A truck loading problem q

A vehicle with m compartments transports q different products of various sizes from a source to n different destinations. The operational problem is how to load the compartments of the vehicle so that the replenishment time is maximized for a given route of destinations. A mixed integer linear programming model is developed for this class of problems. An investigation of the structure of the model reveals that a subproblem can be obtained in the form of a weighted distribution problem. Consequently, a simple subalgorithm finds an integer solution to this subproblem. The main algorithm bisects the interval of uncertainty until it becomes sufficiently small. There is another subalgorithm to test whether a feasible solution exists in the final interval of uncertainty by solving a Phase I problem. Our numerical experience has shown its computational efficiency and the quality of the solutions obtained. A problem of size 30 can be solved by this method in a fraction of a second. Further, an optimal solution is obtained in 82% of the randomly chosen problems.