An improved dynamic programming algorithm for the single-machine mean absolute deviation problem with a restrictive common due date

1995 ◽  
Vol 17 (3) ◽  
pp. 149-152 ◽  
Author(s):  
Jose A. Ventura ◽  
Michael X. Weng
Keyword(s):  
Dynamic Programming ◽  
Single Machine ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Mean Absolute Deviation ◽  
Due Date ◽  
Absolute Deviation ◽  
Common Due Date ◽  
Deviation Problem ◽  
Improved Dynamic Programming

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.

Minimizing mean absolute deviation of completion times about a common due date

1986 ◽  
Vol 33 (2) ◽  
pp. 227-240 ◽  
Author(s):  
Uttarayan Bagchi ◽  
Robert S. Sullivan ◽  
Y. L. Chang
Keyword(s):  
Mean Absolute Deviation ◽  
Due Date ◽  
Absolute Deviation ◽  
Common Due Date ◽  
Completion 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.

scholarly journals Batch Scheduling on a Single Machine with Maintenance Interval

2020 ◽  
Author(s):  
Zhang Honglin ◽  
Bin Qian ◽  
Yaohua Wu
Keyword(s):  
Dynamic Programming ◽  
Single Machine ◽  
Manufacturing Industry ◽  
Dynamic Programming Algorithm ◽  
Batch Scheduling ◽  
Programming Algorithm ◽  
Small Scale ◽  
Field Representation ◽  
Machine Failure ◽  
Delivery Costs

In the manufacturing industry, orders are typically scheduled and delivered through batches, and the probability of machine failure under high-load operation is high. On this basis, we focus on a single machine batch scheduling problem with a maintenance interval (SMBSP-MI). The studied problem is expressed by three-field representation as 1|B,MI|\sum{F_j+\mu}m, and the optimization objective is to minimize total flow time and delivery costs. Firstly, 1|B,MI|\sum{F_j+\mu}m is proved to be NP-hard by Turing reduction. Secondly, shortest processing time (SPT) order is shown the optimal scheduling of SMBSP-MI, and a dynamic programming algorithm based on SPT (DPA-SPT) with the time complexity of O(n^3T_1) is proposed. A small-scale example is designed to verify the feasibility of DPA-SPT. Finally, DPA-SPT is approximated to a fully-polynomial dynamic programming approximation algorithm based on SPT (FDPAA-SPT) by intervals partitioning technique. The proposed FDPAA-SPT runs in O(\frac{n^5}{\varepsilon^2})\ time with the approximation (1+\varepsilon).

An Improved Dynamic Programming Algorithm for Bitonic TSP

2013 ◽  
Vol 347-350 ◽  
pp. 3094-3098 ◽  
Author(s):  
Jian Li
Keyword(s):  
Dynamic Programming ◽  
Time Complexity ◽  
Dynamic Programming Algorithm ◽  
Space Complexity ◽  
Programming Algorithm ◽  
Time And Space ◽  
Space Requirement ◽  
Classical Algorithm ◽  
Computing Speed ◽  
Improved Dynamic Programming

This paper puts forward an improved dynamic programming algorithm for bitonic TSP and it proves to be correct. Divide the whole loop into right-and-left parts through analyzing the key point connecting to the last one directly; then construct a new optimal sub-structure and recursion. The time complexity of the new algorithm is O(n2) and the space complexity is O(n); while both the time and space complexities of the classical algorithm are O(n2). Experiment results showed that the new algorithm not only reduces the space requirement greatly but also increases the computing speed by 2-3 times compared with the classical algorithm.

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