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 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.

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 characterization of optimal multiprocessor schedules and new dominance rules

2020 ◽  
Vol 40 (4) ◽  
pp. 876-900
Author(s):  
Rico Walter ◽  
Alexander Lawrinenko
Keyword(s):  
Parallel Machines ◽  
Computational Study ◽  
Search Space ◽  
Point Of View ◽  
Theoretical Point ◽  
Optimal Solutions ◽  
Identical Parallel Machines ◽  
Makespan Minimization ◽  
Structural Pattern

Abstract The paper on hand approaches the classical makespan minimization problem on identical parallel machines from a rather theoretical point of view. Using an approach similar to the idea behind inverse optimization, we identify a general structural pattern of optimal multiprocessor schedules. We also show how to derive new dominance rules from the characteristics of optimal solutions. Results of our computational study attest to the efficacy of the new rules. They are particularly useful in limiting the search space when each machine processes only a few jobs on average.

scholarly journals Rescheduling Production on Identical Parallel Machines upon new jobs arrivals

2019 ◽  
Vol 52 (13) ◽  
pp. 2525-2530
Author(s):  
Nathália C.O. Silva ◽  
Cassius T. Scarpin ◽  
Angel Ruiz ◽  
José E. Pécora
Keyword(s):  
Parallel Machines ◽  
Identical Parallel Machines ◽  
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