On Startup or Learning Curves: An Expanded View

Pegels, C. Carl

doi:10.1080/05695556908974435

Cited by 76 publications

(40 citation statements)

References 5 publications

(1 reference statement)

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“…He also developed polynomial time solution algorithms for some special cases of the following objective functions: the weighted sum of completion times and the maximum lateness. Wang and Xia [9] and Wang [10] also extended their results to the model: Pegels' learning curve [11]. Mosheiov and Sidney [12] considered a job-dependent learning curve, where the learning rate of some jobs is faster than that of the others.…”

Section: Introductionmentioning

confidence: 94%

Single machine past-sequence-dependent setup times scheduling with general position-dependent and time-dependent learning effects

Wang

2011

Applied Mathematical Modelling

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a b s t r a c tIn this paper we consider the single machine past-sequence-dependent (p-s-d) setup times scheduling problems with general position-dependent and time-dependent learning effects. By the general position-dependent and time-dependent learning effects, we mean that the actual processing time of a job is not only a function of the total normal processing times of the jobs already processed, but also a function of the job's scheduled position. The setup times are proportional to the length of the already processed jobs. We consider the following objective functions: the makespan, the total completion time, the sum of the hth (h P 0) power of job completion times, the total lateness, the total weighted completion time, the maximum lateness, the maximum tardiness and the number of tardy jobs. We show that the problems of makespan, the total completion time, the sum of the hth (h P 0) power of job completion times and the total lateness can be solved by the smallest (normal) processing time first (SPT) rule, respectively. We also show that the total weighted completion time minimization problem, the maximum lateness minimization problem, maximum tardiness minimization problem and the number of tardy jobs minimization problem can be solved in polynomial time under certain conditions.

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Section: Introductionmentioning

confidence: 94%

Single machine past-sequence-dependent setup times scheduling with general position-dependent and time-dependent learning effects

Wang

2011

Applied Mathematical Modelling

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“…作業者が１つの製品を組立から検査,包装まで完了する全工程を行う生産方式は，一人屋台生産方式と呼ばれている (1) ．また，いくつかの工程を１人の作業者が受け持つセル生産方式は，トヨタ生産方式の多工程持ちに相当する (2) ．両方の生産方式を採用することにより，生産効率，作業者の意欲，達成感などの向上が図られている．これらの方式の導入時に見られるように，はじめは 1 つの製品を完成させるのにかなりの時間を要するが，作業回数が増加するにつれて作業のスピードが上がり，製品個数の増加と共に作業時間が減少していき，安定した時間に落ち着く．この時間を標準作業時間 (3) として作業改善に反映させることは，生産計画に有用である．この現象は習熟効果ないし経験効果といわれ，作業時間の他に生産コストが減少していくパターンがある．この種のパターンは，進歩曲線，習熟ないし学習曲線，経験曲線など (4) と呼ばれ，経済，工学，教育の各分野において研究されている．習熟曲線モデルとしてよく知られる関数にベキ乗関数があり，この他にPegels (5) …”

Section: 緒言unclassified

A Comparison of Methods Estimating Parameters in Exponential Function Type of Learning Model

Yamashiro

2012

Trans.JSME(C)

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“…They then provided some solvable cases for the singlemachine and multiple-machine flowshop. Wang and Xia (2005) and Wang (2005) extended their results to the model: Pegels' learning curve (Pegels 1969), i.e., if job J j is scheduled in position k in a sequence, its actual processing time is p jk = p j [αa k−1 + β], where α, a and β are parameters obtained empirically. considered the single machine scheduling problem with exponential time-dependent learning effect and pastsequence-dependent setup times, where the actual processing time a job J j at position k in sequence π is p jk = p j (αa k−1 i=1 p π(i) + β), where α ≥ 0, β ≥ 0, 0 < a ≤ 1 with α + β = 1 and k−1 i=1 p π(i) calculates the total normal processing times of jobs processed before J j in sequence π .…”

mentioning

confidence: 96%

Single-machine scheduling problems with time and position dependent processing times

et al. 2011

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We consider single-machine scheduling problems with time and position dependent job processing times. In many industrial settings, the processing time of a job changes due to either job deterioration over time or machine/worker's learning through experiences. In the models we study, each job has its normal processing time. However, a job's actual processing time depends on when its processing starts and how many jobs have completed before its start. We prove that the classical SPT (Shortest Processing Time) rule remains optimal when we minimize the makespan or the total completion time. For problems of minimizing the total weighted completion time, the maximum lateness, and the discounted total weighted completion time, we present heuristic sequencing rules and analyze the worstcase bounds for performance ratios. We also show that these heuristic rules can be optimal under some agreeable conditions between the normal processing times and job due dates or weights.Keywords Single-machine scheduling · Learning effect · Performance ratio · Worst-case error 1 Introductions and literature review

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On Startup or Learning Curves: An Expanded View

Cited by 76 publications

References 5 publications

Single machine past-sequence-dependent setup times scheduling with general position-dependent and time-dependent learning effects

Single machine past-sequence-dependent setup times scheduling with general position-dependent and time-dependent learning effects

A Comparison of Methods Estimating Parameters in Exponential Function Type of Learning Model

Single-machine scheduling problems with time and position dependent processing times

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