Dynamic Control and Optimization of Enterprise Production
It is essential and important for a company to have a reasonable purchasing and production plan.Most relevant literature to this problem is the newsboy modeling one,which is a classic problem in operations research and management.It is noteworthy that the optimization objective of most relevant literature is to maximize the expected profit or minimize the cost.In addition,how to pay dividends to shareholders is also one of the prob-lems considered by producers in the process of production and operation of enterprises.More common dividend methods are barrier dividend strategy,threshold dividend strategy and so on,and many studies have discussed them around the optimization of dividends.This study extends and explores the newsboy modeling problem from a new perspective based on existing research.In this study,we assume that the firm produces and sells a class of products,similar to the multi-period newsboy model,and assume that the producer uses the barrier dividend strategy to pay dividends to share-holders.The main model used in this study is the discrete Markov decision model and the objective is to find the production strategy that maximizes the expected discounted dividend.Specifically,we consider two scenarios of production models.First,assuming that a firm produces,sells and stores a class of products for a given amount of principal,the market demand in different periods is a non-negative,independent and identically distributed discrete random variable.During any production cycle,the decision maker may face an inventory or supply shortage problem.We assume that the inventory charge for the current surplus product is paid at the end of each period,and the barrier dividend strategy is used to pay dividends to shareholders.In this paper,based on the above assumptions,we construct an iterative formula for maximizing the expected discounted dividend using the full-expectation formula.Under the condition that the length of the examination period is limited,Python software is used to carry out several iterations to obtain the optimal production strategy and the optimal value function in a limited period of time.In addition,we further consider a case where the length of the inspection period is unbounded until production is terminated when the producer's holdings of the prior are insufficient to cover the production and inventory costs in the next period.Similarly,the Bellman equation maximizing the expected discounted dividend is developed.The existence and uniqueness of the optimal value function,i.e.,the optimal value function is the immovable point of Bellman equation,can be proved by the principle of compression map-ping.Secondly,this study assumes that the unit cost in each period is correlated with the unit selling price and the market demand in the previous period as random variables,and the three follow a joint distribution and they are independent and identically distributed random vectors.We establish the iterative formulation in finite time and Bellman equation in the case of no time constraints,and obtain the optimal value function and the optimal production strategy in such a multivariate situation.In conclusion,for a dividend optimization problem similar to a multi-period newsboy model,this study provides a method for finding an optimal solution which is useful in obtaining the expected discounted dividend that maximizes the expected discounted dividend and its corresponding optimal production schedule.However,there are some limitations in this study,for example,only a simple form of Markov decision-making problem is discussed in this paper,and more meaningful conclusions can be obtained if more complex conditions such as capital injection,investment,and Markov environmental process are further incorporated in the model.
optimal production strategybarrier dividend strategyBellman equationfixed point theorem
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