【作者】 吴程彧；

【导师】 张成科；

【作者基本信息】 广东工业大学 ， 管理科学与工程， 2023， 博士

【摘要】 生产规划与库存管理是供应链决策的重要组成要素之一。作为一个生产型企业来说,产品的生产水平和库存水平优化控制对企业的经营效益有直接影响。在竞争市场中企业生产库存决策会受到各种不确定环境的影响,本学位论文用不确定性理论来描述企业面临的不确定性,综合考虑产品生产水平和库存水平,按照企业在竞争市场的属性将研究对象企业分为完全竞争市场生产企业和寡头市场生产企业两个类别,分别从最优控制和微分博弈视角研究企业的生产库存问题和原材料库存投资组合问题。本学位论文主要从理论研究和应用研究两个方面入手,首先对论文所研究问题要使用到的不确定最优控制理论和微分博弈理论进行了系统研究,然后利用这些理论方法深入研究了企业生产库存控制问题和企业对生产原材料库存投资组合问题。研究方法主要是利用不确定最优控制极大值原理和不确定微分博弈理论中常用的配方法和构造法,以及数值模拟仿真方法。论文研究内容选择和安排上遵循从理论到应用、由简单到复杂、从特殊到一般的逻辑结构。论文分三章节四个板块对所提出的问题进行了系统研究。具体研究结果如下:(1)针对企业的生产库存问题、以及对生产原材料库存投资组合问题上所涉及到的不确定最优控制模型、离散线性和仿线性二次型不确定微分博弈模型、连续跳不确定微分博弈模型、连续跳不确定随机混杂系统微分博弈模型和确定性动态生产库存系统微分博弈模型,进行了系统研究,分别给出了这些模型的最优控制策略和均衡策略存在性定理以及求解方法,丰富和完善了不确定最优控制、微分博弈模型的求解理论与方法。(2)从不确定最优控制(单人微分博弈)视角研究了完全竞争市场下企业的生产库存控制问题,主要是利用本学位论文研究所得到的不确定最优控制方法探究了三种不确定情境模型下的企业生产库存最优控制问题。其一是针对企业的离散系统生产库存问题,研究了不确定系统的生产库存最优控制策略。其二针对企业连续系统生产库存中存在跳不确定的情形,利用跳不确定微分方程来描述,研究其生产库存最优控制策略。其三是针对生产库存系统既存在主观不确定又存在客观不确定情形,利用不确定随机微分方程来描述这种混杂不确定的连续系统,研究其生产库存最优控制策略。这些研究一方面弥补了该问题研究的不足,另一方面也为本论文第四章研究双寡头市场企业博弈情形提供进行对比研究的必要准备。(3)从微分博弈视角,就离散系统和连续系统两种情形系统地研究了不确定环境下双寡头市场企业的生产库存控制问题。首先分析求出了均衡生产水平和库存水平。其次研究了连续不确定系统双寡头市场企业的生产库存问题,分别在收益最大和成本最小目标下给出了连续不确定系统双寡头市场企业的生产库存均衡策略;同时针对连续双寡头市场企业生产库存问题,对比研究了微分博弈方法分析结果和最优控制方法分析结果的差异性,结果表明微分博弈方法分析结果是稳定可行的,而直接使用最优控制方法分析寡头市场企业生产库存问题得到的结果是不稳定的。最后,就所研究的生产库存问题都进行了数值仿真分析,计算结果表明所得结论是有效性的。(4)从微分博弈视角研究了双寡头市场企业对生产原材料库存投资组合决策问题。利用连续跳不确定随机混杂系统构建了两个寡头市场企业对生产原材料库存投资组合决策的微分博弈模型,给出了原材料库存组合投资的均衡策略存在性条件及其求解方法,并且进行了数值模拟仿真。本论文的研究结果,一方面从方法论角度说明对竞争市场企业生产库存问题的分析,必须将研究对象企业按照其竞争市场属性划分类别,并且应该使用不同的研究方法;论文研究所得到的不确定最优控制方法和微分博弈方法,是在理论与方法层次上弥补了现有文献成果对企业生产库存现实情境模型研究的不足,有理论方法创新。另一方面,论文提出的应该综合考虑生产水平和库存水平,将它们共同纳入同一个微分博弈模型来分析;以及从微分博弈视角研究跳不确定环境下寡头市场企业的原材料库存投资组合问题,为该研究方向提供了新视角和新分析方法。因此,对当今企业生产库存管理具有一定的实用价值和指导意义。更多还原

【Abstract】 Production planning and inventory management are important components of supply chain decision-making.As a production-oriented enterprise,the optimal control of production and inventory has a direct impact on the operating efficiency of the enterprise.In competitive market,production and inventory decision of enterprise will be affected by various uncertain circumstances.This thesis adopts uncertainty theory to describe uncertain circumstance in reality,and studies the production and inventory decision-making problem and raw material inventory portfolio problem of enterprise from the perspective of optimal control and differential game,respectively considering perfectly competitive market and oligopoly market.This thesis mainly starts from theoretical research and applied research.First of all,the uncertainty optimal control theory and the uncertainty differential game theory used in the research problem of the thesis is systematically studied,and then these theoretical methods are used to deeply study the problem of enterprise production and inventory control and production material investment.As for research methods,this thesis mainly uses the maximum principle,the completion of square method and construction method in uncertain differential game theory,as well as numerical simulation method.The selection and construction of the thesis contents basically follows the logical structures that from theory to application,from simple to complex,and from special to general.This thesis is divided into four sections and three chapters to systematically study the questions raised and the specific results are as follows:(1)This thesis aims at the uncertain optimal control model,linear and para-linear discrete quadratic form uncertain differential game model,continuous time uncertain differential game with jumps and uncertain stochastic differential game with jumps,which are involved in the problem of enterprise production and inventory control and production material investment.Through systematical analysis,this thesis finds out the existence theorem of equilibrium strategy and the solution of equilibrium strategy,which enrich the optimal control theory and the differential game theory of the corresponding models.(2)From the perspective of uncertain optimal control(one-person differential game),the production and inventory control problem of enterprise in perfectly competitive market is studied under three realistic models.Firstly,in view of the situation that the production and inventory system of enterprise is a discrete system,the uncertain optimal control strategy of enterprise production and inventory is studied.Secondly,aiming at the continuous uncertain system with jumps in the production and inventory system of enterprise,the uncertainty differential equation with jumps is used to find out the optimal control strategy of enterprise production and inventory.Thirdly,aiming at the situation that there is subjective uncertainty and objective uncertainty in the production and inventory system,the uncertain stochastic differential equation is used to find out the optimal control strategy of enterprise production and inventory.On the one hand,these studies fill the research gap in the typical field.On the other hand,these studies also provide preparation for the research of oligopoly competitive game in Chapter 4 of this thesis.(3)From the perspective of differential game,the production and inventory control problem of uncertain system in oligopoly market is systematically studied in terms of discrete system and continuous system.Firstly,through analyzing the production and inventory problem of the discrete uncertain system in oligopoly market,this thesis obtains an equilibrium level of production and inventory.Secondly,the production and inventory competition strategies in oligopoly market in terms of the largest benefits and the lowest cost of the continuous uncertain system are achieved.At the same time,for the production and inventory control problem in oligopoly market,this thesis compares the difference between the analysis results of the differential game method and the optimal control method.The results obtained by analyzing the production and inventory control problem in oligopoly market are more stable than in perfectly competitive market.Finally,through numerical simulation,the validity of the conclusions is proved.This thesis constructs a new method to analyze the production and inventory equilibrium strategy of enterprises in oligopoly market.(4)From the perspective of differential game,this thesis studies enterprises production material investment problem in oligopoly market,by constructing continuous uncertain stochastic system with jumps.Through analysis,this thesis finds out the equilibrium strategy,and carries out numerical simulations to verify the effectiveness of the uncertain stochastic differential game with jumps theory applied in enterprises production material investment problem.The conclusions of this thesis,on the one hand,from the methodological point of view,explain that the analysis of the production and inventory control problem of enterprises must be divided into categories according to their market types,namely perfectly competitive market or oligopoly market,and different research methods should be used;the optimal control method and the differential game method in this thesis enrich the existing literature related to different realistic model of production and inventory control problem,and have innovations both in theory and method.On the other hand,this thesis proposes that the production level and inventory level should be considered comprehensively,and they should be included in the same differential game model for analysis,and the study of raw material inventory portfolio problems of oligopolistic enterprises in an uncertain environment from the perspective of differential games,which provides a new perspective and new analysis method for this research direction.Therefore,it has certain practical value and guiding significance for the production and inventory management for enterprises.更多还原