中文摘要：

针对一类带最小批量约束的计划问题，提出了基于拉格朗日松弛策略求解算法．通过拉格朗日松弛策略，将原问题转为一系列带最小批量约束的动态经济批量W—W（Wagner-Whitin）子问题．提出了解决子问题且其时间复杂度O（T^3）的最优前向递推算法．对于拉格朗日对偶问题，用次梯度算法求解，获得原问题的下界．若对偶问题的解是不可行的，通过固定装设变量，求解一个剩余的线性规划问题来进行可行化处理．最后，数据仿真验证了算法的有效性．

英文摘要：

A Lagrange relaxation heuristic-based procedure is presented to solve the capacitated lot-size problem（CLSP） with minimum lot-size constraint. The problem is first decomposed into a series of sub-problems W-W（Wagner-Whitin） with dynamic economic minimum lot-size constraint. To deal with the sub-problems, an optimal forward iterative algorithm with runtime complexity of O（T^3） is proposed. The Lagrange dual problem is then handled by the sub-gradient optimization algorithm to obtain a tight lower bound. If the solution to the Lagrange dual problem is infeasible, the setup variables are fixed and the remaining problem is reformulated as a linear programming problem which can be solved efficiently by any off-the-shelf solver. Finally, the computational experiments demonstrate the algorithm＇s efficiency.