Dynamic Control and Optimization of Production with Capital Injection
A common problem in the production and management of enterprises,especially retail enterprises,how to make reasonable purchasing and production plans to achieve the business objectives of enterprises,is studied in this paper.In addition to production,sales,inventory and other activities,paying dividends to shareholders and accepting capital injection from shareholders are also essential links of enterprises.It is of practical significance to formulate purchasing and production strategies with the goal of maximizing sharehold-ers'interests.On the basis of previous relevant studies,it is considered that enterprises operate a class of products,similar to the multi-cycle newsboy model.An enterprise controls the purchase or production and capital flow,adopts the barrier dividend strategy to pay dividends to shareholders at the end of each cycle,or accepts capital injection from shareholders when the amount of cash held is insufficient to pay the optimal produc-tion cost in the next period.In addition,it is assumed that the unit production cost of any period,the unit selling price of the previous period and the quantity demanded obey a joint distribution.In this paper,a discrete time Markov decision model is proposed to maximize the future cumulative expected discounted returns of sharehold-ers,the aim is to find the optimal production strategy and the corresponding optimal value function.Under the condition that the assessment period is limited,the iterative relation satisfied by the optimal value function is given by the formula of total expectation.When the assessment period is unlimited,the Bellman equation satisfi ed by the value function is given,and the optimal value function is proved to be the only solution by the contrac-tion mapping principle.Finally,a numerical example is given according to the method provided in this paper,and the results mainly provide the following information:1)When the duration of the assessment period is limited,the optimal production strategy of each period which is far away from the expiration time basically remains unchanged.When other conditions remain unchanged,the optimal production of each period shows a monotonous trend with the increase of the initial inventory.When the inventory reaches a certain value,the production is 0,indicating that the inventory should be sold first and no reproduction is needed.2)When the duration of the assessment period is unlimited,the value function of a finite assessment period with sufficient length can approximate the optimal value function of the infinite case.The length of the finite assessment period can be calculated when the error is given.3)No matter the assessment period is finite or infinite,the value of the optimal value function is affected by the dividend barrier,and the decision maker can adjust the dividend bar-rier appropriately to achieve the optimal state.A decision method for enterprises is provided,and the research on enter prise decision making is enriched.
capital injection strategybarrier dividend strategyoptimal production strategyBellman equa-tioncontraction mapping
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维普
