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

• Published in: Omega (Oxford) Vol. 40; no. 4; pp. 415 - 423
• Main Authors: Qin, Hu, Luo, Meifeng, Gao, Xiang, Lim, Andrew
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.08.2012; Elsevier; Pergamon Press Inc
• Series: Omega
• Subjects: Algorithms; Applied sciences; Discount rates; Exact sciences and technology; Filter-and-fan; Freight; Freight allocation; Freight allocation Quantity discount Heuristic Filter-and-fan Tabu search; Ground, air and sea transportation, marine construction; Heuristic; Heuristik; Integer programming; Internationaler Güterverkehr; Lieferkette; Linear programming; Logistics; Marine and water way transportation and traffic; Mathematical programming; Operational research and scientific management; Operational research. Management science; Operations Research; Optimization algorithms; Quantity discount; Reliability theory. Replacement problems; Shipping; Studies; Tabu search; Transportproblem; Tabu search; Quantity discount; Filter-and-fan; Freight allocation; Heuristic; Costs; Linear programming; Mixed integer programming; Experimental study; Modeling; Search algorithm; Discounting; Distributor; Heuristic method; NP hard problem; Maritime transportation; Reliability; Contract; Logistics
• ISSN: 0305-0483; 1873-5274
• DOI: 10.1016/j.omega.2011.05.005

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 N P − 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. ► Studied a freight allocation problem encountered by a major international retailer. ► Proposed a linear programming formulation for the problem. ► Devised the first heuristic solution for large practical instance. ► Generated benchmark data based on practical scenarios. ► Designed computational experiments to show the effectiveness of the approach.