The assignment and loading transportation problem

Gabriel Homsi, Jeremy Jordan, Silvano Martello and Michele Monaci

European Journal of Operational Research, 2021, vol. 289, issue 3, 999-1007

Abstract: We consider a generalization of the multiple knapsack problem that combines assignment and loading. The problem can arise in military and emergency situations in which one is required to refurnish a unit with a number of different goods available at different locations. We present a mathematical model and study Lagrangian and surrogate relaxations. We propose heuristic and metaheuristic approaches which we use to develop two overall approximation algorithms: a self-contained polynomial-time heuristic and a more time consuming matheuristic approach that makes use of a MILP solver. Solution times and accuracy of lower and upper bounds are computationally evaluated on a real military data set and on sets of both realistic and randomly generated instances.

Keywords: Multiple knapsack problem; Assignment problem; Loading constraints; Integer linear programming formulations; Heuristic algorithms (search for similar items in EconPapers)
Date: 2021
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ejores:v:289:y:2021:i:3:p:999-1007

DOI: 10.1016/j.ejor.2019.07.039

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