【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.通过拉格明日松弛策略,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.更多还原

【Abstract】 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.更多还原