A robust optimization approach for the winner determination problem with uncertainty on shipment volumes and carriers’ capacity

• Published in: Transportation research. Part B: methodological Vol. 123; pp. 127 - 148
• Main Authors: Remli, Nabila, Amrouss, Amine, El Hallaoui, Issmail, Rekik, Monia
• Format: Journal Article
• Language: English
• Published: Oxford Elsevier Ltd 01.05.2019; Elsevier Science Ltd; Elsevier
• Subjects: Algorithms; Basic converters; Combinatorial auctions; Computer applications; Computer Science; Constraint generation; Optimization; Procurement; TL services; Transportation; Two-stage robust optimization; Uncertain carriers’ capacity; Uncertain shipment volumes; Uncertainty; Winner determination problem; Combinatorial auctions; Uncertain shipment volumes; Winner determination problem; Two-stage robust optimization; Uncertain carriers’ capacity; TL services; Constraint generation
• ISSN: 0191-2615; 1879-2367
• DOI: 10.1016/j.trb.2019.03.017

•A two-stage robust formulation for the WDP with two uncertain parameters.•An improved exact constraint generation algorithm to solve medium instances.•Improvement strategies consist in adding multiple valid cuts at each iteration.•Adding uncertainty on carriers’ capacity induces changes in winning carriers/bids.•Handling uncertainty on carriers’ capacity reduces operational costs. This paper addresses the winner determination problem (WDP) for TL transportation procurement auctions under uncertain shipment volumes and uncertain carriers’ capacity. It extends an existing two-stage robust formulation proposed for the WDP with uncertain shipment volumes. The paper identifies and theoretically validates a number of accelerating strategies to speed up the convergence of a basic constraint generation algorithm proposed in the literature. Experimental results prove the high computational performance of the proposed new algorithm and the relevance of considering uncertainty on the carriers’ capacity when solving the WDP.