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The due date assignment scheduling problem with delivery times and truncated sum-of-processing-times-based learning effect.

due date assignment problem

1. Introduction

2. literature review, 3. notation and problem statement, 4. research method, 4.1. the problem 1 | p j [ k ] a = p j max { ( 1 + ∑ i = 1 k − 1 p [ i ] ) a , β } , q p s d , c o n | ∑ j = 1 n ( α u j + δ v j + η d ).

, , , , a, r, , n
The optimal sequence, d All jobs were sorted by increasing processing time, i.e., . When h was from 0 to n, the objective function values were calculated, respectively. The optimal position of h was determined by the smallest value of the objective function, and the optimal sequence was arrangedn an ascending order of normal processing time.

4.2. The Problem 1 | p j [ k ] A = p j max { ( 1 + ∑ i = 1 k − 1 p [ i ] ) a , β } , q p s d , S L K | ∑ j = 1 n ( α U j + δ V j + η q )

, , , , a, r, , n
The optimal sequence, q All jobs were sorted by the increasing processing time, i.e., . When h was from 0 to n, the objective function values were calculated, respectively. The optimal position of h was determines by the smallest value of the objective function, and the optimal sequence was arranged in an ascending order of the normal processing time.

4.3. The Problem 1 | p j [ k ] A = p j max { ( 1 + ∑ i = 1 k − 1 p [ i ] ) a , β } , q p s d , D I F | ∑ j = 1 n ( α U j + δ V j + η d j )

, , , , a, r, , n
The optimal sequence, The optimal sequence was sequenced by an increasing order of normal processing time, i.e., . The due date was determined by the relationship between and .

5. Discussion of Results

5.1. numerical discussion, 5.2. extension, 6. conclusions, author contributions, data availability statement, acknowledgments, conflicts of interest.

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Click here to enlarge figure

SymbolMeaning
nthe number of jobs
the normal processing time of
the normal processing time for the jth position
the actual processing time of
the waiting time of
the completion time of
the makespan
the delivery time of
dthe due date
athe learning index,
rthe delivery rate,
the truncation parameter,
the weights
the job arranged at the jth position
CONthe common due date
SLKthe slack due date
DIFthe different due date
Job
43521
Value111.522.5
Value0123.55.5
Value00.10.20.350.55
Value12.13.75.858.55
Value111.522.5
Value2.12.12.63.13.6
Value3.23.23.74.24.7
Value4.854.855.355.856.35
Value7.057.057.558.058.55
Value59.89.497.213.87
Value0514.824.2931.5
Value00.51.482.4293.15
Value515.325.7633.92938.52
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Share and Cite

Qian, J.; Zhan, Y. The Due Date Assignment Scheduling Problem with Delivery Times and Truncated Sum-of-Processing-Times-Based Learning Effect. Mathematics 2021 , 9 , 3085. https://doi.org/10.3390/math9233085

Qian J, Zhan Y. The Due Date Assignment Scheduling Problem with Delivery Times and Truncated Sum-of-Processing-Times-Based Learning Effect. Mathematics . 2021; 9(23):3085. https://doi.org/10.3390/math9233085

Qian, Jin, and Yu Zhan. 2021. "The Due Date Assignment Scheduling Problem with Delivery Times and Truncated Sum-of-Processing-Times-Based Learning Effect" Mathematics 9, no. 23: 3085. https://doi.org/10.3390/math9233085

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A single machine group scheduling problem with due date assignment and position-dependent costs.

  • Ying Chen , 
  • Guiqing Zhang , and 
  • Yongxi Cheng

School of Management, Xi’an Jiaotong University, Xi’an 710049, P. R. China

E-mail Address: [email protected]

Search for more papers by this author

School of Economics and Management, Xi’an University of Technology, Xi’an 710054, P. R. China

School of Economics and Finance, Xi’an Jiaotong University, Xi’an 710049, P. R. China

Corresponding author.

State Key Lab for Manufacturing Systems Engineering, Xi’an 710049, P. R. China

In this paper, we study a single machine scheduling problem with due date assignment under a group technology environment. The due dates of jobs are assignable according to the following three methods: the common (CON) due date assignment, the slack (SLK) due date assignment, and the different (DIF) due date assignment. Our objective is to determine a group sequence and job sequences within all groups, together with a due date assignment, to minimize a total cost function including earliness, tardiness, due date assignment and flow time costs, in which all unit costs are different and position-dependent. We present a unified O ( n log n ) time algorithm to solve the problem for all the three due date assignment methods.

  • Single machine scheduling
  • group technology
  • due date assignment
  • position-dependent costs
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Two due date assignment problems in scheduling a single machine

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We study the earliness-tardiness scheduling problem on a single machine with due date assignment and controllable processing times. We analyze the problem with three different due date assignment methods and two different processing time functions. For each combination of these, we provide a polynomial- time algorithm to find the optimal job sequence, due date values and resource allocation minimizing an objective function which includes earliness, tardiness, due date assignment, makespan and total resource consumption costs.

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Due date assignment single-machine scheduling with delivery times, position-dependent weights and deteriorating jobs

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Bibliometrics & citations, view options, recommendations, common due date assignment and scheduling with a rate-modifying activity to minimize the due date, earliness, tardiness, holding, and batch delivery cost.

e consider a single-machine batch delivery scheduling and common due date assignment problem. In addition to making decisions on sequencing the jobs, determining the common due date, and scheduling job delivery, we consider the option of performing a ...

Due date assignment and single machine scheduling with deteriorating jobs to minimize the weighted number of tardy jobs

In this paper, we explore a single-machine scheduling problem in which the processing time of a job is a linear increasing function of its starting time. The objective is to determine the optimal due date and schedule simultaneously to minimize a cost ...

Single machine scheduling with past-sequence-dependent setup times and deteriorating jobs

This paper considers single machine scheduling problems with setup times and deteriorating jobs. The setup times are proportional to the length of the already processed jobs, that is, the setup times are past-sequence-dependent (p-s-d). It is assumed ...

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Single-machine due date assignment problem with deteriorating jobs and resource-dependent processing times

  • Original Article
  • Published: 07 February 2013
  • Volume 67 , pages 255–260, ( 2013 )

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due date assignment problem

  • Xiao-Yuan Wang 1 &
  • Jian-Jun Wang 2  

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We study a single-machine earliness–tardiness scheduling problem with due date assignment, in which the processing time of a job is a function of its starting time and its resource allocation. We analyze the problem with two different processing time functions and three different due date assignment methods. The goal is to minimize an integrated objective function, which includes earliness, tardiness, due date assignment, and total resource consumption costs. For each combination of due date assignment method and processing time function, we provide a polynomial-time algorithm to find the optimal job sequence, due date values, and resource allocations.

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Xiao-Yuan Wang

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Jian-Jun Wang

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Wang, XY., Wang, JJ. Single-machine due date assignment problem with deteriorating jobs and resource-dependent processing times. Int J Adv Manuf Technol 67 , 255–260 (2013). https://doi.org/10.1007/s00170-013-4771-x

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Received : 15 June 2012

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Published : 07 February 2013

Issue Date : July 2013

DOI : https://doi.org/10.1007/s00170-013-4771-x

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  • DOI: 10.1155/2015/683269
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Scheduling Problems with Due Date Assignment

  • Yunqiang Yin , Shuenn-Ren Cheng , +3 authors Chin-Chia Wu
  • Published in Due Date-Related Scheduling… 12 April 2015
  • Computer Science
  • Due Date-Related Scheduling with Two Agents

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  1. The due date assignment scheduling problem with the ...

    This paper considers the single machine scheduling problem with three different due dates in which the actual processing time of the job is a simple deterioration function of the starting time. The goal is to minimize the total costs that contain the earliness, tardiness and due date. We prove that these problems are polynomial time solvable, and we propose the corresponding algorithms to ...

  2. The Due Date Assignment Scheduling Problem with Delivery Times and

    This paper considers a single-machine scheduling problem with past-sequence-dependent delivery times and the truncated sum-of-processing-times-based learning effect. The goal is to minimize the total costs that comprise the number of early jobs, the number of tardy jobs and due date. The due date is a decision variable. There will be corresponding penalties for jobs that are not completed on ...

  3. A heuristic for single machine common due date assignment problem with

    The single machine common due date assignment problem where all jobs have the same earliness/tardiness weight has a polynomial-time algorithm to solve it optimally. Furthermore, some properties for the problem where the common due date is an input have been revealed by researchers in the literature. This paper proposes a heuristic algorithm for ...

  4. A common due-date assignment problem with job rejection on parallel

    The most popular setting within due-date assignment models is the well-known Common Due-Date (CON) model, in which all the jobs share the same due-date. For a survey paper on due-date assignment and scheduling problems with a common due-date, we refer the reader to Gordon, Proth, and Chu ( Citation 2002 ).

  5. Single-machine due-date assignment scheduling with generalized

    This paper studies the single-machine due-date assignment problem with past-sequence-dependent setup times (denoted by \(ST_{psd}\)).Under common due-date (denoted by CON-DD) assignment, slack due-date (denoted by SLK-DD) and different due-date (denoted by DIF-DD) assignment, the objective function is to minimize the linear weighted sum of earliness-tardiness, number of early and delayed jobs ...

  6. Two due date assignment problems in scheduling a single machine

    This is also the case for the version of the problem with common due date assignment [7]. We will prove that the TWNTD problem is strongly NP-hard, but it is polynomially solvable in some special cases of interest. 3.1. Analysis and complexityWe analyze now some properties of the optimal due date assignment strategy for a given π.

  7. Optimal due-date assignment problem with learning effect and resource

    In this paper, we consider a single-machine earliness-tardiness scheduling problem with due-date assignment, in which the processing time of a job is a function of its position in a sequence and its resource allocation. The due date assignment methods studied include the common due date, and the slack due date, which reflects equal waiting time allowance for the jobs. For each combination of ...

  8. Due-Date assignment with acceptable lead-times on parallel machines

    We study scheduling and due-date assignment problems with acceptable lead times. •. The machines settings are: parallel identical, uniform and unrelated machines. •. A common lead-time is assumed in the first set of problems. •. Then, job-dependent lead-times and identical earliness and tardiness costs are assumed. •.

  9. Scheduling Problems with Due Date Assignment

    The issue on scheduling problems with due date assignment inspires many researchers to address many interesting manuscripts most of which are discussed widely over single-machine, flowshop, or parallel settings. One manuscript addresses the topic on common due date assignment over a parallel-batching machine. H. Gong et al. consider the ...

  10. A common due-date assignment problem with job rejection on parallel

    ABSTRACT We study a common due-date assignment problem on two parallel uniform machines. The jobs are assumed to have identical processing times, and job-dependent and asymmetric earliness and tardi-ness unit costs. The scheduler may process only a subset of the jobs, i.e. the option of job-rejection is allowed.

  11. Due-date assignment and maintenance activity scheduling problem

    In this note we study a classical due-date assignment problem with the option of scheduling a maintenance activity. Panwalker, Smith and Seidmann [3] addressed the following single machine scheduling and common due-date assignment problem: "…All jobs have a common (but unknown) due-date. The objective is to find an optimal value of the due ...

  12. A Single Machine Group Scheduling Problem with Due Date Assignment and

    In this paper, we study a single machine scheduling problem with due date assignment under a group technology environment. The due dates of jobs are assignable according to the following three methods: the common (CON) due date assignment, the slack (SLK) due date assignment, and the different (DIF) due date assignment.

  13. Two due date assignment problems in scheduling a single machine

    These two papers started extensive research in the area of due date assignment, with most papers focusing on the common due date assignment problem (e.g., [1,2,4,6,7,12,15]). A recent survey on common due date assignment problems was given in [9].

  14. Due-date assignment and parallel-machine

    The due-date assignment problem arises when a firm offers a due-date to its customers during sale negotiations. The firm has to offer a price reduction if the offered due-date far ex ceeds the one expected by the customers. In many instances, due-dates are negotiated rather than simply dictated by the customers. The later the due-dates are ...

  15. Due-date assignment and maintenance activity scheduling problem

    Panwalker, S.S., Smith, M.L. and Seidmann, A., Common due-date assignment to minimize total penalty for the one machine scheduling problem. Operations Research. v30. 391-399. ... e consider a single-machine batch delivery scheduling and common due date assignment problem. In addition to making decisions on sequencing the jobs, determining the ...

  16. Due date assignment single-machine scheduling with delivery times

    Qian J and Han H The due date assignment scheduling problem with the deteriorating jobs and delivery time J Appl Math Comput 2022 68 2173-2186. Crossref. Google Scholar [16] Sun X, Geng X-N, and Liu T Due-window assignment scheduling in the proportionate flow shop setting Ann Oper Res 2020 292 113-131.

  17. Scheduling Problems with Due Date Assignment

    This part is composed of five sections. In Sect. 4.1, we present the results concerning the problems where the due dates of jobs from both of the two agents are determined by the DIF, CON, or SLK due date assignment method. In Sects. 4.2 and 4.3, we present the results concerning the problems where the due dates of jobs from the first agent are determined by the DIF, CON, or SLK due date ...

  18. A note: Minmax due-date assignment problem with lead-time cost

    1. Introduction. Due-date assignment problems are usually difficult due to the inherent trade-off between short due-dates, which clearly make the scheduler/producer more competitive, and late due-dates, which can be easily met. Within the wide range of due-date assignment problems, we find three major classes (see e.g. Gordon et al. [1]): (i) assigning a common due-date for all the jobs (also ...

  19. Due date assignment and scheduling on a single machine with two

    For each due date assignment method, we consider two types of optimisation problem, namely a linear combination optimisation problem (minimising the total integrated cost of the two agents) and a constrained optimisation problem (minimising the objective of one agent, subject to an upper bound on the objective of the other agent).

  20. Common Due Date Assignment to Minimize Total Penalty for the One

    A due-date assignment problem with learning effect and deteriorating jobs. Applied Mathematical Modelling, Vol. 34, No. 2. Scheduling and due date assignment to minimize earliness, tardiness, holding, due date assignment and batch delivery costs. International Journal of Production Economics, Vol. 123, No. 1.

  21. Optimal assignment of due-dates for a single processor scheduling problem

    Abstract. Given processing times of n jobs on a single machine with penalties for earliness and tardiness and penalties associated with assignment of due-dates, the objective is to select optimal due-dates and optimal sequence. Scheduling procedure for the solution of this problem is presented along with proof of optimality and illustrative numerical examples.

  22. A common due-date assignment problem with job rejection on parallel

    We study a common due-date assignment problem on two parallel uniform machines. The jobs are assumed to have identical processing times, and job-dependent and asymmetric earliness and tardiness unit costs. The scheduler may process only a subset of the jobs, i.e. the option of job-rejection is allowed. The objective function consists of three cost components: the total earliness-tardiness cost ...

  23. Single-machine due date assignment problem with ...

    We study a single-machine earliness-tardiness scheduling problem with due date assignment, in which the processing time of a job is a function of its starting time and its resource allocation. We analyze the problem with two different processing time functions and three different due date assignment methods. The goal is to minimize an integrated objective function, which includes earliness ...

  24. Scheduling Problems with Due Date Assignment

    This chapter is devoted to scheduling problems with due date assignment in the context of two-agent scheduling, where the due dates of jobs from either one or both of the two agents are decision variables, which are part of the decision process along with sequence decision. This chapter is devoted to scheduling problems with due date assignment in the context of two-agent scheduling. The main ...