A new Lagrangian Relaxation algorithm for single-stage chemical scheduling

2008 ◽  
Author(s):  
Yanyan Zhang ◽  
Lixin Tang
Keyword(s):  
Lagrangian Relaxation ◽  
Single Stage ◽  
Relaxation Algorithm ◽  
Lagrangian Relaxation Algorithm

Multi Project Scheduling and Material Planning Using Lagrangian Relaxation Algorithm

2021 ◽  
Vol 20 (4) ◽  
pp. 580-587
Author(s):  
Alim Al Ayub Ahmed ◽  
Ngakan Ketut Acwin Dwijendra ◽  
NareshBabu Bynagari ◽  
A.K. Modenov ◽  
M. Kavitha ◽  
...  
Keyword(s):  
Lagrangian Relaxation ◽  
Project Scheduling ◽  
Relaxation Algorithm ◽  
Lagrangian Relaxation Algorithm

Hybrid Flowshop Scheduling with Finite Transportation Capacity

2011 ◽  
Vol 65 ◽  
pp. 574-578 ◽  
Author(s):  
Hua Xuan
Keyword(s):  
Lagrangian Relaxation ◽  
Programming Model ◽  
Optimal Schedule ◽  
Release Time ◽  
Flowshop Scheduling ◽  
Hybrid Flowshop ◽  
Relaxation Algorithm ◽  
Hybrid Flowshop Scheduling ◽  
Transportation Capacity ◽  
Lagrangian Relaxation Algorithm

This paper studies a class of hybrid flowshop scheduling problem characterized by release time, transportation time and transportation capacity of one unit for each transporter. This problem is formulated as an integer programming model and a Lagrangian relaxation algorithm is designed to solve it. Testing results on problems of small to medium sizes show that the Lagrangian relaxation algorithm can obtain an acceptable near optimal schedule within a shorter CPU time.

scholarly journals An Improved Lagrangian Relaxation Algorithm for the Robust Generation Self-Scheduling Problem

2018 ◽  
Vol 2018 ◽  
pp. 1-12 ◽  
Author(s):  
Ping Che ◽  
Zhenhao Tang ◽  
Hua Gong ◽  
Xiaoli Zhao
Keyword(s):  
Lagrangian Relaxation ◽  
Single Unit ◽  
Mixed Integer ◽  
Scheduling Problem ◽  
Two Stage ◽  
Splitting Technique ◽  
Relaxation Algorithm ◽  
Special Cases ◽  
Lagrangian Relaxation Algorithm ◽  
Relaxed Problem

The robust generation self-scheduling problem under electricity price uncertainty is usually solved by the commercial solver, which is limited in computation time and memory requirement. This paper proposes an improved Lagrangian relaxation algorithm for the robust generation self-scheduling problem where the quadratic fuel cost and the time-dependent exponential startup cost are considered. By using the optimal duality theory, the robust generation self-scheduling problem, which has a max-min structure, is reformulated as a minimization mixed integer nonlinear programming (MINLP) problem. Upon the reformulation, the Lagrangian relaxation algorithm is developed. To obtain a solvable relaxed problem, the variable splitting technique is introduced before the relaxation. The obtained relaxed problem is decomposed into a linear programming-type subproblem and multiple single-unit subproblems. Each single-unit subproblem is solved optimally by a two-stage backward dynamic programming procedure. The special cases of the problem are discussed and a two-stage algorithm is proposed. The proposed algorithms are tested on test cases of different sizes and the numerical results show that the algorithms can find near-optimal solutions in a reasonable time.

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