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.

scholarly journals Sum-of-Processing-Times-Based Two-Agent Single-Machine Scheduling with Aging Effects and Tardiness

2015 ◽  
Vol 2015 ◽  
pp. 1-12 ◽  
Author(s):  
Do Gyun Kim ◽  
Jin Young Choi
Keyword(s):  
Genetic Algorithm ◽  
Single Machine ◽  
Optimal Solution ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Total Weighted Tardiness ◽  
Aging Effects ◽  
Weighted Tardiness ◽  
Processing Times ◽  
Tardy Jobs

We consider a two-agent single-machine scheduling problem that minimizes the total weighted tardiness of one agent under the restriction that the second agent is prohibited from having tardy jobs. The actual processing times of all jobs are affected by a sum-of-processing-times-based aging effect. After showing the NP-hardness of the problem, we design a branch-and-bound (B&B) algorithm to find an optimal solution by developing dominance properties and a lower bound for the total weighted tardiness to increase search efficiency. Because B&B takes a long time to find an optimal solution, we propose a genetic algorithm as an efficient, near optimal solution approach. Four methods for generating initial populations are considered, and edge recombination crossover is adopted as a genetic operator. Through numerical experiments, we verify the outstanding performance of the proposed genetic algorithm.

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.

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.

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.

scholarly journals Minimizing Tardiness Penalty Costs in Job Shop Scheduling under Maximum Allowable Tardiness

Processes ◽  
2020 ◽  
Vol 8 (11) ◽  
pp. 1398
Author(s):  
Jae-Gon Kim ◽  
Hong-Bae Jun ◽  
June-Young Bang ◽  
Jong-Ho Shin ◽  
Seong-Hoon Choi
Keyword(s):  
Job Shop ◽  
Job Shop Scheduling ◽  
Service Industries ◽  
Dispatching Rules ◽  
Scheduling Problem ◽  
Job Shop Scheduling Problem ◽  
Breach Of Contract ◽  
Shop Scheduling ◽  
Penalty Costs ◽  
Tardy Jobs

In many manufacturing or service industries, there exists maximum allowable tardiness for orders, according to purchase contracts between the customers and suppliers. Customers may cancel their orders and request compensation for damages, for breach of contract, when the delivery time is expected to exceed maximum allowable tardiness, whereas they may accept the delayed delivery of orders with a reasonable discount of price within maximum allowable tardiness. Although many research works have been produced on the job shop scheduling problem relating to minimizing total tardiness, none of them have yet considered problems with maximum allowable tardiness. In this study, we solve a job shop scheduling problem under maximum allowable tardiness, with the objective of minimizing tardiness penalty costs. Two kinds of penalty costs are considered, i.e., one for tardy jobs, and the other for canceled jobs. To deal with this problem within a reasonable time at actual production facilities, we propose several dispatching rules by extending well-known dispatching rules for the job shop scheduling problem, in cooperation with a probabilistic conception of those rules. To evaluate the proposed rules, computational experiments were carried out on 300 test instances. The test results show that the suggested probabilistic dispatching rules work better than the existing rules and the optimization solver CPLEX, with a time limit.

Improved High Resolution Post-Transit Spectroscopy for Determining the Density of States in Amorphous Semiconductors

2000 ◽  
Vol 609 ◽  
Author(s):  
Charlie Main ◽  
Steve Reynolds ◽  
Rashad I. Badran ◽  
Joe M. Marshall
Keyword(s):  
Function Approximation ◽  
Delta Function ◽  
Amorphous Semiconductors ◽  
Rate Equations ◽  
Release Time ◽  
Disordered Materials ◽  
Trapping Rate ◽  
Laplace Inversion ◽  
Crystalline Materials ◽  
Release Times

ABSTRACTWe show that the analysis of post-transit photocurrent i(t) in a multi-trapping context to determine the density of trapping states g(E) is capable of resolving features less than kT in width. A commonly used method uses a Laplace inversion of i(t) data giving the well-known result g(E) ∼ t i(t) but employs a delta function approximation for trap release times, which results in loss of energy resolution. We show that it is possible to retain the exponential distribution function for trap release time and solve the multi-trapping rate equations directly, giving significantly improved resolution. The analysis is performed on computer generated post-transit data for distributed and discrete traps, and compared with the earlier method and other related Fourier transform methods for determining g(E). In addition, the versatility of the new method in handling cases with either distributed traps or with discrete traps means that it can be applied to disordered materials or to crystalline materials with well-defined defect levels.

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