scholarly journals Fuzzy Order Acceptance and Scheduling on Identical Parallel Machines

Symmetry ◽  
2021 ◽  
Vol 13 (7) ◽  
pp. 1236
Author(s):  
Menşure Zühal Erişgin Barak ◽  
Melik Koyuncu
Keyword(s):  
Parallel Machines ◽  
Optimization Problems ◽  
Fundamental Property ◽  
Optimal Solution ◽  
Order Acceptance ◽  
Identical Parallel Machines ◽  
Distance Method ◽  
General Symmetry ◽  
Order Acceptance And Scheduling ◽  
Fuzzy Order

In this study, we focus on the fuzzy order acceptance and scheduling problem in identical parallel machines (FOASIPM), which is a scheduling and optimization problem to decide whether the firm should accept or outsource the order. In general, symmetry is a fundamental property of optimization models used to represent binary relations such as the FOASIPM problem. Symmetry in optimization problems can be considered as an engineering tool to support decision-making. We develop a fuzzy mathematical model (FMM) and a Genetic Algorithm (GA) with two crossover operators. The FOASIPM is formulated as an FMM where the objective is to maximize the total net profit, which includes the revenue, the penalty of tardiness, and the outsourcing. The performance of the proposed methods is tested on the sets of data with orders that are defined by fuzzy durations. We use the signed distance method to handle the fuzzy parameters. While FMM reaches the optimal solution in a reasonable time for datasets with a small number of orders, it cannot find a solution for datasets with a large number of orders due to the NP-hard nature of the problem. Genetic algorithms provide fast solutions for datasets with a medium and large number of orders.

Order acceptance and scheduling on two identical parallel machines

2015 ◽  
Vol 66 (10) ◽  
pp. 1755-1767 ◽  
Author(s):  
Xiuli Wang ◽  
Guodong Huang ◽  
Xiuwu Hu ◽  
T C Edwin Cheng
Keyword(s):  
Parallel Machines ◽  
Order Acceptance ◽  
Identical Parallel Machines ◽  
Order Acceptance And Scheduling

scholarly journals A Column Generation Algorithm for the Resource-Constrained Order Acceptance and Scheduling on Unrelated Parallel Machines

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Yujian Song ◽  
Ming Xue ◽  
Changhua Hua ◽  
Wanli Wang
Keyword(s):  
Column Generation ◽  
Mixed Integer Linear Programming ◽  
Parallel Machines ◽  
Set Partitioning ◽  
Mixed Integer ◽  
Order Acceptance ◽  
Generation Algorithm ◽  
Order Acceptance And Scheduling ◽  
Linear Programming Formulation ◽  
Integer Linear Programming Formulation

In this paper, we investigate the resource-constrained order acceptance and scheduling on unrelated parallel machines that arise in make-to-order systems. The objective of this problem is to simultaneously select a subset of orders to be processed and schedule the accepted orders on unrelated machines in such a way that the resources are not overutilized at any time. We first propose two formulations for the problem: mixed integer linear programming formulation and set partitioning. In view of the complexity of the problem, we then develop a column generation approach based on the set partitioning formulation. In the proposed column generation approach, a differential evolution algorithm is designed to solve subproblems efficiently. Extensive numerical experiments on different-sized instances are conducted, and the results demonstrate that the proposed column generation algorithm reports optimal or near-optimal solutions that are evidently better than the solutions obtained by solving the mixed integer linear programming formulation.

scholarly journals Multiobjective Order Acceptance and Scheduling on Unrelated Parallel Machines with Machine Eligibility Constraints

2018 ◽  
Vol 2018 ◽  
pp. 1-12
Author(s):  
Bailin Wang ◽  
Haifeng Wang
Keyword(s):  
Parallel Machines ◽  
Mixed Integer ◽  
List Scheduling ◽  
Unrelated Parallel Machines ◽  
Order Acceptance ◽  
Trade Off ◽  
Pareto Ranking ◽  
Machine Eligibility ◽  
Net Profit ◽  
Order Acceptance And Scheduling

This paper studies the order acceptance and scheduling problem on unrelated parallel machines with machine eligibility constraints. Two objectives are considered to maximize total net profit and minimize the makespan, and the mathematical model of this problem is formulated as multiobjective mixed integer linear programming. Some properties with respect to the objectives are analysed, and then a classic list scheduling (LS) rule named the first available machine rule is extended, and three new LS rules are presented, which focus on the maximization of the net profit, the minimization of the makespan, and the trade-off between the two objectives, respectively. Furthermore, a list-scheduling-based multiobjective parthenogenetic algorithm (LS-MPGA) is presented with parthenogenetic operators and Pareto-ranking and selection method. Computational experiments on randomly generated instances are carried out to assess the effectiveness and efficiency of the four LS rules under the framework of LS-MPGA and discuss their application environments. Results demonstrate that the performance of the LS-MPGA developed for trade-off is superior to the other three algorithms.

scholarly journals A genetic algorithm for fuzzy order acceptance and scheduling problem

2019 ◽  
Vol 9 (2) ◽  
pp. 186-196
Author(s):  
Esra Karakaş ◽  
Hakan Özpalamutçu
Keyword(s):  
Genetic Algorithm ◽  
Order Acceptance ◽  
Due Dates ◽  
Processing Times ◽  
Production Environments ◽  
Fuzzy Processing Times ◽  
Order Acceptance And Scheduling ◽  
Fuzzy Ranking ◽  
Set Up ◽  
Fuzzy Order

In light of the imprecise and fuzzy nature of real production environments, the order acceptance and scheduling (OAS) problem is associated with fuzzy processing times, fuzzy sequence dependent set up time and fuzzy due dates. In this study, a genetic algorithm (GA) which uses fuzzy ranking methods is proposed to solve the fuzzy OAS problem. The proposed algorithm is illustrated and analyzed using examples with different order sizes. As illustrative numerical examples, fuzzy OAS problems with 10, 15, 20, 25, 30 and 100 orders are considered. The feasibility and effectiveness of the proposed method are demonstrated. Due to the NP-hard nature of the problem, the developed GA has great importance to obtain a solution even for big scale fuzzy OAS problem.  Also, the proposed GA can be utilized easily by all practitioners via the developed user interface.

scholarly journals A Novel Approach for Solving Nonsmooth Optimization Problems with Application to Nonsmooth Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-10
Author(s):  
Hamid Reza Erfanian ◽  
M. H. Noori Skandari ◽  
A. V. Kamyad
Keyword(s):  
Nonsmooth Optimization ◽  
Optimization Problems ◽  
Piecewise Linear ◽  
Linear Optimization ◽  
Optimal Solution ◽  
Piecewise Linear Function ◽  
Nonsmooth Equations ◽  
Smooth Functions ◽  
Generalized Derivative ◽  
Novel Approach

We present a new approach for solving nonsmooth optimization problems and a system of nonsmooth equations which is based on generalized derivative. For this purpose, we introduce the first order of generalized Taylor expansion of nonsmooth functions and replace it with smooth functions. In other words, nonsmooth function is approximated by a piecewise linear function based on generalized derivative. In the next step, we solve smooth linear optimization problem whose optimal solution is an approximate solution of main problem. Then, we apply the results for solving system of nonsmooth equations. Finally, for efficiency of our approach some numerical examples have been presented.

Study on Mix-Variable Collaborative Design Optimization

2012 ◽  
Vol 215-216 ◽  
pp. 592-596
Author(s):  
Li Gao ◽  
Rong Rong Wang
Keyword(s):  
Design Optimization ◽  
Product Design ◽  
Optimization Algorithm ◽  
Collaborative Design ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Collaborative Optimization ◽  
Continuous Variables ◽  
Complex Product ◽  
Divide And Rule

In order to deal with complex product design optimization problems with both discrete and continuous variables, mix-variable collaborative design optimization algorithm is put forward based on collaborative optimization, which is an efficient way to solve mix-variable design optimization problems. On the rule of “divide and rule”, the algorithm decouples the problem into some relatively simple subsystems. Then by using collaborative mechanism, the optimal solution is obtained. Finally, the result of a case shows the feasibility and effectiveness of the new algorithm.

Application of High-Performance Computing to Numerical Simulation of Human Movement

1995 ◽  
Vol 117 (1) ◽  
pp. 155-157 ◽  
Author(s):  
F. C. Anderson ◽  
J. M. Ziegler ◽  
M. G. Pandy ◽  
R. T. Whalen
Keyword(s):  
Computer Architecture ◽  
High Performance ◽  
Large Scale ◽  
Optimization Problems ◽  
Optimal Solution ◽  
Human Movement ◽  
Parallel Machine ◽  
Optimal Controls ◽  
Processing Machine ◽  
Vector Processing

We have examined the feasibility of using massively-parallel and vector-processing supercomputers to solve large-scale optimization problems for human movement. Specifically, we compared the computational expense of determining the optimal controls for the single support phase of gait using a conventional serial machine (SGI Iris 4D25), a MIMD parallel machine (Intel iPSC/860), and a parallel-vector-processing machine (Cray Y-MP 8/864). With the human body modeled as a 14 degree-of-freedom linkage actuated by 46 musculotendinous units, computation of the optimal controls for gait could take up to 3 months of CPU time on the Iris. Both the Cray and the Intel are able to reduce this time to practical levels. The optimal solution for gait can be found with about 77 hours of CPU on the Cray and with about 88 hours of CPU on the Intel. Although the overall speeds of the Cray and the Intel were found to be similar, the unique capabilities of each machine are better suited to different portions of the computational algorithm used. The Intel was best suited to computing the derivatives of the performance criterion and the constraints whereas the Cray was best suited to parameter optimization of the controls. These results suggest that the ideal computer architecture for solving very large-scale optimal control problems is a hybrid system in which a vector-processing machine is integrated into the communication network of a MIMD parallel machine.

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