确定性需求下的最优保理融资与生产策略  

Optimal Factoring and Production Policy with Deterministic Demand

作　　者：李沿海 胡夏莲 LI Yan-hai;HU Xia-lian(School of Economics and Management, Fuzhou University, Fuzhou 350116, China)

机构地区：[1]福州大学经济与管理学院,福建福州350116

出　　处：《运筹与管理》2022年第3期233-239,共7页Operations Research and Management Science

基　　金：国家自然科学基金资助项目(72001044);福建省自然科学基金资助项目(2021J01572)。

摘　　要：企业为下游买方提供赊销,由于大量的资金被应收账款占用,企业可能因资金不足而无法生产足够的产品。企业可以通过保理(出售应收账款)进行融资,减小需求损失。在离散时间多周期的确定需求下,使用决策变量描述各周期的系统状态及其状态转移方程,将此问题建模为线性规划。通过分析此问题的结构特点,再提出了一种新颖且等价的建模方法,可以有效减少决策变量和约束条件的数量。在连续时间模型和混合模型中,这种建模方法同样适用,将优化问题写为连续线性规划,极大地降低了优化问题的复杂度。此连续线性规划问题可通过适当的区间划分进行离散化,用分片常量函数代替优化模型中的一般函数(无限维)决策变量,通过求解有限维线性规划得到原问题的可行近似解。最后,通过数值例子分析了贴现率对企业利润的影响。The convention of selling on credit results in mass accumulation of accounts receivable on the firm’s balance sheet.The financially constrained firm has no enough working capital to invest in accounts receivable and cover the production cost incurred during the credit period.To finance future business,the firm can employ factoring to advance cash from its accounts receivable,i.e.,selling the accounts receivable to a financial institution(called a factor)at a discount.In such a financing scheme,the discrete-time dynamic inventory control problem with deterministic demand can be formulated as a linear program.Based on the structural property of this optimization problem,a novel and equivalent modelling approach is proposed to reduce the number of decision variables and constraint conditions.This new modelling approach is also applicable in the continuous-time case and mixed case,and can formulate the firm’s problem as a continuous linear program.By replacing the functional(infinite-dimensional)decision variables with piece-wise constant functions,the continuous and mixed models can be converted into discretization(finite-dimensional)problems.The optimal solution of the discretization problem is a feasible and approximate optimal solution of the original optimization model.Finally,the numerical examples are conducted to analyze the impact of discount rate on the firm’s profit.

关 键 词：应收账款 保理 贴现 资金约束 线性规划 

分 类 号：F252[经济管理—国民经济]