Just-In-Time Scheduling with Generalized Due Dates and Identical Due Date Intervals

2018 ◽  
Vol 35 (06) ◽  
pp. 1850046 ◽  
Author(s):  
Byung-Cheon Choi ◽  
Myoung-Ju Park
Keyword(s):  
Single Machine Scheduling ◽  
Just In Time ◽  
Scheduling Problem ◽  
Np Hard ◽  
Due Dates ◽  
Due Date ◽  
Time Scheduling ◽  
Weighted Number ◽  
Polynomially Solvable ◽  
Tardy Jobs

We consider a single-machine scheduling problem such that the due dates are assigned not to the jobs but to the position at which the job is processed. We focus on the case with identical due date intervals. The objective is to minimize the weighted number of early and tardy jobs. First, we show that the problem is strongly NP-hard and has no [Formula: see text]-approximation algorithm for any fixed value [Formula: see text]. Then, we investigate polynomially solvable cases. Finally, we show that the preemption version is weakly NP-hard through its equivalence to the problem of minimizing the weighted number of tardy jobs.

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.

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.

Due-Date Assignment on a Single Machine Scheduling Problem with Nonlinear Deterioration Function

2013 ◽  
Vol 645 ◽  
pp. 280-284
Author(s):  
Hua Ping Wu ◽  
Min Huang ◽  
Vincent Cho ◽  
W.H. Ip ◽  
Xing Wei Wang
Keyword(s):  
Single Machine ◽  
Real World ◽  
Processing Time ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Due Dates ◽  
Due Date ◽  
Due Date Assignment ◽  
Non Linear ◽  
Normal Processing

The paper considers the due-date assignment problem with a non-linear deterioration in which the due dates are determined by the equal slack method. Here, the processing time of a job is defined by a non-linear function of total normal processing time of jobs in front of it in the sequence. The objective is to minimize the total tardiness penalties. According to the needs from the real world, the problem is divided into two cases, i.e., allowing with early jobs and no early jobs respectively. The related lemma, corollary and theorems for the problems are proposed and proved. At the same time, it shows that the problems in this paper can be solved in the polynomial times.

scholarly journals The Due Date Assignment Scheduling Problem with Delivery Times and Truncated Sum-of-Processing-Times-Based Learning Effect

Mathematics ◽  
2021 ◽  
Vol 9 (23) ◽  
pp. 3085
Author(s):  
Jin Qian ◽  
Yu Zhan
Keyword(s):  
Polynomial Time ◽  
Learning Effect ◽  
Single Machine Scheduling ◽  
Decision Variable ◽  
Scheduling Problem ◽  
Due Date ◽  
Optimal Sequence ◽  
Processing Times ◽  
Delivery Times ◽  
Tardy Jobs

This paper considers a single-machine scheduling problem with past-sequence-dependent delivery times and the truncated sum-of-processing-times-based learning effect. The goal is to minimize the total costs that comprise the number of early jobs, the number of tardy jobs and due date. The due date is a decision variable. There will be corresponding penalties for jobs that are not completed on time. Under the common due date, slack due date and different due date, we prove that these problems are polynomial time solvable. Three polynomial time algorithms are proposed to obtain the optimal sequence.

AN EFFICIENT OPTIMAL SOLUTION OF A TWO-CRANE SCHEDULING PROBLEM

2009 ◽  
Vol 26 (01) ◽  
pp. 31-58 ◽  
Author(s):  
WEIHUA ZHOU ◽  
XIAOBO WU
Keyword(s):  
Access Point ◽  
Scheduling Problem ◽  
Due Dates ◽  
Safe Distance ◽  
Due Date ◽  
Feasible Schedule ◽  
Crane Scheduling ◽  
Number Of Tardy Jobs ◽  
Maximum Tardiness ◽  
Tardy Jobs

This paper studies a two-crane scheduling problem in a port terminal. These two cranes are deployed in a block of a port terminal. They can move along a bi-directional traveling lane and must maintain a safe distance between them to avoid collision. A group of export containers in a block is required to be transported by cranes from their storage location to an access point of the block. Each container is associated with a due date. The problem is to find a schedule such that all containers are carried to the access point before their due dates. If such schedule does not exist, then the problem becomes to find schedules to minimize the maximum tardiness, the number of tardy jobs, respectively. In this paper, we first identify the necessary and sufficient conditions for the existence of a feasible schedule, i.e., a schedule transports all containers to the access point before their due dates and does not violate the requirement to maintain a safe distance between two cranes. We prove that if there exists at least one feasible schedule, then there must be a permutation schedule with containers sequenced in earliest due date (EDD) order to be feasible. An efficient algorithm is developed to find a feasible schedule given its existence. Furthermore, we provide efficient algorithms for minimizing the maximum tardiness, the number of tardy jobs, the makespan and the total completion time, respectively.

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