We address the robust vehicle routing problem with time windows (RVRPTW) under customer demand and travel time uncertainties. As presented thus far in the literature, robust counterparts of standard formulations have challenged general-purpose optimization solvers and specialized branch-and-cut methods. Hence, optimal solutions have been reported for small-scale instances only. Additionally, although the most successful methods for solving many variants of vehicle routing problems are based on the column generation technique, the RVRPTW has never been addressed by this type of method. In this paper, we introduce a novel robust counterpart model based on the well-known budgeted uncertainty set, which has advantageous features in comparison with other formulations and presents better overall performance when solved by commercial solvers. This model results from incorporating dynamic programming recursive equations into a standard deterministic formulation and does not require the classical dualization scheme typically used in robust optimization. In addition, we propose a branch-price-and-cut method based on a set partitioning formulation of the problem, which relies on a robust resource-constrained elementary shortest path problem to generate routes that are robust regarding both vehicle capacity and customer time windows. Computational experiments using Solomon’s instances show that the proposed approach is effective and able to obtain robust solutions within a reasonable running time. The results of an extensive Monte Carlo simulation indicate the relevance of obtaining robust routes for a more reliable decision-making process in real-life settings.
This paper addresses the problem faced by a Brazilian oil and gas company of recovering flights for passenger transportation (mainly teams of employees) to maritime units. Due to unexpected events such as bad weather or aircraft mechanical failures, the original timetable very often cannot be fully met, resulting in flight delays on the same day or even postponements to the following days. As a result, the operation of the maritime units and the scheduling of employee shifts are affected to some extent. Based on a case study conducted at the company, we present a detailed continuous-time mixed-integer programming model that aims to include pending flights in the daily scheduling of an aerodrome with a minimum overall delay and usage of aircraft (helicopters), subject to flights with different rescheduling priorities, aerodrome and aircraft time windows, single runways at the aerodrome and single landing spots at each maritime unit, postponement and shift regulations, heterogeneous fleet of helicopters, mandatory stops for the crew to rest and have lunch, among others. We also present a discrete-time simplification of the former model and some simple solution approaches based on these models in order to cope with larger problem instances. The approach performance is assessed using real-life problem instances whose data were collected in the case study, using a general-purpose optimization software. The results show the potential of these approaches in dealing with this short-term flight rescheduling problem.
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