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This paper treats the Piggyback Transportation Problem: A large vehicle moves successive batches of small vehicles from a depot to a single launching point. Here, the small vehicles depart toward assigned customers, supply shipments, and return to the depot. Once the large vehicle has returned and another batch of small vehicles has been loaded at the depot, the process repeats until all customers are serviced. With autonomous driving on the verge of practical application, this general setting occurs whenever small autonomous delivery vehicles with limited operating range, e.g., unmanned aerial vehicles (drones) or delivery robots, need to be brought in the proximity of the customers by a larger vehicle, e.g., a truck. We aim at the most elementary decision problem in this context, which is inspired by Amazon’s novel last-mile concept, the flying warehouse. According to this concept, drones are launched from a flying warehouse and – after their return to an earthbound depot – are resupplied to the flying warehouse by an air shuttle. We formulate the Piggyback Transportation Problem, investigate its computational complexity, and derive suited solution procedures. From a theoretical perspective, we prove different important structural problem properties. From a practical point of view, we explore the impact of the two main cost drivers, the capacity of the large vehicle and the fleet size of small vehicles, on service quality.

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.

A parallel machine schedule updating game with compensations and clients averse to uncertain loss
(2019)

There is a finite number of non-cooperating clients, who are averse to uncertain loss and compete for execution of their jobs not later than by their respective due dates in a parallel service eironment. For each client, a due date violation implies a cost. In order to address the minimization of the total scheduling cost of all clients as a social criterion, a game mechanism is suggested. It is designed such that no client has an incentive to claim a false due date or cost. The game mechanism allows the clients to move their jobs to complete earlier in a given schedule. However, they must compensate costs of those clients whose jobs miss their due dates because of these moves. Algorithmic aspects are analyzed. Furthermore, that determines an equilibrium of the considered game is suggested and embedded into the game mechanism. Computational tests analyze the performance and practical suitability of the resulting game mechanism.

We address an optimization problem that arises at seaports where containers are transported between stacking areas and small buffer areas of restricted capacity that are located within the reach of quay cranes. The containers are transported by straddle carriers that have to be routed such that given unloading and loading sequences of the containers at the quay cranes are respected. The objective is to minimize the turnaround times of the vessels. We analyze the problem’s computational complexity, present an integer program, and propose a heuristic framework that is based on decomposing the problem into its routing component and a component that handles the time variables and buffer capacities. The framework is analyzed in computational tests that are based on real-world data. Based on these tests, we analyze the question of whether or not it pays off to deviate from the approach of permanently assigning a fixed number of straddle carriers to each quay crane, which is the strategy that is currently implemented at the port.

Single-machine batch scheduling to minimize the total setup cost in the presence of deadlines
(2018)

We address the single-machine batch scheduling problem with the objective of minimizing the total setup cost. This problem arises when there are n jobs that are partitioned into F families and when setup operations are required whenever the machine switches from processing a job of one family to processing a job of another family. We assume that setups do not require time but are associated with a fixed cost which is identical for all setup operations. Each job has a processing time and an associated deadline. The objective is to schedule all jobs such that they are on time with respect to their deadlines and the total setup cost is minimized. We show that the decision version of this problem is NP-complete in the strong sense. Furthermore, we present properties of optimal solutions and an O(nlogn+nF) algorithm that approximates the cost of an optimal schedule by a factor of F. The algorithm is analyzed in computational tests.

We consider the problem of designing truthful mechanisms for machine scheduling problems with parallel identical machines where some of the jobs’ characteristics are private information of their respective owners and a central decision maker is in charge of computing the schedule. We study a two-parameter setting, where weights and due dates are private information while processing times are publicly known. The global objective is to minimize the sum of the weights of those jobs that are completed after their due dates. We derive a set of properties that is equivalent to the well known condition of cycle monotonicity, which is a general condition for truthful mechanisms in non-coex valuation function domains. Our results utilize knowledge about the underlying scheduling problem, so that the resulting properties are easier to implement and verify than the general condition of cycle monotonicity. We illustrate the use of our results by analyzing an example algorithm that has recently been proposed in the literature for the case of one machine.

Globalization and digitalization have lead to new challenges and perspectives in intermodal transport logistics of large city sea ports and megahubs. In particular, due to an enormous increase of the container throughput over the last decades and the automatization of megahubs, new planning problems in this field must consistently be addressed by smart software solutions. In this research article, we sketch some challenges that arise at megahubs and outline how mechanism design, as a popular tool that combines ideas from game theory and computer science, can be an approach to tackle logistics problems that iolve multiple selfish players.

This paper provides a literature overview on (direct revelation) algorithmic mechanism design in the context of machine scheduling problems. Here, one takes a game-theoretic perspective and assumes that part of the relevant data of the machine scheduling problem is private information of selfish players (usually machines or jobs) who may try to influence the solution determined by the scheduling algorithm by submitting false data. A central planner is in charge of controlling and designing the algorithm and a rewarding scheme that defines payments among planner and players based on the submitted data. The planner may, for example, want to design algorithm and payments such that reporting the true data always maximizes the utility functions of rationally acting players, because this enables the planner to generate fair solutions with respect to some social criterion that considers the interests of all players. We review the categories and characterizing problem features of machine scheduling settings in the algorithmic mechanism design literature and extend the widely accepted classification scheme of Graham et al. (Ann Discrete Math 5:287–326, <a aria-controls="popup-references" aria-expanded="false" role="button" title="View reference" href="https://link.springer.com/article/10.1007/s00291-018-0512-8#CR54">1979</a>) for scheduling problems to include aspects relating to mechanism design. Based on this hierarchical scheme, we give a systematic overview of recent contributions in this field of research.

We consider a basic partition problem that subdivides Stock Keeping Units (SKUs) into disjoint subsets, such that the minimum number of groups has to be accessed when retrieving a given order set under a pick-by-order policy. We formalize this SKU partition problem and show its applicability in a wide range of storage systems that are based on separating their storage space into groups of SKUs stored in separate areas; examples are carousel racks and mobile shelves. We analyze the computational complexity and propose two mathematical models for the problem under consideration. Furthermore, we present an ejection chain heuristic and a branch and bound procedure. We analyze these algorithms and the mathematical models in computational tests.

In this paper we analyze the effect of including price competition into a classical (market entrant’s) competitive location problem. The multinomial logit approach is applied to model the decision process of utility maximizing customers. We provide complexity results and show that, given the locations of all facilities, a fixed-point iteration approach that has previously been introduced in the literature can be adapted to reliably and quickly determine local price equilibria. We present examples of problem instances that demonstrate the potential non-existence of price equilibria and the case of multiple local equilibria in prices. Furthermore, we show that different price sensitivity levels of customers may actually affect optimal locations of facilities, and we provide first insights into the performance of heuristic algorithms for the location problem.

There is a finite number of non-cooperating clients competing for execution of their jobs by a single service provider in order to minimize job completion time costs. The clients can move their jobs to complete earlier in a given sequence. However, they have to compensate the cost increase to the other clients whose jobs are completed later due to this move. All clients are assumed to be fully risk averse. A game mechanism is suggested, such that no client has an incentive to claim false cost and a social criterion, i.e. the minimization of the total cost of all clients, is addressed. A polynomial time algorithm that finds a game equilibrium is suggested and embedded into the game mechanism. Computational tests analyze the performance and practical suitability of the resulting mechanism. We outline potential directions for future research in a similar setting in a parallel service eironment.