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.

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 Batch Delivery Scheduling and Common due Date Assignment with Identical Processing Times

2014 ◽  
Vol 635-637 ◽  
pp. 1884-1889 ◽  
Author(s):  
Xing Zi Xie ◽  
Xiu Li Wang
Keyword(s):  
Single Machine ◽  
Optimal Schedule ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Due Date ◽  
Common Due Date ◽  
Processing Times ◽  
Batch Delivery ◽  
Weighted Earliness ◽  
Delivery Scheduling

This paper considers the problem of single-machine batch delivery scheduling with an assignable common due date where all jobs have identical processing times. Finished jobs are delivered in batches and the cost per batch delivery is fixed and independent of the number of jobs in the batch. For our problem, the penalties of earliness-tardiness are assumed to be arbitrarily weighted but the holding costs are equally weighted. The objective is to determine the common due date and find an optimal schedule to minimize the sum of total weighted earliness, tardiness, holding, due date, and delivery costs. We present some basic properties of the structure of the optimal schedule for the problem, and provide a polynomial dynamic programming algorithm.

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.

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 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 ) .

Supply Chain Scheduling with Transportation Cost on a Single Machine

2011 ◽  
Vol 382 ◽  
pp. 106-109
Author(s):  
Jing Fan
Keyword(s):  
Supply Chain ◽  
Single Machine ◽  
System Integration ◽  
Production Cost ◽  
Dynamic Programming Algorithm ◽  
Optimal Solution ◽  
Transportation Cost ◽  
Programming Algorithm ◽  
Scheduling Problem ◽  
Supply Chain Scheduling

Supply chain scheduling problem is raised from modern manufacturing system integration, in which manufacturers not only process orders but also transport products to customer’s location. Therefore, the system ought to consider how to appropriately send finished jobs in batches to reduce transportation costs while considering the processing sequence of jobs to reduce production cost. This paper studies such a supply chain scheduling problem that one manufacturer produces with a single machine and deliveries jobs within limited transportation times to one customer. The objective function is to minimize the total sum of production cost and transportation cost. The NP hard property of the problem is proved in the simpler way, and the pseudo-dynamic programming algorithm in the literature is modified as the MDP algorithm to get the optimal solution which is associated with the total processing times of jobs.

A SINGLE-MACHINE TWO-AGENT SCHEDULING PROBLEM BY GA APPROACH

2012 ◽  
Vol 29 (02) ◽  
pp. 1250013 ◽  
Author(s):  
SHUENN-REN CHENG
Keyword(s):  
Single Machine ◽  
Completion Time ◽  
Learning Effect ◽  
Control Parameter ◽  
Optimal Schedule ◽  
Total Weighted Completion Time ◽  
Scheduling Problem ◽  
Processing Times ◽  
Agent Scheduling ◽  
Weighted Completion Time

A single-machine two-agent scheduling problem with a truncation learning effect is being addressed in the study. The truncation learning effect means that the actual processing time of a job is a function of the sum of processing times of already scheduled jobs and a control parameter. The aim is to find an optimal schedule to minimize the total weighted completion time of jobs of the first agent under the circumstances that no tardy job is allowed for the second agent. A branch-and-bound and three heuristic-based genetic algorithms (GAs) are proposed to solve the problem. Also presented in the study are the computational results of all proposed algorithms.

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