is analyzed. Secondly, a simple upper rounding algorithm is present for a special case of the loader problem without labor constraint with its performance analysis. Thirdly, a branch and bound algorithm is proposed by observing the upper bounds, lower bounds, branch rules and dominate rules. Finally, computational experiments are given to show the efficiency of these algorithms