A new Lagrangian relaxation algorithm for hybrid flowshop scheduling to minimize total weighted completion time

2006 ◽  
Vol 33 (11) ◽  
pp. 3344-3359 ◽  
Author(s):  
Lixin Tang ◽  
Hua Xuan ◽  
Jiyin Liu
Keyword(s):  
Lagrangian Relaxation ◽  
Completion Time ◽  
Total Weighted Completion Time ◽  
Flowshop Scheduling ◽  
Hybrid Flowshop ◽  
Relaxation Algorithm ◽  
Hybrid Flowshop Scheduling ◽  
Weighted Completion Time ◽  
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.

Dynamic Hybrid Flowshop Scheduling with Batching Production

2011 ◽  
Vol 65 ◽  
pp. 562-567 ◽  
Author(s):  
Ying Cao ◽  
Hua Xuan ◽  
Jing Liu
Keyword(s):  
Programming Model ◽  
Computation Time ◽  
Steel Tube ◽  
Total Weighted Completion Time ◽  
Flowshop Scheduling ◽  
Feasible Schedule ◽  
Hybrid Flowshop ◽  
Hybrid Flowshop Scheduling ◽  
Dynamic Hybrid ◽  
Lagrangian Relaxation Algorithm

Based on the background of steel-tube production, this paper presents the dynamic hybrid flowshop scheduling with batching scheduling at the first stage, and establishes an integer programming model for this problem. The objective is to minimize the total weighted completion time. The Lagrangian relaxation algorithm is constructed to slove the above model where dynamic programming is presented to solve batch-level subproblems, and a two-stage heuristic is presented to construct a feasible schedule. Testing results on small to medium problem sizes show that this method can obtain satisfactory quality solution in a shorter computation time.

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