Modeling soft unloading constraints in the multi-drop container loading problem

The multi-drop container loading problem (MDCLP) requires loading a truck so that boxes can be unloaded at each drop-off point without rearranging other boxes to deliver later. However, modeling such unloading constraints as hard constraints, as done in the literature, considerably limits the flexibility to optimize the packing and utilize the vehicle capacity. We thus propose a more general approach that considers soft unloading constraints. Specifically, we penalize unnecessary relocations of boxes using penalty functions that depend on the volume and weight of the boxes to move as well as the type of move. Our goal is to maximize the total value of the loaded cargo including penalty functions due to violations of the unloading constraints. We provide a mixed-integer linear programming formulation for the MDCLP with soft unloading constraints, which can solve to optimality small scale instances but is intractable for larger ones. We thus propose a heuristic framework to solve large instances, which is based on a randomized extreme-point constructive phase and a subsequent improvement phase. The latter phase iteratively destroys regions in the packing space where high penalties originate, and reconstructs them. Extensive numerical experiments involving different penalties show that our approach significantly outperforms: (i) the hard unloading constraints approach, and (ii) a sequential heuristic that neglects unloading constraints first and evaluates the penalties afterwards. Our findings underscore the relevance of accounting for soft unloading constraints in the MDCLP

Modeling soft unloading constraints in the multi-drop container loading problem

The multi-drop container loading problem (MDCLP) requires loading a truck so that boxes can be unloaded at each drop-off point without rearranging other boxes to deliver later. However, modeling such unloading constraints as hard constraints, as done in the literature, limits the flexibility to optimize the packing and utilize the vehicle capacity. We instead propose a more general approach that considers soft unloading constraints. Specifically, we penalize unnecessary relocations of boxes using penalty functions that depend on the volume and weight of the boxes to move as well as the type of move. Our goal is to maximize the value of the loaded cargo including penalties due to violations of the unloading constraints. We provide a mixed-integer linear programming formulation for the MDCLP with soft unloading constraints, which can solve to optimality small-scale instances but is intractable for larger ones. We thus propose a heuristic framework based on a randomized extreme-point constructive phase and a subsequent improvement phase. The latter phase iteratively destroys regions in the packing space where high penalties originate, and reconstructs them. Extensive numerical experiments involving different instances and penalties highlight the advantages of our method compared to a commercial optimization solver and a heuristic from the literature developed for a related problem. They also show that our approach significantly outperforms: (i) the hard unloading constraints approach, and (ii) a sequential heuristic that neglects unloading constraints first and evaluates the penalties afterwards. Our findings underscore the relevance of accounting for soft unloading constraints in the MDCLP.ISSN:0377-2217ISSN:1872-686

Accelerating logic-based Benders decomposition for railway rescheduling by exploiting similarities in delays

The operation of a railway system is subject to unpredictable delays or disruptions. Operators control the railway system to minimize losses in performance. Real-time rescheduling is the adaptation of a railway schedule to any unforeseen delay or disturbance and recovers an optimal system state. In this work we propose the extension of an existing Benders decomposition scheme used so far for timetabling, to the case of railway rescheduling. We show how to increase its computational speed by a factor 2, by considering libraries of Benders cuts computed for other instances, to be reused in the solution. We show how including extra cuts has to balance a speedup potential, with a general slowdown due to optimization problems of increased sizes. We show that, if delays in an instance of rescheduling are in fact unknown, but come from a known statistical distribution, we can use a similarity measure to identify a-priori the most promising libraries of Benders cuts, which lead to speedups up to 20%.ISSN:0305-0548ISSN:1873-765