Lagrangean relaxation approach to joint optimization for production planning and scheduling of synchronous assembly lines
针对同步装配线，提出一个混合整数规划模型同时优化生产计划和详细调度，并用拉格朗日松弛法分解求解，测试表明算法有效。
This paper focuses on simultaneous optimisation of production planning and scheduling problem over a time period for synchronous assembly lines. Differing from traditional top-down approaches, a mixed integer programming model which jointly considers production planning and detailed scheduling constraints is formulated, and a Lagrangian relaxation method is developed for the proposed model, whereby the integrated problem is decomposed into planning, batch sequencing, tardiness and earliness sub-problems. The scheduling sub-problem is modelled as a time-dependent travelling salesman problem, which is solved using a dynasearch algorithm. A proposition of Lagrangian multipliers is established to accelerate the convergence speed of the proposed algorithm. The average direction strategy is employed to solve the Lagrangian dual problem. Test results demonstrate that the proposed model and algorithm are effective and efficient.