The scale of freight forwarding to the hinterland becomes an issue from the perspective of both – transport policy and cost efficiency of service providers. This problem is sharply visible in areas where ports, depots, inland intermodal terminals, exporters and importers are located, and full and empty containers satisfying demand and supply are frequently distributed creating a lot of traffic. Therefore solutions meeting the challenges of sustainable transport, responding to climate change and regulation of CO2 emissions are in need. In this paper, a variant of a Mixed Fleet Heterogeneous Dial-a-Ride Problem is proposed for optimal routing of trucks carrying full and empty 20-foot and 40-foot containers, with multiple pick-ups and deliveries. Transportation is performed by alternatively fueled vehicles (AFVs) for environmental reasons which causes a constraint of a limited driving range and a need of refueling. The main objective is minimising the total distance subject to matching the empty container demand and supply, necessary refueling of the trucks, and service time windows.

Constraint programming solvers are known to perform remarkably well for most scheduling problems. However, when comparing the performance of different available solvers, there is usually no clear winner over all relevant problem instances. This gives rise to the question of how to select a promising solver when knowing the concrete instance to be solved. In this article, we aim to provide first insights into this question for the flexible job shop scheduling problem. We investigate relative performance differences among five constraint programming solvers on problem instances taken from the literature as well as randomly generated problem instances. These solvers include commercial and non-commercial software and represent the state-of-the-art as identified in the relevant literature. We find that two solvers, the IBM ILOG CPLEX CP Optimizer and Google’s OR-Tools, outperform alternative solvers. These two solvers show complementary strengths regarding their ability to determine provably optimal solutions within practically reasonable time limits and their ability to quickly determine high quality feasible solutions across different test instances. Hence, we leverage the resulting performance complementarity by proposing algorithm selection approaches that predict the best solver for a given problem instance based on instance features or parameters. The approaches are based on two machine learning techniques, decision trees and deep neural networks, in various variants. In a computational study, we analyze the performance of the resulting algorithm selection models and show that our approaches outperform the use of a single solver and should thus be considered as a relevant tool by decision makers in practice.

We study the scheduling problem with calibrations and time slot costs. In this problem, the machine has to be calibrated to run a job and such a calibration only remains valid for a fixed time period of length T, after which it must be recalibrated in order to execute jobs. On the other hand, a certain cost will be incurred when the machine executes a job and such a cost is determined by the time slot that is occupied by the job in the schedule. We consider jobs with release times, deadlines and identical processing times. The objective is to schedule the jobs on a single machine and minimize the total cost while calibrating the machine at most K times. We investigate the structure of the optimal schedule and based on that we propose dynamic programs for different scenarios of the problem. At last, for another variant of the problem without the consideration of machine calibration, a greedy algorithm is proposed, which is based on matroid theory.

One of the most known results in the machine scheduling is Lawler’s algorithm to minimize the maximum cost of jobs processed by a single machine subject to precedence constraints. We consider an uncertain version of the same min-max cost scheduling problem. The cost function of each job depends on the job completion time and on an additional generalized numerical parameter, which may be a tuple of parameters. For each job, both, its processing time and the additional parameter are uncertain, only intervals of possible values of these parameters are known. We analyse certain classes of cost functions and develop polynomial algorithms which construct min-max regret solutions. The considered problems cover the most general range of studied cases of interval uncertainty. In the only two papers that present algorithms for minimizing the maximum regret for the problem with uncertain job processing times, the algorithms are based on extremal scenarios, where some uncertain parameters take their maximum values, while all others take their minimum possible values. We show that it is impossible to always limit the search to extremal scenarios. Our approach is based on new ideas different from those underlying previous work. Finally, we show that our approach outperforms all known results for constructing min-max regret solutions for the min-max cost scheduling problem under uncertainty of job processing times.