A multi-product loading problem: A model and solution method

An important operational problem arises during the transportation and delivery of several products, which cannot be mixed, in the same vehicle at regular intervals. The vehicle has compartments to keep the products separately. Therefore, a scheme of allocation of compartments is presented, which we call the vehicle loading problem to maximize the efficiency of the system while the demands for the products at the destination(s) are satisfied. A mixed binary model is developed for this multi-product loading problem. The solution method is based on simultaneously exploring the primal and dual structures derived from the Lagrangian relaxation. Subset sum problems are obtained as subproblems to the partial Lagrangian. An algorithm is developed and its convergence is proved. The efficiency of the method is demonstrated by running randomly chosen test problems. An initial solution finding method is also developed.