%0 Journal Article
%A Tang, Lixin
%E Liu, Guoli
%I Elsevier B.V
%D 2007
%C AMSTERDAM
%G English
%B European Journal of Operational Research
%@ 0377-2217
%@ 1872-6860
%T A mathematical programming model and solution for scheduling production orders in Shanghai Baoshan Iron and Steel Complex
%J European journal of operational research
%V 182
%N 3
%P 1453-1468
%U http://bonn.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwzV3db9MwED9NICHQxKCACB-VHybxgCK5tfP1WKZV8MCEtPHCi-X4g3Vak6qpEPvvuXOcriA2jTeqOI1kx7Xcy93vLvbvAA5zV1ruvU9L700qPZdpaVAZ1lNbyEz6elJTaODzSTX_lp8dVyd7MCQZG2JKwQb8e1TpOng0xJi-rNsQOdx142509WK4SRJFoAzeQtDtIu9dvq2GJxAQ3k4URTpFTB834_TrxtxFu44vOSo8-E0GL1qA_ZXu8N_wfRoNhMhrt3Lmr2YwmLz5wX87WU_gcUTRbNaL_VPYc80IHgyL-EdwMCSrYFF3jeDRDvPiM7iaseWWsBZ7isvUlljJQnIgphvLhueSIbJnHYq3pXX736m17Vl3WaAu7diiYacUej_XC_ZBtx1es09rrKduTjcOO6QhXbqfz-Hr_Pjs6GMas1CkRhScp0QoJypdIRLMa2um2riCW4EX1vNJWWpCdM5U1hvLpa2rrNK2dlnlRT2xiDBfwL6m3QrNJuxqtC-BuZxLw53JED1KLjKdaSJaK72WiCqKOoHJIDPKRK52ShlyqYZFeReK5IySiOaKV3jwBN5v71n1TCW3ts4GUVRRyHoMpdCU3nrfO5JbReoPR2R03MXRNo6IxNQM8b2QBS_yBMa_ifb1oEo0EtOiTGAeZH1b4fCDP-c69UMJjY4vnq-wUDgdvxZYBJYVVcpMkNdaqvPNMoHD3Ydl298f4omTepdmR3G-iRNi8-puXb-GhyHmH_aovoH7Hk2Hewv36rZpxkF3jIOj9guhIJgZ
%X In this paper, we investigate the production order scheduling problem derived from the production of steel sheets in Shanghai Baoshan Iron and Steel Complex (Baosteel). A deterministic mixed integer programming (MIP) model for scheduling production orders on some critical and bottleneck operations in Baosteel is presented in which practical technological constraints have been considered. The objective is to determine the starting and ending times of production orders on corresponding operations under capacity constraints for minimizing the sum of weighted completion times of all orders. Due to large numbers of variables and constraints in the model, a decomposition solution methodology based on a synergistic combination of Lagrangian relaxation, linear programming and heuristics is developed. Unlike the commonly used method of relaxing capacity constraints, this methodology alternatively relaxes constraints coupling integer variables with continuous variables which are introduced to the objective function by Lagrangian multipliers. The Lagrangian relaxed problem can be decomposed into two sub-problems by separating continuous variables from integer ones. The sub-problem that relates to continuous variables is a linear programming problem which can be solved using standard software package OSL, while the other sub-problem is an integer programming problem which can be solved optimally by further decomposition. The subgradient optimization method is used to update Lagrangian multipliers. A production order scheduling simulation system for Baosteel is developed by embedding the above Lagrangian heuristics. Computational results for problems with up to 100 orders show that the proposed Lagrangian relaxation method is stable and can find good solutions within a reasonable time.
%K Steel production
%K Production order scheduling
%K Subgradient optimization
%K Combinatorial optimization
%K Lagrangian relaxation
%K Business & Economics
%K Operations Research & Management Science
%K Social Sciences
%K Management
%K Technology
%K Science & Technology
%K Scheduling, sequencing
%K Operational research and scientific management
%K Flows in networks. Combinatorial problems
%K Inventory control, production control. Distribution
%K Exact sciences and technology
%K Applied sciences
%K Operational research. Management science
%K Mathematical programming
%K Steel
%K Steel production
%K Production order scheduling
%K Subgradient optimization
%K Combinatorial optimization
%K Lagrangian relaxation
%K combinatorial optimization
%K production order scheduling
%K subgradient optimization
%K steel production
%K RELAXATION APPROACH
%K Bottleneck
%K Linear relaxation
%K Software package
%K Embedding
%K Iron
%K Modeling
%K Lagrange multiplier
%K Linear combination
%K Sheet metal
%K Relaxation method
%K Lagrangian method
%K Mathematical programming
%K Completion time
%K Production system
%K Lagrangian
%K Linear programming
%K Mixed integer programming
%K Scheduling
%K Order picking
%K Integer programming
%K Production management
%K Heuristic method
%K Capacity constraint
%K Objective function
%K Lagrangian function