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.

scholarly journals Parallel Batch Scheduling of Deteriorating Jobs with Release Dates and Rejection

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Juan Zou ◽  
Cuixia Miao
Keyword(s):  
Approximation Scheme ◽  
Deteriorating Jobs ◽  
Time Algorithm ◽  
Batch Scheduling ◽  
Release Dates ◽  
Ordinary Sense ◽  
Starting Time ◽  
Total Penalty ◽  
Batching Machine ◽  
Increasing Function

We consider the unbounded parallel batch scheduling with deterioration, release dates, and rejection. Each job is either accepted and processed on a single batching machine, or rejected by paying penalties. The processing time of a job is a simple linear increasing function of its starting time. The objective is to minimize the sum of the makespan of the accepted jobs and the total penalty of the rejected jobs. First, we show that the problem is NP-hard in the ordinary sense. Then, we present two pseudopolynomial time algorithms and a fully polynomial-time approximation scheme to solve this problem. Furthermore, we provide an optimalO(nlog⁡n)time algorithm for the case where jobs have identical release dates.

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.

A STOCHASTIC BATCHING AND SCHEDULING PROBLEM

2001 ◽  
Vol 15 (4) ◽  
pp. 465-479 ◽  
Author(s):  
Ger Koole ◽  
Rhonda Righter
Keyword(s):  
Optimal Policy ◽  
Semiconductor Manufacturing ◽  
Processing Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Flow Time ◽  
Batch Scheduling ◽  
Scheduling Problem ◽  
Processing Times ◽  
Deterministic Problem

We consider a batch scheduling problem in which the processing time of a batch of jobs equals the maximum of the processing times of all jobs in the batch. This is the case, for example, for burn-in operations in semiconductor manufacturing and other testing operations. Processing times are assumed to be random, and we consider minimizing the makespan and the flow time. The problem is much more difficult than the corresponding deterministic problem, and the optimal policy may have many counterintuitive properties. We prove various structural properties of the optimal policy and use these to develop a polynomial-time algorithm to compute the optimal policy.

scholarly journals Polynomial Algorithm for Constructing Pareto-Optimal Schedules for Problem 1∣rj∣Lmax,Cmax

2020 ◽  
Author(s):  
Alexander A. Lazarev ◽  
Nikolay Pravdivets
Keyword(s):  
Completion Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Single Machine Scheduling ◽  
Maximum Lateness ◽  
Pareto Optimal ◽  
Due Dates ◽  
Processing Times ◽  
Pareto Optimal Set ◽  
Maximum Completion Time

In this chapter, we consider the single machine scheduling problem with given release dates, processing times, and due dates with two objective functions. The first one is to minimize the maximum lateness, that is, maximum difference between each job due date and its actual completion time. The second one is to minimize the maximum completion time, that is, to complete all the jobs as soon as possible. The problem is NP-hard in the strong sense. We provide a polynomial time algorithm for constructing a Pareto-optimal set of schedules on criteria of maximum lateness and maximum completion time, that is, problem 1 ∣ r j ∣ L max , C max , for the subcase of the problem: d 1 ≤ d 2 ≤ … ≤ d n ; d 1 − r 1 − p 1 ≥ d 2 − r 2 − p 2 ≥ … ≥ d n − r n − p n .

Proportionate Flow Shop Scheduling with Rejection

2017 ◽  
Vol 34 (04) ◽  
pp. 1750015 ◽  
Author(s):  
Shi-Sheng Li ◽  
De-Liang Qian ◽  
Ren-Xia Chen
Keyword(s):  
Processing Time ◽  
Flow Shop ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Flow Shop Scheduling ◽  
Total Weighted Completion Time ◽  
Processing Times ◽  
Proportionate Flow Shop ◽  
Total Penalty ◽  
Scheduling With Rejection

We consider the problem of scheduling [Formula: see text] jobs with rejection on a set of [Formula: see text] machines in a proportionate flow shop system where the job processing times are machine-independent. The goal is to find a schedule to minimize the scheduling cost of all accepted jobs plus the total penalty of all rejected jobs. Two variations of the scheduling cost are considered. The first is the maximum tardiness and the second is the total weighted completion time. For the first problem, we first show that it is [Formula: see text]-hard, then we construct a pseudo-polynomial time algorithm to solve it and an [Formula: see text] time for the case where the jobs have the same processing time. For the second problem, we first show that it is [Formula: see text]-hard, then we design [Formula: see text] time algorithms for the case where the jobs have the same weight and for the case where the jobs have the same processing time.

TWO-MACHINE FLOW SHOP SCHEDULING WITH INDIVIDUAL OPERATION'S REJECTION

2014 ◽  
Vol 31 (01) ◽  
pp. 1450002 ◽  
Author(s):  
QIANG GAO ◽  
XIWEN LU
Keyword(s):  
Approximation Scheme ◽  
Flow Shop ◽  
Dynamic Programming Algorithm ◽  
Flow Shop Scheduling ◽  
Programming Algorithm ◽  
Polynomial Time Approximation Scheme ◽  
Time Approximation ◽  
Shop Scheduling ◽  
Processing Times ◽  
Total Penalty

A two-machine flow shop scheduling problem with rejection is considered in this paper. The objective is to minimize the sum of makespan of accepted operations and total penalty of rejected operations. Each job has two operations that could be rejected, respectively. Operations on the first machine have penalties α1 times of their processing times and operations on the second machine have penalties α2 times of their processing times. A [Formula: see text]-approximation algorithm is presented for the case where min{α1, α2} < 1 and max{α1, α2} ≥ 1. A dynamic programming algorithm is provided for general α1 and α2. A fully polynomial-time approximation scheme (FPTAS) is designed for all NP-hard cases.

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 primal-dual approximation algorithm for the k-means problem with penalties

2021 ◽  
pp. 1-13
Author(s):  
Chunying Ren ◽  
Dachuan Xu ◽  
Donglei Du ◽  
Min Li
Keyword(s):  
Approximation Algorithm ◽  
Polynomial Time ◽  
Best Approximation ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Approximation Ratio ◽  
Data Set ◽  
Penalty Cost ◽  
Primal Dual ◽  
Total Penalty

Abstract In the k-means problem with penalties, we are given a data set ${\cal D} \subseteq \mathbb{R}^\ell $ of n points where each point $j \in {\cal D}$ is associated with a penalty cost p j and an integer k. The goal is to choose a set ${\rm{C}}S \subseteq {{\cal R}^\ell }$ with |CS| ≤ k and a penalized subset ${{\cal D}_p} \subseteq {\cal D}$ to minimize the sum of the total squared distance from the points in D / D p to CS and the total penalty cost of points in D p , namely $\sum\nolimits_{j \in {\cal D}\backslash {{\cal D}_p}} {d^2}(j,{\rm{C}}S) + \sum\nolimits_{j \in {{\cal D}_p}} {p_j}$ . We employ the primal-dual technique to give a pseudo-polynomial time algorithm with an approximation ratio of (6.357+ε) for the k-means problem with penalties, improving the previous best approximation ratio 19.849+∊ for this problem given by Feng et al. in Proceedings of FAW (2019).

scholarly journals Parallel-Batch Scheduling and Transportation Coordination with Waiting Time Constraint

2014 ◽  
Vol 2014 ◽  
pp. 1-8 ◽  
Author(s):  
Hua Gong ◽  
Daheng Chen ◽  
Ke Xu
Keyword(s):  
Waiting Time ◽  
Processing Time ◽  
Optimal Algorithm ◽  
Dynamic Programming Algorithm ◽  
Time Constraint ◽  
Batch Scheduling ◽  
Programming Algorithm ◽  
Np Hard ◽  
Processing Times ◽  
Equal Processing Times

This paper addresses a parallel-batch scheduling problem that incorporates transportation of raw materials or semifinished products before processing with waiting time constraint. The orders located at the different suppliers are transported by some vehicles to a manufacturing facility for further processing. One vehicle can load only one order in one shipment. Each order arriving at the facility must be processed in the limited waiting time. The orders are processed in batches on a parallel-batch machine, where a batch contains several orders and the processing time of the batch is the largest processing time of the orders in it. The goal is to find a schedule to minimize the sum of the total flow time and the production cost. We prove that the general problem is NP-hard in the strong sense. We also demonstrate that the problem with equal processing times on the machine is NP-hard. Furthermore, a dynamic programming algorithm in pseudopolynomial time is provided to prove its ordinarily NP-hardness. An optimal algorithm in polynomial time is presented to solve a special case with equal processing times and equal transportation times for each order.

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