不确定影响下的生产与库存最优控制研究
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摘要
本文研究了基于动态时变需求下,存在生产产出和库存损失以及销售收入等不确定约束下的多品种、多周期、多循环的动态的库存最优控制的模型的建立和求解,在模型中的生产率和库存变化是时变的函数,结合应用最优控制理论,对于存在控制约束和状态约束的最优控制问题,给出了基于控制向量和状态向量切比雪夫参数化将最优控制问题转化为非线性规划,再进行求解的方法。提出了一种采用切比雪夫多项式逼近和高斯-切比雪夫数值积分求解库存最优控制模型的数值方法。
针对现实中存在的不确定需求和资金到账不确定等因素的影响用模糊的可能性和必要性来表达,以最小采购资金占用及原料库存成本最低和最大毛收益为目标函数,以库存的变动方程为状态约束,建立单级库存的模糊最优控制模型。在建立相应的模糊不确定库存优化控制模型后,对不确定的影响因素去模糊化处理,再转化为确定性的非线性规划来求解。最后,对不同可能性置信度水平约束情况下的模型进行了求解,得到相应的生产(采购)与库存的最优控制目标值。
针对供应链中库存随着需求的变化可能导致的积压和对生产(或采购)产生的不利影响,为了更好的协调生产(或采购)并减少库存,本文研究了存在库存约束和动态需求等不确定机会约束下的采购与库存的不确定最优控制模型,对不确定的需求和采购资金预算用满足某种概率的测度机会约束表达,应用去模糊技术将不确定最优控制模型转换为确定性的最优控制模型,利用切比雪夫逼近参数化最优控制问题,将最优控制问题转化为非线性规划后,结合应用库恩-塔克条件进行数值求解。针对不确定性因素,分别考虑了随机不确定性因素和模糊不确定因素情况进行求解比较。
针对工厂中生产不确定因素的影响,考虑到炼厂生产过程中各种产品的产出高度相关且产出率不确定的实际情况,应用供应链零库存管理思想,建立炼厂生产与库存三级联动的最优库存控制模型。为使目标函数即炼厂的利润最大或是成本最小,对控制变量为各产品的产量进行优化生产。考虑到这类复杂系统的最优控制模型中,存在约束条件相互制约而导致无解的情况,采用去模糊方法转化约束条件,应用前述研究求解,得到最符合各个约束条件的妥协解。
Inventory is a key node in supply chain. Inventory control is an optimization method which studies on how to order goods or organize production,and how many products should be subscribed or manufactured to maximize the gross income or minimize the total expenditure in supply chain system. With the aggravation of competition among enterprises, each factory need store a certain amount of goods and materials to guarantee the orderly development in production and operation activities. So, production and inventory control become a crucial problem in supply chain operation. Thus, the study on production and inventory control has important significance both in theory and practice.
Considering the cases of optimal control problems with unconstraints, control constraints and state constraints, the Gauss–Chebyshev method is applied to parameterize the control and state vectors. The primitive optimal control problem is converted to a nonlinear programming problem with a large number of decision variables. Then, based on modified Newton method, the converted problem can be solved.
For the established single stage inventory control model, process demand, capital and inventory loss are considered to be fuzzy variables.Possibility and necessity combined method that deals with fuzzy constraints is applied to change the uncertain problem into a deterministic optimal control problem. As to some complicated inequality constrains, Kuhn-Tucker conditions are adopted to convert them to equality constraints. Then, combining with the proposed method from Chapter three or sequential quadratic programming to solve the converted nonlinear programming problem.
Taking the uncertainties of actual environment into account, this paper researches the modeling and solving on a single stage inventory control problem. In the model, process demand and investment are set to be stochastic variables. Chance constrained and fuzzy programming are adopted respectively to translate the uncertain problem into a deterministic optimial control problem. Then, the optimial control problem is converted to a nonlinear programming problem and be solved based on the proposed method. Also an adaptive evolution algorithm can be used to compute the converted problem.
With regard to the influence of uncertain production factors in factories, considering the facts that various products in productive process are highly relevant and the rate of output is uncertain, the paper applies zero inventory management idea in supply chain, establishes optimal inventory control model of production and inventory with three linkage in a refinery. Control variables, production of various products, are optimized to gain the optimum value of objective function, that is maximizing profit or minimizing cost in a refinery. In this complicated optimial model, there may be conflict constraints and lead to no solution. Fuzzy or Chance optimization and the proposed method are used to obtain compromise solution that fits each constraint best. Finally, based on the empirical research findings, some recommendations on production and inventory control are put forward to guide operation in refinery.
针对现实中存在的不确定需求和资金到账不确定等因素的影响用模糊的可能性和必要性来表达,以最小采购资金占用及原料库存成本最低和最大毛收益为目标函数,以库存的变动方程为状态约束,建立单级库存的模糊最优控制模型。在建立相应的模糊不确定库存优化控制模型后,对不确定的影响因素去模糊化处理,再转化为确定性的非线性规划来求解。最后,对不同可能性置信度水平约束情况下的模型进行了求解,得到相应的生产(采购)与库存的最优控制目标值。
针对供应链中库存随着需求的变化可能导致的积压和对生产(或采购)产生的不利影响,为了更好的协调生产(或采购)并减少库存,本文研究了存在库存约束和动态需求等不确定机会约束下的采购与库存的不确定最优控制模型,对不确定的需求和采购资金预算用满足某种概率的测度机会约束表达,应用去模糊技术将不确定最优控制模型转换为确定性的最优控制模型,利用切比雪夫逼近参数化最优控制问题,将最优控制问题转化为非线性规划后,结合应用库恩-塔克条件进行数值求解。针对不确定性因素,分别考虑了随机不确定性因素和模糊不确定因素情况进行求解比较。
针对工厂中生产不确定因素的影响,考虑到炼厂生产过程中各种产品的产出高度相关且产出率不确定的实际情况,应用供应链零库存管理思想,建立炼厂生产与库存三级联动的最优库存控制模型。为使目标函数即炼厂的利润最大或是成本最小,对控制变量为各产品的产量进行优化生产。考虑到这类复杂系统的最优控制模型中,存在约束条件相互制约而导致无解的情况,采用去模糊方法转化约束条件,应用前述研究求解,得到最符合各个约束条件的妥协解。
Inventory is a key node in supply chain. Inventory control is an optimization method which studies on how to order goods or organize production,and how many products should be subscribed or manufactured to maximize the gross income or minimize the total expenditure in supply chain system. With the aggravation of competition among enterprises, each factory need store a certain amount of goods and materials to guarantee the orderly development in production and operation activities. So, production and inventory control become a crucial problem in supply chain operation. Thus, the study on production and inventory control has important significance both in theory and practice.
Considering the cases of optimal control problems with unconstraints, control constraints and state constraints, the Gauss–Chebyshev method is applied to parameterize the control and state vectors. The primitive optimal control problem is converted to a nonlinear programming problem with a large number of decision variables. Then, based on modified Newton method, the converted problem can be solved.
For the established single stage inventory control model, process demand, capital and inventory loss are considered to be fuzzy variables.Possibility and necessity combined method that deals with fuzzy constraints is applied to change the uncertain problem into a deterministic optimal control problem. As to some complicated inequality constrains, Kuhn-Tucker conditions are adopted to convert them to equality constraints. Then, combining with the proposed method from Chapter three or sequential quadratic programming to solve the converted nonlinear programming problem.
Taking the uncertainties of actual environment into account, this paper researches the modeling and solving on a single stage inventory control problem. In the model, process demand and investment are set to be stochastic variables. Chance constrained and fuzzy programming are adopted respectively to translate the uncertain problem into a deterministic optimial control problem. Then, the optimial control problem is converted to a nonlinear programming problem and be solved based on the proposed method. Also an adaptive evolution algorithm can be used to compute the converted problem.
With regard to the influence of uncertain production factors in factories, considering the facts that various products in productive process are highly relevant and the rate of output is uncertain, the paper applies zero inventory management idea in supply chain, establishes optimal inventory control model of production and inventory with three linkage in a refinery. Control variables, production of various products, are optimized to gain the optimum value of objective function, that is maximizing profit or minimizing cost in a refinery. In this complicated optimial model, there may be conflict constraints and lead to no solution. Fuzzy or Chance optimization and the proposed method are used to obtain compromise solution that fits each constraint best. Finally, based on the empirical research findings, some recommendations on production and inventory control are put forward to guide operation in refinery.
引文
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