Azizul Baten

Extended optimal stochastic production control model with application to economics

This study considers an inventory control system meeting uncertain demand in continuous time.The demand is a function of both time and price, with the price evolves as a Wiener process with no drift. The goal is to use the stochastic optimal control principle to completely solve a production planning model for the demand rate.A stochastic optimal control problem is formulated in which the stochastic differential equations of a type known as Ito’s equations are considered which are perturbed by a Markov diffusion process and analyzed by the optimal control of a single dimension stochastic production planning model. The existence of a complete solution to the associated HJB equation is established and the optimal policy is characterized. Numerical examples and solutions of this optimal control model are then presented.

Optimizing the throughput of an M/G/C/C topological network

An M/G/C/C state dependent queuing network approach models the behavior of entities (e.g., pedestrians and vehicles) flowing through a space. For a space consisting of various complex topological networks, the challenge is how to control such flow so that its throughput can be optimized. This paper discusses the throughput optimization of an M/G/C/C system using a network flow programming model. For this, we first decompose each available network and analyze its performance separately. The performance reports the effect of arrival rates to the throughput, blocking probability, expected number of pedestrians and expected travel time of each of the network. The best arrival rate of each network is then searched and fed to the network flow programming model to find the optimal arrival rates of source networks. The effect of the optimal arrival rates to the performance of the whole network is then analyzed and compared to that of using arbitrary arrival rates. Results show that with the right control of arriv...

Some Results on Bellman Equations of Optimal Production Control in a Stochastic Manufacturing System

The paper studies the production inventory problem of minimizing the expected discounted present value of production cost control in a manufacturing system with degenerate stochastic demand. We establish the existence of a unique solution of the Hamilton-Jacobi-Bellman (HJB) equations associated with this problem. The optimal control is given by a solution to the corresponding HJB equation.