scholarly journals Hierarchical minimization of two maximum costs on a bounded serial-batching machine

2020 ◽  
Author(s):  
Cheng He ◽  
Hao Lin ◽  
Li Li
Keyword(s):  
Processing Time ◽  
Optimization Problem ◽  
Setup Time ◽  
Time Algorithm ◽  
Hierarchical Optimization ◽  
Objective Functions ◽  
Processing Times ◽  
Hierarchical Minimization ◽  
Batching Machine ◽  
Special Case

This paper studies a hierarchical optimization problem of scheduling $n$ jobs on a serial-batching machine, in which two objective functions are maximum costs. By a hierarchical optimization problem, we mean the problem of optimizing the secondary criterion under the constraint that the primary criterion is optimized. A serial-batching machine is a machine that can handle up to $b$ jobs in a batch and jobs in a batch start and complete respectively at the same time and the processing time of a batch is equal to the sum of the processing times of jobs in the batch. When a new batch starts, a constant setup time $s$ occurs. We confine ourselves to the bounded model, where $b<n$. We present an $O(n^4)$-time algorithm for this hierarchical optimization problem. For the special case where two objective functions are maximum lateness, we give an $O(n^3\log n)$-time algorithm.

Hierarchical optimization on an unbounded parallel-batching machine

2018 ◽  
Vol 52 (1) ◽  
pp. 55-60
Author(s):  
Cheng He ◽  
Li Li
Keyword(s):  
Optimization Problem ◽  
Time Algorithm ◽  
Decision Makers ◽  
Hierarchical Optimization ◽  
Scheduling Problem ◽  
Objective Functions ◽  
Hierarchical Scheduling ◽  
Parallel Batching ◽  
Batching Machine

This paper studies a hierarchical optimization problem on an unbounded parallel-batching machine, in which two objective functions are maximum costs, representing different purposes of two decision-makers. By a hierarchical optimization problem, we mean the problem of optimizing the secondary criterion under the constraint that the primary criterion is optimized. A parallel-batching machine is a machine that can handle several jobs in a batch in which all jobs start and complete respectively at the same time. We present an O(n4)-time algorithm for this hierarchical scheduling problem.

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.

BATCHING MACHINE SCHEDULING WITH BICRITERIA: MAXIMUM COST AND MAKESPAN

2014 ◽  
Vol 31 (04) ◽  
pp. 1450025 ◽  
Author(s):  
CHENG HE ◽  
HAO LIN ◽  
JINJIANG YUAN ◽  
YUNDONG MU
Keyword(s):  
Processing Time ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Pareto Optimal ◽  
Pareto Optimal Solutions ◽  
Optimal Solutions ◽  
Maximum Cost ◽  
Parallel Batching ◽  
Multicriteria Problem ◽  
Batching Machine

In this paper, the problem of minimizing maximum cost and makespan simultaneously on an unbounded parallel-batching machine is considered. An unbounded parallel-batching machine is a machine that can handle any number of jobs in a batch and the processing time of a batch is the largest processing time of jobs in the batch. The main goal of a multicriteria problem is to find Pareto optimal solutions. We present a polynomial-time algorithm to produce all Pareto optimal solutions of this bicriteria scheduling problem.

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.

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.

Single-Machine Due-Window Assignment and Scheduling with Learning Effect and Resource-Dependent Processing Times

2014 ◽  
Vol 31 (05) ◽  
pp. 1450036 ◽  
Author(s):  
Ji-Bo Wang ◽  
Ming-Zheng Wang
Keyword(s):  
Resource Allocation ◽  
Single Machine ◽  
Processing Time ◽  
Window Size ◽  
Polynomial Time Algorithm ◽  
Time Algorithm ◽  
Earliness And Tardiness ◽  
Processing Times ◽  
Due Window ◽  
Due Window Assignment

We consider a single-machine common due-window assignment scheduling problem, in which the processing time of a job is a function of its position in a sequence and its resource allocation. The window location and size, along with the associated job schedule that minimizes a certain cost function, are to be determined. This function is made up of costs associated with the window location, window size, earliness, and tardiness. For two different processing time functions, we provide a polynomial time algorithm to find the optimal job sequence and resource allocation, respectively.

scholarly journals Single-Machine Scheduling Problems with the General Sum-of-Processing-Time and Position-Dependent Effect Function

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Kunping Shen ◽  
Yuke Chen ◽  
Shangchia Liu
Keyword(s):  
Polynomial Time ◽  
Single Machine ◽  
Completion Time ◽  
Processing Time ◽  
Objective Functions ◽  
Dependent Effect ◽  
Effect Function ◽  
Processing Times ◽  
Time Problem ◽  
Normal Processing

This paper considers the combination of the general sum-of-processing-time effect and position-dependent effect on a single machine. The actual processing time of a job is defined by functions of the sum of the normal processing times of the jobs processed and its position and control parameter in the sequence. We consider two monotonic effect functions: the nondecreasing function and the nonincreasing function. Our focus is the following objective functions, including the makespan, the sum of the completion time, the sum of the weighted completion time, and the maximum lateness. For the nonincreasing effect function, polynomial algorithm is presented for the makespan problem and the sum of completion time problem, respectively. The latter two objective functions can also be solved in polynomial time if the weight or due date and the normal processing time satisfy some agreeable relations. For the nondecreasing effect function, assume that the given parameter is zero. We also show that the makespan problem can remain polynomially solvable. For the sum of the total completion time problem and a 1 is the deteriorating rate of the jobs, there exists an optimal solution for a 1 ≥ M ; a V-shaped property with respect to the normal processing times is obtained for 0 < a 1 ≤ 1 . Finally, we show that the sum of the weighted completion problem and the maximum lateness problem have polynomial-time solutions for a 1 > M under some agreeable conditions, respectively.

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 Batch Scheduling of Deteriorating Products

2007 ◽  
Vol 1 (2) ◽  
pp. 25-34
Author(s):  
Maksim S. Barketau ◽  
T.C. Edwin Cheng ◽  
Mikhail Y. Kovalyov ◽  
C.T. Daniel Ng
Keyword(s):  
Completion Time ◽  
Processing Time ◽  
Setup Time ◽  
Time Algorithm ◽  
Batch Scheduling ◽  
Performance Guarantee ◽  
Negative Number ◽  
Time Approximation ◽  
Starting Time ◽  
Increasing Function

In this paper we consider the problem of scheduling N jobs on a single machine, where the jobs are processed in batches and the processing time of each job is a simple linear increasing function depending on job’s waiting time, which is the time between the start of the processing of the batch to which the job belongs and the start of the processing of the job. Each batch starts from the setup time S. Jobs which are assigned to the batch are being prepared for the processing during time S0 S. After this preparation they are ready to be processed one by one. The non-negative number bi is associated with job i. The processing time of the i-th job is equal to bi(si − (sib + S0)), where sib and si are the starting time of the b-th batch to which the i-th job belongs and the starting time of this job, respectively. The objective is to minimize the completion time of the last job. We show that the problem is NP-hard. After that we present an O(N) time algorithm solving the problem optimally for the case bi = b. We further present an O(N2) time approximation algorithm with a performance guarantee 2.

Sign in / Sign up

Export Citation Format

Share Document