The freight allocation problem with all‐units quantity‐based discount: A heuristic algorithm

This paper studies a problem encountered by a buying office for one of the largest retail distributors in the world. An important task for the buying office is to plan the distribution of goods from Asia to various destinations across Europe. The goods are transported along shipping lanes by shipping companies, which offer different discount rates depending on the freight quantity. To increase the reliability of transportation, the shipper imposes a quantity limit on each shipping company on each shipping lane. To guarantee a minimum business volume, each shipping company requests a minimum total freight quantity over all lanes if it is contracted. The task involves allocating projected demand of each shipping lane to shipping companies subject to the above conditions such that the total cost is minimized. Existing work on this and related problems employs commercial linear programming software to solve their models. However, since the problem is $\mathcal{N}\mathcal{P}‐\text{hard}$ in the strong sense, it is unlikely to be solvable optimally in reasonable time for large cases. Hence, we propose the first heuristic‐based algorithm for the problem, which combines a filter‐and‐fan search scheme with a tabu search mechanism. Experiments on randomly generated test instances show that as the size of the problem increases, our algorithm produces superior solutions in less time compared to a leading mixed‐integer programming solver.