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Robust optimization for the vehicle routing problem with multiple deliverymen

Jonathan De La Vega (), Pedro Munari () and Reinaldo Morabito ()
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Jonathan De La Vega: Federal University of São Carlos
Pedro Munari: Federal University of São Carlos
Reinaldo Morabito: Federal University of São Carlos

Central European Journal of Operations Research, 2019, vol. 27, issue 4, 905-936

Abstract: Abstract This paper addresses the vehicle routing problem with time windows and multiple deliverymen in which the customer demands are uncertain and belong to a predetermined polytope. In addition to the routing decisions, this problem attempts to define the number of deliverymen used to service to the customers on each route. A new mathematical formulation is presented for the deterministic counterpart based on auxiliary variables that define the assignment of customers to routes. Building on this formulation, we apply a static robust optimization approach to obtain a robust counterpart formulation that captures the random nature of customer demand. Due to the difficulty in solving this formulation, we propose a constructive heuristic to generate a robust solution, which is used as a starting point for solving the robust counterpart formulation. The heuristic is an extension of Solomon’s heuristic I1. Computational results using problem instances from the literature and risk analysis via Monte-Carlo simulation indicate the potential of static robust optimization to address the trade-off between cost and risk. The results also reveal that the proposed approach provides good results even without exact knowledge of some probabilistic measure of the customer demand.

Keywords: Vehicle routing problem with multiple deliverymen; Static robust linear optimization; Uncertain demand; Heuristics (search for similar items in EconPapers)
Date: 2019
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