A Hybrid Exact–Local Search Approach for One-Machine Scheduling with Time-Dependent Capacity

Abstract

Machine scheduling is a hard combinatorial problem having many manifestations in real life. Due to the schedule followed, the possibility of installations of machines operating sub-optimally is high. In this work, we examine the problem of a single machine with time-dependent capacity that performs jobs of deterministic durations, while for each job, its due time is known in advance. The objective is to minimize the aggregated tardiness in all tasks. The problem was motivated by the need to schedule charging times of electric vehicles effectively. We formulate an integer programming model that clearly describes the problem and a constraint programming model capable of effectively solving it. Due to the usage of interval variables, global constraints, a powerful constraint programming solver, and a heuristic we have identified, which we call the “due times rule”, the constraint programming model can reach excellent solutions. Furthermore, we employ a hybrid approach that exploits three local search improvement procedures in a schema where the constraint programming part of the solver plays a central role. These improvement procedures exhaustively enumerate portions of the search space by exchanging consecutive jobs with a single job of the same duration, moving cost-incurring jobs to earlier times in a consecutive sequence of jobs or even exploiting periods where capacity is not fully utilized to rearrange jobs. On the other hand, subproblems are given to the exact constraint programming solver, allowing freedom of movement only to certain parts of the schedule, either in vertical ribbons of the time axis or in groups of consecutive sequences of jobs. Experiments on publicly available data show that our approach is highly competitive and achieves the new best results in many problem instances.

Scheduling of Jobs with Multiple Weights on a Single Machine for Minimizing the Total Weighted Number of Tardy Jobs

“…Other recently related studies can be found in Zhang et al [12], Masadeh et al [13], Zhang et al [14], Kim and Kim [15], Valouxis et al [16], and Wang et al [17] among many others.…”

Special Issue “Scheduling: Algorithms and Applications”

“…In the paper [11], single machine scheduling problems with time-dependent capacity and the objective to minimize the total aggregated tardiness are considered. The authors formulate linear programming and constraint programming models.…”

Solving the Distributed Permutation Flow-Shop Scheduling Problem Using Constrained Programming

“…Examples of problems belonging to the first case are the problem of scheduling independent tasks to heterogeneous multiprocessors [26] and the machine reassignment problem [27]. On the other hand, an example of the second case is the one-machine scheduling problem [28] that is an abstraction of a real-world scheduling problem that is aimed at achieving efficient charging of electrical vehicles. Another paper that proposes an approximation approach for the one-machine problem, this time including release and delivery times for the jobs, is [29].…”