A dynamic programming algorithm for the single-machine scheduling problem with deteriorating processing times

2006 ◽  
Vol 25 ◽  
pp. 139-142 ◽  
Author(s):  
Alberto Bosio ◽  
Giovanni Righini
Keyword(s):  
Dynamic Programming ◽  
Single Machine ◽  
Dynamic Programming Algorithm ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Programming Algorithm ◽  
Scheduling Problem ◽  
Processing Times

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

2014 ◽  
Vol 1006-1007 ◽  
pp. 498-503 ◽  
Author(s):  
Yu Fang Zhao
Keyword(s):  
Single Machine ◽  
Dynamic Programming Algorithm ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Programming Algorithm ◽  
Due Date ◽  
Due Date Assignment ◽  
Processing Times ◽  
Delivery Times ◽  
Tardy Jobs

This paper considers single machine scheduling and due date assignment 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 depends 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 analyze the problems with two different due date assignment methods and conclude that the problems are polynomial time solvable. We provide a dynamic programming algorithm with O(n3) times for the problems.

Single Machine Scheduling with Discretely Compressible Processing Times

2013 ◽  
Vol 787 ◽  
pp. 1020-1024
Author(s):  
Shu Xia Zhang ◽  
Yu Zhong Zhang
Keyword(s):  
Dynamic Programming ◽  
Single Machine ◽  
Processing Time ◽  
Machine Scheduling ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Release Times

In this paper, we address the single machine scheduling problem with discretely compressible processing times, where processing any job with a compressed processing time incurs a corresponding compression cost. We consider the following problem: scheduling with discretely compressible processing times to minimize makespan with the constraint of total compression cost. Jobs may have different release times. We design a pseudo-polynomial time algorithm by approach of dynamic programming and an FPTAS.

scholarly journals Two-Machine Job-Shop Scheduling with Equal Processing Times on Each Machine

Mathematics ◽  
2019 ◽  
Vol 7 (3) ◽  
pp. 301 ◽  
Author(s):  
Evgeny Gafarov ◽  
Frank Werner
Keyword(s):  
Dynamic Programming ◽  
Job Shop ◽  
Job Shop Scheduling ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Scheduling Problem ◽  
Single Track ◽  
Shop Scheduling ◽  
Processing Times ◽  
Equal Processing Times

In this paper, we consider a two-machine job-shop scheduling problem of minimizing total completion time subject to n jobs with two operations and equal processing times on each machine. This problem occurs e.g., as a single-track railway scheduling problem with three stations and constant travel times between any two adjacent stations. We present a polynomial dynamic programming algorithm of the complexity O ( n 5 ) and a heuristic procedure of the complexity O ( n 3 ) . This settles the complexity status of the problem under consideration which was open before and extends earlier work for the two-station single-track railway scheduling problem. We also present computational results of the comparison of both algorithms. For the 30,000 instances with up to 30 jobs considered, the average relative error of the heuristic is less than 1 % . In our tests, the practical running time of the dynamic programming algorithm was even bounded by O ( n 4 ) .

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.

Single Machine Scheduling with an Availability Constraint and Rejection

2014 ◽  
Vol 31 (05) ◽  
pp. 1450037 ◽  
Author(s):  
Chuanli Zhao ◽  
Hengyong Tang
Keyword(s):  
Single Machine ◽  
Approximation Scheme ◽  
Dynamic Programming Algorithm ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Programming Algorithm ◽  
Time Interval ◽  
Availability Constraint ◽  
Np Hard Problem ◽  
Rejection Penalty

This paper considers single machine scheduling with an availability constraint and rejection. It is assumed that the machine is not available for processing during a given time interval. A job is either rejected, in which case a rejection penalty has to be paid, or accepted and processed on the machine. The objective is to minimize the sum of the weighted total completion time of the accepted jobs and the total rejection penalty of the rejected jobs. For this NP-hard problem, we present a pseudo-polynomial dynamic programming algorithm and a fully polynomial-time approximation scheme (FPTAS).

scholarly journals Stochastic Single Machine JIT Scheduling with Geometric Processing Times and Due Dates

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yuncheng Luo
Keyword(s):  
Single Machine ◽  
Optimal Schedule ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Scheduling Problem ◽  
Due Dates ◽  
Common Mean ◽  
Processing Times ◽  
Tardy Jobs ◽  
Special Case

In this paper, we investigate a static stochastic single machine JIT scheduling problem in which the jobs’ processing times are stochastically independent and follow geometric distributions whose mean is provided, due dates are geometrically distributed with a common mean, and both the unit penalty of earliness/tardiness and the fixed penalty of earliness/tardiness are deterministic and different. The objective is to minimize the expected total penalties for quadratic earliness, quadratic tardiness, and early and tardy jobs. We prove that the optimal schedule to minimize this problem is V-shaped with respect to the ratio of mean processing time to unit tardiness penalty under the specific condition. Also, we show a special case and two theorems related to this JIT scheduling problem under specific situations where the optimal solutions exist. Finally, based on the V-shaped characteristic, a dynamic programming algorithm is designed to achieve an optimal V-shaped schedule in pseudopolynomial time.

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