One-Machine Scheduling with Time-Dependent Capacity via Efficient Memetic Algorithms

Mencía, Raúl; Mencía, Carlos

doi:10.3390/math9233030

Cited by 1 publication

(12 citation statements)

References 55 publications

(135 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…A detailed description of the problem exists in [6], so we give a brief description in this section. The problem involves n jobs and one machine with a certain capacity that varies over time.…”

Section: Problem Descriptionmentioning

confidence: 99%

“…In line with the definitions of terms in [6], we use S i , p i , d i , and C i for the start time, duration, due time, and completion time, respectively, of a job i in a given schedule. Then, T i is the tardiness of job i which is max{0, C i − d i }.…”

Section: Terminologymentioning

confidence: 99%

“…A dataset consisting of a relatively large number of artificially generated problem instances is publicly available in [8]. The procedure for generating these instances is described in [6], and special care has been taken so that the problems' structures resemble the structure manifested during the process of electric vehicle charging [9]. In total, 190 problem instances exist, as seen in Table 2.…”

Section: Datasetmentioning

confidence: 99%

“…In [6], the authors present the schedule builder algorithm, where jobs are ordered in an arbitrary sequence, and each job is scheduled to start at the earliest possible time. After positioning each job, the capacity of the machine is updated in accordance with the partial schedule.…”

Section: Heuristically Constructed Schedulesmentioning

confidence: 99%

“…In this work, we study a variation in the one-machine scheduling with time-dependent capacity problem that Mencia et al introduced in [4][5][6]. The problem emerged in the context of scheduling charge times for a fleet of electric vehicles and is an abstraction of the real problem.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

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

et al. 2022

View full text Add to dashboard Cite

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.

show abstract

Section: Problem Descriptionmentioning

confidence: 99%

Section: Terminologymentioning

confidence: 99%