Min-Max Regret Version of the Linear Time–Cost Tradeoff Problem with Multiple Milestones and Completely Ordered Jobs

2015 ◽  
Vol 32 (05) ◽  
pp. 1550039 ◽  
Author(s):  
Byung-Cheon Choi ◽  
Myoung-Ju Park
Keyword(s):  
Linear Time ◽  
Performance Measure ◽  
Maximum Deviation ◽  
Time Cost ◽  
Processing Times ◽  
Weighted Number ◽  
Polynomially Solvable ◽  
Crashing Cost ◽  
Tardy Jobs ◽  
Np Hardness

We consider a linear time–cost tradeoff problem with multiple milestones and uncertain processing times such that all jobs are completely ordered. The performance measure is expressed as the sum of total weighted number of tardy jobs and total crashing cost. The processing times uncertainty is described through two types of scenarios: discrete and interval scenarios. The objective is to minimize maximum deviation from optimality over all scenarios. For the discrete scenario case, we prove its NP-hardness, develop a pseudo-polynomial time approach, and present a polynomially solvable case. Finally, we show that the interval scenario case is also NP-hard.

Two-Machine Ordered Flow Shop Scheduling with Generalized Due Dates

2020 ◽  
Vol 37 (01) ◽  
pp. 1950032
Author(s):  
Myoung-Ju Park ◽  
Byung-Cheon Choi ◽  
Yunhong Min ◽  
Kyung Min Kim
Keyword(s):  
Flow Shop ◽  
Flow Shop Scheduling ◽  
Due Dates ◽  
Shop Scheduling ◽  
Processing Times ◽  
Specific Position ◽  
Polynomially Solvable ◽  
Definition Of ◽  
Tardy Jobs ◽  
Np Hardness

We consider a two-machine flow shop scheduling with two properties. The first is that each due date is assigned for a specific position different from the traditional definition of due dates, and the second is that a consistent pattern exists in the processing times within each job and each machine. The objective is to minimize maximum tardiness, total tardiness, or total number of tardy jobs. We prove the strong NP-hardness and inapproximability, and investigate some polynomially solvable cases. Finally, we develop heuristics and verify their performances through numerical experiments.

Single Machine Scheduling and due Date Assignment with Past-Sequence-Dependent Delivery Times and General Position-Dependent Processing Times

2014 ◽  
Vol 624 ◽  
pp. 675-680
Author(s):  
Yu Fang Zhao
Keyword(s):  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problems ◽  
Due Date ◽  
Due Date Assignment ◽  
Processing Times ◽  
Delivery Times ◽  
Weighted Number ◽  
Tardy Jobs

We studied single machine scheduling problems in which the jobs need to be delivered to customers after processing. It is assumed that the delivery times are proportional to the length of the already processed jobs, and a job's processing time depended on its position in a sequence. The objective functions include total earliness, the weighted number of tardy jobs and the cost of due date assignment. We analyzed these problems with two different due date assignment methods and conclude that the problems are polynomial time solvable.

scholarly journals A Single-Machine Scheduling Problem with Uncertainty in Processing Times and Outsourcing Costs

2017 ◽  
Vol 2017 ◽  
pp. 1-8 ◽  
Author(s):  
Myoung-Ju Park ◽  
Byung-Cheon Choi
Keyword(s):  
Single Machine ◽  
Operating Cost ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Performance Measure ◽  
Total Weighted Completion Time ◽  
Maximum Deviation ◽  
Scheduling Problem ◽  
Processing Times ◽  
Special Cases

We consider a single-machine scheduling problem with an outsourcing option in an environment where the processing time and outsourcing cost are uncertain. The performance measure is the total cost of processing some jobs in-house and outsourcing the rest. The cost of processing in-house jobs is measured as the total weighted completion time, which can be considered the operating cost. The uncertainty is described through either an interval or a discrete scenario. The objective is to minimize the maximum deviation from the optimal cost of each scenario. Since the deterministic version is known to be NP-hard, we focus on two special cases, one in which all jobs have identical weights and the other in which all jobs have identical processing times. We analyze the computational complexity of each case and present the conditions that make them polynomially solvable.

OUTSOURCING DECISIONS IN m-MACHINE PERMUTATION FLOW SHOP SCHEDULING PROBLEMS WITH MACHINE-DEPENDENT PROCESSING TIMES

2014 ◽  
Vol 31 (04) ◽  
pp. 1450028 ◽  
Author(s):  
BYUNG-CHEON CHOI ◽  
MYOUNG-JU PARK
Keyword(s):  
Flow Shop ◽  
Performance Measure ◽  
Flow Shop Scheduling ◽  
Scheduling Problems ◽  
Processing Times ◽  
Permutation Flow Shop Scheduling ◽  
Permutation Flow Shop ◽  
Polynomially Solvable ◽  
Special Case ◽  
Processing Requirement

We consider m-machine permutation flow shop problems with an outsourcing option for a special case where each job's processing time equals the job's processing requirement plus a characteristic value of the machine. The objective is to minimize the sum of the performance measure for in-house jobs (the total completion time or the makespan) and the total outsourcing cost. We prove that two problems are polynomially solvable when the number of machines is fixed.

A Time–Cost Tradeoff Problem with Multiple Assessments and Release Times on a Chain Precedence Graph

2021 ◽  
pp. 2150012
Author(s):  
Myoung-Ju Park ◽  
Byung-Cheon Choi ◽  
Jibok Chung
Keyword(s):  
Total Weighted Tardiness ◽  
Release Time ◽  
Time Cost ◽  
Penalty Cost ◽  
Processing Times ◽  
Release Times ◽  
Penalty Costs ◽  
Precedence Graph ◽  
A Chain ◽  
Tardy Jobs

We consider two variants of a time–cost tradeoff problem with multiple assessments on a chain precedence graph. Furthermore, each job can only be started after a release time, and a penalty cost is incurred when a job is not finished before its due date. The motivation is from the project such that a project owner can control the duration of each job and the support level of each project partner to avoid the penalty cost from the tardy jobs. We describe the penalty costs of the first and the second variants as the total weighted number of tardy jobs and the total weighted tardiness, respectively. These can be avoided by compressing the processing times or advancing the release times, which incurs a compression cost or release cost according to the linear and the piecewise constant functions, respectively. The objective is to minimize the total penalty, compression cost and release cost. In this paper, we propose the procedure based on the reduction to a shortest path problem, and show that the procedure can solve two variants in strongly polynomial time.

Common Due-Window Assignment and Group Scheduling with Position-Dependent Processing Times

2015 ◽  
Vol 32 (06) ◽  
pp. 1550045 ◽  
Author(s):  
Shang-Chia Liu
Keyword(s):  
Single Machine ◽  
Group Technology ◽  
Window Size ◽  
Setup Time ◽  
Single Machine Scheduling ◽  
Processing Times ◽  
Weighted Number ◽  
Due Window ◽  
Tardy Jobs ◽  
Due Window Assignment

This paper investigates a single-machine scheduling problem involving both the due-window assignment and position-dependent processing times under a group technology environment. By position-dependent processing times, we mean that the processing time of a job is dependent of its processing position in the job sequence within the group it belongs to. A setup time is incurred whenever the single machine transfers job processing from a group to another group. Each group is assigned an assignable common due-window. A job completed earlier (respectively, later) than the common due-window of the group it belongs to will incur an earliness (respectively, tardiness) penalty. The objective is to determine the optimal group sequence, the optimal job sequence, and the optimal due-window assignment so as to minimize the total cost including the earliness and tardiness (or weighted number of tardy jobs) penalties, black and the due-window starting time and due-window size costs. We show that both the problems can be solved in polynomial times.

scholarly journals Due-Window Assignment Scheduling with Variable Job Processing Times

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Yu-Bin Wu ◽  
Ping Ji
Keyword(s):  
Processing Time ◽  
Learning Effect ◽  
Window Size ◽  
Starting Time ◽  
Processing Times ◽  
Due Windows ◽  
Weighted Number ◽  
Due Window ◽  
Tardy Jobs ◽  
Due Window Assignment

We consider a common due-window assignment scheduling problem jobs with variable job processing times on a single machine, where the processing time of a job is a function of its position in a sequence (i.e., learning effect) or its starting time (i.e., deteriorating effect). The problem is to determine the optimal due-windows, and the processing sequence simultaneously to minimize a cost function includes earliness, tardiness, the window location, window size, and weighted number of tardy jobs. We prove that the problem can be solved in polynomial time.

JUST-IN-TIME SCHEDULING UNDER SCENARIO-BASED UNCERTAINTY

2013 ◽  
Vol 30 (02) ◽  
pp. 1250055 ◽  
Author(s):  
DAE-YOUNG CHUNG ◽  
BYUNG-CHEON CHOI
Keyword(s):  
Computational Complexity ◽  
Single Machine Scheduling ◽  
Performance Measure ◽  
Just In Time ◽  
Maximum Deviation ◽  
Scheduling Problem ◽  
Due Dates ◽  
Finite Set ◽  
Time Scheduling ◽  
Weighted Number

This paper considers the single-machine scheduling problem, where job parameters are uncertain and the performance measure is to maximize the weighted number of just-in-time jobs, defined as jobs completed exactly on their due dates. Uncertainty is described through a finite set of well-defined scenarios. The criteria for this environment is to minimize the maximum deviation from optimality for all scenarios. We present the computational complexity results for several cases.

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