Research On Optimal Control Of Production And Inventory Under Uncertainty

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.