Minimizing sum of completion times for batch scheduling of jobs with deteriorating processing times

2008 ◽  
Vol 187 (3) ◽  
pp. 1090-1099 ◽  
Author(s):  
Joseph Y.-T. Leung ◽  
C.T. Ng ◽  
T.C. Edwin Cheng
Keyword(s):  
Batch Scheduling ◽  
Processing Times ◽  
Completion Times ◽  
Sum Of Completion Times

An Efficient Batch Scheduling Model for Hospital Sterilization Services Using Genetic Algorithm

2021 ◽  
pp. 928-946
Author(s):  
Shubin Xu ◽  
John Wang
Keyword(s):  
Genetic Algorithm ◽  
Medical Devices ◽  
Programming Model ◽  
Flow Time ◽  
Nonlinear Integer Programming ◽  
Batch Scheduling ◽  
Scheduling Problem ◽  
Work In Process ◽  
Completion Times ◽  
Sum Of Completion Times

A major challenge faced by hospitals is to provide efficient medical services. The problem studied in this article is motivated by the hospital sterilization services where the washing step generally constitutes a bottleneck in the sterilization services. Therefore, an efficient scheduling of the washing operations to reduce flow time and work-in-process inventories is of great concern to management. In the washing step, different sets of reusable medical devices may be washed together as long as the washer capacity is not exceeded. Thus, the washing step is modeled as a batch scheduling problem where washers have nonidentical capacities and reusable medical device sets have different sizes and different ready times. The objective is to minimize the sum of completion times for washing operations. The problem is first formulated as a nonlinear integer programming model. Given that this problem is NP-hard, a genetic algorithm is then proposed to heuristically solve the problem. Computational experiments show that the proposed algorithm is capable of consistently obtaining high-quality solutions in short computation times.

A Note on Flow Shop Scheduling with the Effects of Learning and Deterioration

2014 ◽  
Vol 513-517 ◽  
pp. 2149-2152
Author(s):  
Yu Ping Niu ◽  
Ji Bo Wang
Keyword(s):  
Learning Effect ◽  
Flow Shop ◽  
Flow Shop Scheduling ◽  
Scheduling Problems ◽  
Shop Scheduling ◽  
Processing Times ◽  
Polynomially Solvable ◽  
Machine Scheduling Problems ◽  
Completion Times ◽  
Sum Of Completion Times

In this note, we consider the machine scheduling problems with the effects of learning and deterioration. In this model, job processing times are defined by functions dependent on their starting times and positions in the sequence. The scheduling objectives are makespan, sum of completion times. It is shown that even with the introduction of learning effect and deterioration jobs to job processing times, several flow shop problems remain polynomially solvable.

scholarly journals Single-Machine Group Scheduling Problems with Deterioration to Minimize the Sum of Completion Times

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Yong He ◽  
Li Sun
Keyword(s):  
Single Machine ◽  
Group Scheduling ◽  
Scheduling Problems ◽  
Minimization Problems ◽  
Processing Times ◽  
Machine Group ◽  
Polynomially Solvable ◽  
Decreasing Functions ◽  
Completion Times ◽  
Sum Of Completion Times

We consider two single-machine group scheduling problems with deteriorating group setup and job processing times. That is, the job processing times and group setup times are linearly increasing (or decreasing) functions of their starting times. Jobs in each group have the same deteriorating rate. The objective of scheduling problems is to minimize the sum of completion times. We show that the sum of completion times minimization problems remains polynomially solvable under the agreeable conditions.

An Efficient Batch Scheduling Model for Hospital Sterilization Services Using Genetic Algorithm

2018 ◽  
Vol 9 (1) ◽  
pp. 1-17
Author(s):  
Shubin Xu ◽  
John Wang
Keyword(s):  
Genetic Algorithm ◽  
Medical Devices ◽  
Programming Model ◽  
Flow Time ◽  
Nonlinear Integer Programming ◽  
Batch Scheduling ◽  
Work In Process ◽  
Scheduling Model ◽  
Completion Times ◽  
Sum Of Completion Times

A major challenge faced by hospitals is to provide efficient medical services. The problem studied in this article is motivated by the hospital sterilization services where the washing step generally constitutes a bottleneck in the sterilization services. Therefore, an efficient scheduling of the washing operations to reduce flow time and work-in-process inventories is of great concern to management. In the washing step, different sets of reusable medical devices may be washed together as long as the washer capacity is not exceeded. Thus, the washing step is modeled as a batch scheduling problem where washers have nonidentical capacities and reusable medical device sets have different sizes and different ready times. The objective is to minimize the sum of completion times for washing operations. The problem is first formulated as a nonlinear integer programming model. Given that this problem is NP-hard, a genetic algorithm is then proposed to heuristically solve the problem. Computational experiments show that the proposed algorithm is capable of consistently obtaining high-quality solutions in short computation times.

Stochastically Minimizing Total Delay of Jobs Subject to Random Deadlines

1991 ◽  
Vol 5 (3) ◽  
pp. 333-348 ◽  
Author(s):  
Susan H. Xu
Keyword(s):  
Time Distribution ◽  
Processing Time ◽  
Fixed Number ◽  
Parallel Processors ◽  
Threshold Strategy ◽  
Total Delay ◽  
Scheduling System ◽  
Processing Times ◽  
Completion Times ◽  
Sum Of Completion Times

This paper analyzes a scheduling system where a fixed number of nonpreemptive jobs is to be processed on multiple parallel processors with different processing speeds. Each processor has an exponential processing time distribution and the processors are ordered in ascending order of their mean processing times. Each job has its own deadline that is exponentially distributed with rate ß1, independent of the deadlines of other jobs and also independent of job processing times. A job departs the system as soon as either its processing completes or its deadline occurs. We show that there exists a simple threshold strategy that slochastically minimizes the total delay of all jobs. The policy depends on distributions of processing times and deadlines, but is independent of the rate of deadlines. When the rate of the deadline distribution is 0 (no deadlines), the total delay reduces to the flowtime (the sum of completion times of all jobs). If each job has its own probability of being correctly processed, then an extension of this policy stochastically maximizes the total number of correctly processed, nontardy jobs. We discuss possible generalizations and limitations of this result.

Batch Scheduling Algorithm with Approximation of Job Completion Times and Case Studies

2020 ◽  
Vol 43 (4) ◽  
pp. 23-32
Author(s):  
Song-Eun Kim ◽  
◽  
Seong-Hyeon Park ◽  
Su-Min Kim ◽  
Kyungsu Park ◽  
...  
Keyword(s):  
Case Studies ◽  
Scheduling Algorithm ◽  
Batch Scheduling ◽  
Completion Times

A STOCHASTIC BATCHING AND SCHEDULING PROBLEM

2001 ◽  
Vol 15 (4) ◽  
pp. 465-479 ◽  
Author(s):  
Ger Koole ◽  
Rhonda Righter
Keyword(s):  
Optimal Policy ◽  
Semiconductor Manufacturing ◽  
Processing Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Flow Time ◽  
Batch Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Deterministic Problem

We consider a batch scheduling problem in which the processing time of a batch of jobs equals the maximum of the processing times of all jobs in the batch. This is the case, for example, for burn-in operations in semiconductor manufacturing and other testing operations. Processing times are assumed to be random, and we consider minimizing the makespan and the flow time. The problem is much more difficult than the corresponding deterministic problem, and the optimal policy may have many counterintuitive properties. We prove various structural properties of the optimal policy and use these to develop a polynomial-time algorithm to compute the optimal policy.

On the optimality of LEPT and cµ rules for machines in parallel

1992 ◽  
Vol 29 (3) ◽  
pp. 667-681 ◽  
Author(s):  
Cheng-Shang Chang ◽  
Xiuli Chao ◽  
Michael Pinedo ◽  
Richard Weber
Keyword(s):  
Distributed Processing ◽  
Sufficient Conditions ◽  
Weighted Sum ◽  
Scheduling Problems ◽  
Priority Assignment ◽  
Processing Times ◽  
Weighted Number ◽  
Necessary And Sufficient ◽  
Late Jobs ◽  
Completion Times

We consider scheduling problems with m machines in parallel and n jobs. The machines are subject to breakdown and repair. Jobs have exponentially distributed processing times and possibly random release dates. For cost functions that only depend on the set of uncompleted jobs at time t we provide necessary and sufficient conditions for the LEPT rule to minimize the expected cost at all t within the class of preemptive policies. This encompasses results that are known for makespan, and provides new results for the work remaining at time t. An application is that if the cµ rule has the same priority assignment as the LEPT rule then it minimizes the expected weighted number of jobs in the system for all t. Given appropriate conditions, we also show that the cµ rule minimizes the expected value of other objective functions, such as weighted sum of job completion times, weighted number of late jobs, or weighted sum of job tardinesses, when jobs have a common random due date.

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