Single-machine scheduling where jobs have a penalty for being late or for being rejected altogether is an important (sub)problem in manufacturing, logistics, and satellite scheduling. It is known to be NP-hard in the strong sense, and there is no polynomial-time algorithm that can guarantee a constant-factor approximation (unless P=NP). We provide an exact algorithm that is fixed-parameter tractable in the slack and the maximum number of time windows overlapping at any point in time, i.e., the width. This algorithm has a runtime exponential in these parameters, but quadratic in the number of jobs, even when modeling sequence-dependent setup times. We further provide a fixed-parameter fully-polynomial time approximation scheme (FPTAS) with only this width as a parameter, having a runtime bound that is cubic. Finally, we propose a neighbourhood heuristic similar to the Balas-Simonetti neighbourhood. All algorithms use an efficient representation of the state space inspired by decision diagrams, where partial solutions that are provably dominated are excluded from further consideration. Experimental evidence shows that the exact method significantly outperforms the state-of-the-art on instances where the width is smaller than one third of the number of jobs and finds optimal solutions to previously unsolved instances. The FPTAS is competitive to state-of-the-art heuristics only when the width is significantly smaller, but the neighbourhood heuristic outperforms most other heuristics in runtime or quality.

The Order Acceptance and Scheduling (OAS) problem describes a class of real-world problems such as in smart manufacturing and satellite scheduling. This problem consists of simultaneously selecting a subset of orders to be processed as well as determining the associated schedule. A common generalization includes sequence-dependent setup times and time windows. We propose a novel memetic algorithm for this problem, called Sparrow. It comprises a hybridization of biased random key genetic algorithm (BRKGA) and adaptive large neighbourhood search (ALNS). Sparrow integrates the exploration ability of BRKGA and the exploitation ability of ALNS. On a set of standard benchmark instances, this algorithm obtains better-quality solutions with runtimes comparable to state-of-the-art algorithms. To further understand the strengths and weaknesses of these algorithms, their performance is also compared on a set of new benchmark instances with more realistic properties. We conclude that Sparrow is distinguished by its ability to solve difficult instances from the OAS literature, and that the hybrid steady-state genetic algorithm (HSSGA) performs well on large instances in terms of optimality gap, although taking more time than Sparrow.

In intelligent manufacturing, it is important to schedule orders from customers efficiently. Make-to-order companies may have to reject or postpone orders when the production capacity does not meet the demand. Many such real-world scheduling problems are characterised by processing times being dependent on the start time (time dependency) or on the preceding orders (sequence dependency), and typically have an earliest and latest possible start time. We introduce and analyze four algorithmic ideas for this class of time/sequence-dependent over-subscribed scheduling problems with time windows: a novel hybridization of adaptive large neighbourhood search (ALNS) and tabu search (TS), a new randomization strategy for neighbourhood operators, a partial sequence dominance heuristic, and a fast insertion strategy. Through factor analysis, we demonstrate the performance of these new algorithmic features on problem domains with varying properties. Evaluation of the resulting general purpose algorithm on three domains—an order acceptance and scheduling problem, a real-world multi-orbit agile Earth observation satellite scheduling problem, and a time-dependent orienteering problem with time windows—shows that our hybrid algorithm robustly outperforms general algorithms including a mixed integer programming method, a constraint programming method, recent state-of-the-art problem-dependent meta-heuristic methods, and a two-stage hybridization of ALNS and TS.