Parameterized complexity of machine scheduling: 15 open problems

Machine scheduling problems are a long-time key domain of algorithms and complexity research. A novel approach to machine scheduling problems are fixed-parameter algorithms. To stimulate this thriving research direction, we propose 15 open questions in this area whose resolution we expect to lead to the discovery of new approaches and techniques both in scheduling and parameterized complexity theory.Comment: Version accepted to Computers & Operations Researc

Decentralized Multi-Agent Production Control through Economic Model Bidding for Matrix Production Systems

Due to increasing demand for unique products, large variety in product portfolios and the associated rise in individualization, the efficient use of resources in traditional line production dwindles. One answer to these new challenges is the application of matrix-shaped layouts with multiple production cells, called Matrix Production Systems. The cycle time independence and redundancy of production cell capabilities within a Matrix Production System enable individual production paths per job for Flexible Mass Customisation. However, the increased degrees of freedom strengthen the need for reliable production control systems compared to traditional production systems such as line production. Beyond reliability a need for intelligent production within a smart factory in order to ensure goal-oriented production control under ever-changing manufacturing conditions can be ascertained. Learning-based methods can leverage condition-based reactions for goal-oriented production control. While centralized control performs well in single-objective situations, it is hard to achieve contradictory targets for individual products or resources. Hence, in order to master these challenges, a production control concept based on a decentralized multi-agent bidding system is presented. In this price-based model, individual production agents - jobs, production cells and transport system - interact based on an economic model and attempt to maximize monetary revenues. Evaluating the application of learning and priority-based control policies shows that decentralized multi-agent production control can outperform traditional approaches for certain control objectives. The introduction of decentralized multi-agent reinforcement learning systems is a starting point for further research in this area of intelligent production control within smart manufacturing

The Open Shop Scheduling Problem

We discuss the computational complexity, the approximability, the algorithmics and the combinatorics of the open shop scheduling problem. We summarize the most important results from the literature and explain their main ideas, we sketch the most beautiful proofs, and we also list a number of open problems

An approximation algorithm for the three-machine scheduling problem with the routes given by the same partial order

The paper considers a three-machine shop scheduling problem to minimize the makespan, in which the route of a job should be feasible with respect to a machine precedence digraph with three nodes and one arc. For this NP-hard problem that is related to the classical flow shop and open shop models, we present a simple 1.5-approximation algorithm and an improved 1.4-approximation algorithm

Bounding the Running Time of Algorithms for Scheduling and Packing Problems

We investigate the implications of the exponential time hypothesis on algorithms for scheduling and packing problems. Our main focus is to show tight lower bounds on the running time of these algorithms. For exact algorithms we investigate the dependence of the running time on the number n of items (for packing) or jobs (for scheduling). We show that many of these problems, including SUBSET SUM, KNAPSACK, BIN PACKING, P2||Cmax, and P2||∑wjCj, have a lower bound of 2o(n)×∥I∥O(n). We also develop an algorithmic framework that is able to solve a large number of scheduling and packing problems in time 2O(n)×∥I∥O(n). Finally, we show that there is no PTAS for MULTIPLE KNAPSACK and 2D-KNAPSACK with running time 2o(1ε)×∥I∥O(n) and no(1ε)×∥I∥O(n)

Real-Time Message Routing and Scheduling

Exchanging messages between nodes of a network (e.g., embedded computers) is a fundamental issue in real-time systems involving critical routing and scheduling decisions. In order for messages to meet their deadlines, one has to determine a suitable (short) origin-destination path for each message and resolve conflicts between messages whose paths share a communication link of the network. With this paper we contribute to the theoretic foundations of real-time systems. On the one hand, we provide efficient routing strategies yielding origin-destination paths of bounded dilation and congestion. In particular, we can give good a priori guarantees on the time required to send a given set of messages which, under certain reasonable conditions, implies that all messages can be scheduled to reach their destination on time. Finally, for message routing along a directed path (which is already NP-hard), we identify a natural class of instances for which a simple scheduling heuristic yields provably optimal solutions