Stochastic optimal control of some stochastic production planning and advertising dynamical models

SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE AT KING SAUD UNIVERSITY SAUDIA ARABIA, RIYADH AUGUST 2006The first is the stochastic production planning model. In this model both of inventory level and production are stochastic while the demand rate is deterministic and has three cases which are, continuous constant, increasing function of time and exponential function of time. The second is the stochastic Vidale-Wolfe advertising model. In this model both of market share and advertising rate are stochastic. In this study the optimal advertising rate is obtained as a function of the market share. The third is the stochastic consumption model. In this case we have studied the optimal control of Rich’s stochastic optimal control problem. In this study we have obtained both of optimal consumption rate and the fraction of wealth invested in stock at any time in two different cases for utility functio