scholarly journals Supply Chain Batching Problem with Identical Orders and Lifespan

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Shanlin Li ◽  
Maoqin Li ◽  
Hong Yan
Keyword(s):  
Dynamic Programming ◽  
Processing Time ◽  
Recursion Formula ◽  
Dynamic Programming Algorithm ◽  
Setup Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Programming Algorithm ◽  
Short Lifespan ◽  
The Difference

In the real world, there are a large number of supply chains that involve the short lifespan products. In this paper, we consider an integrated production and distribution batch scheduling problem on a single machine for the orders with a short lifespan, because it may be cheaper or faster to process and distribute orders in a batch than to process and distribute them individually. Assume that the orders have the identical processing time and come from the same location, and the batch setup time is a constant. The problem is to choose the number of batches and batch sizes to minimize the total delivery time without violating the order lifespan. We first give a backward dynamic programming algorithm, but it is not an actually polynomial-time algorithm. Then we propose a constant time partial dynamic programming algorithm by doing further research into the recursion formula in the algorithm. Further, using the difference characteristics of the optimal value function, a specific calculating formula to solve the problem with the setup time being integer times of the processing time is obtained.

scholarly journals Batch Scheduling with Proportional-Linear Deterioration and Outsourcing

2017 ◽  
Vol 2017 ◽  
pp. 1-5
Author(s):  
Cuixia Miao ◽  
Fanxiao Meng ◽  
Juan Zou ◽  
Binglin Jia
Keyword(s):  
Dynamic Programming Algorithm ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Third Party ◽  
Batch Scheduling ◽  
Programming Algorithm ◽  
Release Dates ◽  
Linear Deterioration ◽  
Total Penalty ◽  
Maximum Completion Time

We consider the bounded parallel-batch scheduling with proportional-linear deterioration and outsourcing, in which the actual processing time is pj=αj(A+Dt) or pj=αjt. A job is either accepted and processed in batches on a single machine by manufactures themselves or outsourced to the third party with a certain penalty having to be paid. The objective is to minimize the maximum completion time of the accepted jobs and the total penalty of the outsourced jobs. For the pj=αj(A+Dt) model, when all the jobs are released at time zero, we show that the problem is NP-hard and present a pseudo-polynomial time algorithm, respectively. For the pj=αjt model, when the jobs have distinct m (<n) release dates, we provide a dynamic programming algorithm, where n is the number of jobs.

Single Machine Scheduling with Discretely Compressible Processing Times

2013 ◽  
Vol 787 ◽  
pp. 1020-1024
Author(s):  
Shu Xia Zhang ◽  
Yu Zhong Zhang
Keyword(s):  
Dynamic Programming ◽  
Single Machine ◽  
Processing Time ◽  
Machine Scheduling ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Single Machine Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Release Times

In this paper, we address the single machine scheduling problem with discretely compressible processing times, where processing any job with a compressed processing time incurs a corresponding compression cost. We consider the following problem: scheduling with discretely compressible processing times to minimize makespan with the constraint of total compression cost. Jobs may have different release times. We design a pseudo-polynomial time algorithm by approach of dynamic programming and an FPTAS.

Scheduling with Discretely Compressible Processing Times to Minimize Makespan

2014 ◽  
Vol 575 ◽  
pp. 926-930
Author(s):  
Shu Xia Zhang ◽  
Yu Zhong Zhang
Keyword(s):  
Dynamic Programming ◽  
Polynomial Time ◽  
Processing Time ◽  
Parallel Machines ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Identical Parallel Machines ◽  
Processing Times ◽  
Release Times ◽  
Scheduling Model

In this paper, we address the scheduling model with discretely compressible processing times, where processing any job with a compressed processing time incurs a corresponding compression cost. We consider the following problem: scheduling with discretely compressible processing times to minimize makespan with the constraint of total compression cost on identical parallel machines. Jobs may have simultaneous release times. We design a pseudo-polynomial time algorithm by approach of dynamic programming and an FPTAS.

scholarly journals Measurement Aspects of Genome Pattern Investigations - Hardware Implementation

2012 ◽  
Vol 19 (1) ◽  
pp. 49-62
Author(s):  
Andrzej Pułka ◽  
Adam Milik
Keyword(s):  
Dynamic Programming ◽  
Processing Time ◽  
Hardware Implementation ◽  
Dynamic Programming Algorithm ◽  
Programming Algorithm ◽  
Data Path ◽  
Original Algorithm ◽  
A Genome ◽  
Speed Up ◽  
Programmable Devices

Measurement Aspects of Genome Pattern Investigations - Hardware Implementation The work presented in the paper concerns a very important problem of searching for string alignments. The authors show that the problem of a genome pattern alignment could be interpreted and defined as a measuring task, where the distance between two (or more) patterns is investigated. The problem originates from modern computation biology. Hardware-based implementations have been driving out software solutions in the field recently. The complex programmable devices have become very commonly applied. The paper introduces a new, optimized approach based on the Smith-Waterman dynamic programming algorithm. The original algorithm is modified in order to simplify data-path processing and take advantage of the properties offered by FPGA devices. The results obtained with the proposed methodology allow to reduce the size of the functional block and radically speed up the processing time. This approach is very competitive compared with other related works.

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