考虑资金借贷与资金约束的单产品批量问题

Single item lot sizing problem considering loaning and capital constraint

考虑资金借贷与资金约束对企业生产计划的影响,企业在各阶段的资金量必须大于等于零以避免破产,并且企业的现有资金量必须大于等于该阶段的总生产成本时才能生产一定数量的产品,否则需要借贷资金,或者减少生产量.以企业的期末收益最大作为决策目标,构建包含初始借贷资金与资金约束的单产品批量问题模型.通过对问题数学性质的分析,将原问题转换为最长路径问题,提出一个多项式时间的递推算法,并用一个启发式方法对结果调整使其更接近最优解.当各阶段单位可变生产成本相等时,算法可以在多项式时间内得到最优解;当各阶段单位生产成本不相等时,该算法得到可行解,数值实验显示其与最优解的误差较小;当问题规模较大时,本文算法与CPLEX 12.6.2相比具有计算效率优势.

This paper investigates the influence of capital and loaning on an enterprise’s production planning.When an enterprise starts to produce a certain number of products, its capital should be no less than the total production cost and above zero to avoid bankruptcy. Otherwise the enterprise must borrow money, or decrease the production quantity. This paper formulates a profit maximization model considering both the initial loan and capital constraint for the single item lot sizing problem. This problem is converted into a travel salesman problem and a polynomial recursive algorithm and a heuristic adjustment are proposed to solve it. Our algorithm can get an optimal solution when the unit variable production costs are equal and get a feasible solution in other cases. Numerical analysis shows its deviation errors with optimal solutions are rather low and it has computation efficiency advantage compared with CPLEX 12.6.2 when the problem scale is large.