BICRITERIA SCHEDULING ON SINGLE-MACHINE WITH INVENTORY OPERATIONS

2009 ◽  
Vol 01 (02) ◽  
pp. 227-234
Author(s):  
BAOQIANG FAN ◽  
RONGJUN CHEN ◽  
GUOCHUN TANG
Keyword(s):  
Single Machine ◽  
Approximation Scheme ◽  
Optimal Algorithm ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Bicriteria Scheduling ◽  
Processing Times ◽  
Polynomial Formula ◽  
Tardy Jobs ◽  
Special Case

In this paper, we consider the single machine scheduling problem with inventory operations. The objective is to minimize makespan subject to the constraint that the total number of tardy jobs is minimum. We show the problem is strongly NP-hard. A polynomial [Formula: see text]-approximation scheme for the problem is presented, where m is defined as the total job's processing times ∑ pj divided by the capacity c of the storage, and an optimal algorithm for a special case of the problem, in which each job is one unit in size.

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.

An Optimal Algorithm for Scheduling with Variable Job Processing Times and Rejection

2015 ◽  
Vol 775 ◽  
pp. 449-452
Author(s):  
Ji Bo Wang ◽  
Chou Jung Hsu
Keyword(s):  
Objective Function ◽  
Polynomial Time ◽  
Single Machine ◽  
Processing Time ◽  
Optimal Algorithm ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Rejection Penalty

This paper studies a single machine scheduling problem with rejection. Each job has a variable processing time and a rejection penalty. The objective function is to minimize the sum of the makespan of the accepted jobs and the total rejection penalty of the rejected jobs. We show that the problem can be solved in polynomial time.

scholarly journals Dynamic Restructuring Framework for Scheduling with Release Times and Due-Dates

Mathematics ◽  
2019 ◽  
Vol 7 (11) ◽  
pp. 1104 ◽  
Author(s):  
Nodari Vakhania
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Machine Scheduling ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Scheduling Problems ◽  
Due Dates ◽  
Processing Times ◽  
Release Times ◽  
Special Case

Scheduling jobs with release and due dates on a single machine is a classical strongly NP-hard combination optimization problem. It has not only immediate real-life applications but also it is effectively used for the solution of more complex multiprocessor and shop scheduling problems. Here, we propose a general method that can be applied to the scheduling problems with job release times and due-dates. Based on this method, we carry out a detailed study of the single-machine scheduling problem, disclosing its useful structural properties. These properties give us more insight into the complex nature of the problem and its bottleneck feature that makes it intractable. This method also helps us to expose explicit conditions when the problem can be solved in polynomial time. In particular, we establish the complexity status of the special case of the problem in which job processing times are mutually divisible by constructing a polynomial-time algorithm that solves this setting. Apparently, this setting is a maximal polynomially solvable special case of the single-machine scheduling problem with non-arbitrary job processing times.

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.

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