Abstract
In this paper, a discrete two item inventory model for deteriorating items with a linear stock dependent demand rate without regular supply is given first; then, regular supply is taken into account, which may be regarded as feedback control. An objective function is formed to calculate the net profit with respect to possible profits and possible loss. A necessary criterion for the steady state optimal control problem for optimizing the objective function subjected to the constraints given by the difference equations of the inventory is obtained. At last, an improved model is put forward.
Highlights
Inventory management is one of the most important drivers for an effective enterprise
Since the classical economic order quantity model which undoubtedly constitutes the cornerstone of inventory research [1], there are many models in the literature which can illustrate the behavior of inventory management, including the continuoustime framework, and discrete time one, whose origins may be traced in the seminal work of Arrow [8]
By means of the discrete version of Pontryagin’s Maximum Principle, a necessary condition for the steady state optimal control problem for optimizing the objective function subjected to the constraints given by the difference equations of the inventory is obtained
Summary
Inventory management is one of the most important drivers for an effective enterprise. By means of Pontryagin’s Maximum Principle, the author derived a necessary condition for the steady state optimal control problem in which objective function subjected to the constraints given by the competitive ordinary differential equations. To our knowledge, there have been very few corresponding research works focusing on discrete version of Pontryagin’s Maximum Principle on discrete inventory model for deteriorating items. By means of the discrete version of Pontryagin’s Maximum Principle, a necessary condition for the steady state optimal control problem for optimizing the objective function subjected to the constraints given by the difference equations of the inventory is obtained.
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