STOCHASTIC OPTIMAL CONTROL OF ATO SYSTEMS WITH BATCH ARRIVALS VIA DIFFUSION APPROXIMATION

2007 ◽  
Vol 21 (3) ◽  
pp. 477-495 ◽  
Author(s):  
Wanyang Dai ◽  
Qian Jiang
Keyword(s):  
Optimal Control ◽  
Stochastic Optimal Control ◽  
Heavy Traffic ◽  
Infinite Horizon ◽  
Order System ◽  
Planning Problem ◽  
Batch Arrivals ◽  
Renewal Reward Processes ◽  
Sequencing Rule ◽  
Static Planning

We study the stochastic optimal control for an assemble-to-order system with multiple products and components that arrive at the system in random batches and according to renewal reward processes. Our purpose is to maximize expected infinite-horizon discounted profit by selecting product prices, component production rates, and a dynamic sequencing rule for assembly. We refine the solution of some static planning problem and a discrete review policy to batch arrival environment and develop an asymptotically optimal policy for the system operating under heavy traffic, which indicates that the system can be approximated by a diffusion process and exhibits a state space collapse property.

scholarly journals Reducing Response Time in Fork-Join Systems under Heavy Traffic Via Imbalance Control

2013 ◽  
Vol 45 (4) ◽  
pp. 1137-1156
Author(s):  
Saul C. Leite ◽  
Marcelo D. Fragoso
Keyword(s):  
Optimal Control ◽  
Response Time ◽  
Control Problem ◽  
Stochastic Optimal Control ◽  
Numerical Experiments ◽  
Heavy Traffic ◽  
Controlled System ◽  
Reflected Diffusion ◽  
Stochastic Optimal Control Problem ◽  
Workload Imbalance

We consider the problem of reducing the response time of fork-join systems by maintaining the workload balanced among the processing stations. The general problem of modeling and finding an optimal policy that reduces imbalance is quite difficult. In order to circumvent this difficulty, the heavy traffic approach is taken, and the system dynamics are approximated by a reflected diffusion process. This way, the problem of finding an optimal balancing policy that reduces workload imbalance is set as a stochastic optimal control problem, for which numerical methods are available. Some numerical experiments are presented, where the control problem is solved numerically and applied to a simulation. The results indicate that the response time of the controlled system is reduced significantly using the devised control.

scholarly journals Stochastic optimal control problem with infinite horizon driven by G-Brownian motion

2018 ◽  
Vol 24 (2) ◽  
pp. 873-899 ◽  
Author(s):  
Mingshang Hu ◽  
Falei Wang
Keyword(s):  
Optimal Control ◽  
Brownian Motion ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Stochastic Optimal Control ◽  
Value Function ◽  
Infinite Horizon ◽  
Dynamic Programming Principle ◽  
Stochastic Optimal Control Problem ◽  
The Value Function

The present paper considers a stochastic optimal control problem, in which the cost function is defined through a backward stochastic differential equation with infinite horizon driven by G-Brownian motion. Then we study the regularities of the value function and establish the dynamic programming principle. Moreover, we prove that the value function is the unique viscosity solution of the related Hamilton−Jacobi−Bellman−Isaacs (HJBI) equation.

scholarly journals Reducing Response Time in Fork-Join Systems under Heavy Traffic Via Imbalance Control

2013 ◽  
Vol 45 (04) ◽  
pp. 1137-1156
Author(s):  
Saul C. Leite ◽  
Marcelo D. Fragoso
Keyword(s):  
Optimal Control ◽  
Response Time ◽  
Control Problem ◽  
Stochastic Optimal Control ◽  
Numerical Experiments ◽  
Heavy Traffic ◽  
Controlled System ◽  
Reflected Diffusion ◽  
Stochastic Optimal Control Problem ◽  
Workload Imbalance

We consider the problem of reducing the response time of fork-join systems by maintaining the workload balanced among the processing stations. The general problem of modeling and finding an optimal policy that reduces imbalance is quite difficult. In order to circumvent this difficulty, the heavy traffic approach is taken, and the system dynamics are approximated by a reflected diffusion process. This way, the problem of finding an optimal balancing policy that reduces workload imbalance is set as a stochastic optimal control problem, for which numerical methods are available. Some numerical experiments are presented, where the control problem is solved numerically and applied to a simulation. The results indicate that the response time of the controlled system is reduced significantly using the devised control.

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