The Longest Processing Time rule for identical parallel machines revisited

Croce, Federico Della; Scatamacchia, Rosario

doi:10.1007/s10951-018-0597-6

Cited by 29 publications

(26 citation statements)

References 21 publications

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“…More recently, Della Croce and Scatamacchia [6] revisit LPT to propose yet another heuristic, SLACK, by splitting the sorted tasks in tuples of m consecutive tasks (recall that m is the number of processors), and then sorting tuples by non-increasing order of the difference between the largest and smallest task in the tuple. A list-scheduling strategy is then applied with tasks sorted in this order.…”

Section: Beyond Lptmentioning

confidence: 99%

“…Finally, an evaluation of SLACK is done in [6]: this variant of LPT turns out to be much better than LPT on benchmark literature instances, and it remains competitive with the COMBINE heuristic that is more costly and more difficult to implement.…”

Section: Empirical Studiesmentioning

confidence: 99%

“…Then, we revisit LPT and propose an update to these asymptotic optimality results, both from a theoretical perspective and from an empirical one. We also consider related heuristics, in particular a novel strategy recently proposed in [6]. Our contribution is twofold:…”

Section: Introductionmentioning

confidence: 99%

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Update on the Asymptotic Optimality of LPT

Benoît

Canon

Elghazi

et al. 2021

Lecture Notes in Computer Science

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When independent tasks are to be scheduled onto identical processors, the typical goal is to minimize the makespan. A simple and efficient heuristic consists in scheduling first the task with the longest processing time (LPT heuristic), and to plan its execution as soon as possible. While the performance of LPT has already been largely studied, in particular its asymptotic performance, we revisit results and propose a novel analysis for the case of tasks generated through uniform integer compositions. Also, we perform extensive simulations to empirically assess the asymptotic performance of LPT. Results demonstrate that the absolute error rapidly tends to zero for several distributions of task costs, including ones studied by theoretical models, and realistic distributions coming from benchmarks.

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Section: Beyond Lptmentioning

confidence: 99%

Section: Empirical Studiesmentioning

confidence: 99%

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Update on the Asymptotic Optimality of LPT

Benoît

Canon

Elghazi

et al. 2021

Lecture Notes in Computer Science

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“…The inclusion of the LPT heuristic allows placing the shorter jobs (or items) more towards the end of the schedule (or packing process), where they can be used for balancing the loads [12]. The presorting algorithms provide better worst-case performance than the classical online ones [20,21,23,75]. On the other hand, the time complexity of the presorting algorithms is O (n log n) while that of the classical BP algorithms NF, FF, WF and BF is O (n).…”

Section: ) the Bin-packing Problemmentioning

confidence: 99%

“…As such, scheduling daily inspections can be thought of as a Pm‖Cmax scheduling problem [12] where inspection of n firms is to be carried out in parallel by m identical or parallel inspectors (Pm) with maximum work capacity (Cmax) to minimize the time to complete the inspection. One of the earliest algorithms for solving such scheduling problem is the Longest Processing Time (LPT) rule which requires sorting the jobs (or firms) in nonascending order of their processing times and then to assign one job at a time to the machine (or inspector) whose load is smallest until all the jobs are completed [20].…”

Section: Introductionmentioning

confidence: 99%

A Novel Macro and Micro Scheduling Model for Regulated Safety Inspections Based on Probability Integral Transform and Modified Bin Packing Algorithm

Zytoon

2021

IEEE Access

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Occupational safety and health (OSH) inspection is an essential element of OSH regulatory enforcement programs. The effectiveness of regulated OSH inspections is dependent on many factors of which proper planning and scheduling of inspections, and optimum utilization of inspectors are extremely important. In spite of this, there is no published scheduling model to solve the problem of regulated safety inspections. Absence of such models negatively affected the performance of safety inspectorates in many countries which is manifested by low portion of firms being inspected over long periods of time. For these, there is urgent need to introduce new scheduling models to solve such problem that has distinctive characteristics compared to the scheduling problems in other fields. The current paper presents a novel hybrid macro and micro scheduling approach that is based on Probability Integral Transform (PIT) and a modified Bin Packing algorithm that address the Inspector Utilization Problem with Firm Inspection Sharing (IUPFISh). The PIT-IUPFISh model consists of uniform long-term macro scheduling of firms for inspection using PIT approach coupled with short-term micro scheduling of firm inspection using the IUPFISh algorithm to determine the daily scheduling of the firms and inspectors so that maximum utilization of inspectors is achieved. A case study was presented to show the application of the proposed model. The results indicate that the application of the proposed model can improve OSH inspectorate performance through improved planning and scheduling as well as maximizing effective utilization of manpower.

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