Optimal Inventory Control Of Perishable Products In Supply Chain

With the high-speed development of global economy, Supply Chain Management(SCM) is becoming an vital approach to enhance the competitive ability of enterprises. Inventory control is a key step in SCM, which has aroused abroad attentions in business and theory circles. However, the increasing development of technology and the rising living standard have increased the proportion of perishable products in market. It is difficult to deal with this kind of inventory control problem due to the perishable nature of these products. Therefore, whether can have an efficient production and reproduction rate or not will influence enterprises' economic benefits and the sustainable development of the society.Firstly, a production system for one product with perishable nature is introduced, in which the demand rate is inventory-level-dependent as well as timevarying. To maximize the firm's total profit, Pontryagin's maximum principle is used to obtain the necessary conditions for optimal control. Aiming at the three possible singular regimes, subdifferential is also introduced to judge which singular regime occurs. Then an exact production policy is determined. Secondly, a product recovery system for one product with perishable nature is constructed,where backorders are not allowed. The system contains one inventory for serviceable items and one for returned and recoverable items. To minimize the firm's total cost, the Pontryagin's maximum principle is introduced to obtain the optimal production and reproduction policy under four inventory status. Finally,numerical examples are provided to illustrate the efficiency of the method.This thesis in view of the inventory model with a finite or infinite horizon objective, linear or nonlinear production cost function, as well as the problems with constrains involving control variables or state variables, optimal control theory is used to obtain an exact production policy.