# Accession Number:

## ADA030650

# Title:

## Optimal Control of a Brownian Storage System

# Descriptive Note:

## Technical rept.

# Corporate Author:

## STANFORD UNIV CA DEPT OF OPERATIONS RESEARCH

# Personal Author(s):

# Report Date:

## 1976-09-01

# Pagination or Media Count:

## 36.0

# Abstract:

Consider a storage system such as an inventory or bank account whose content fluctuates as a Brownian Motion X Xt, t or 0 in the absence of any control. Let Y Yt, t or 0 and Z ZT, t or 0 by non-decreasing, non-anticipating functionals representing the cumulative input to the system and cumulative output from the system respectively. The problem is to choose Y and Z so as to maximize expected discounted reward subject to the requirement that Xt Yt - Zt or 0 for all t or 0 almost surely. In our first formulation, we assume that a reward of one dollar is received for every unit of output, while a cost of k 1 dollars is incurred for every unit of input. We explicitly compute an optimal policy involving a single critical number. In our second formulation, the cumulative input Y is required to be a step function, and an additional cost of K 0 dollars is incurred each time that an input jump occurs. We explicitly compute an optimal policy involving two critical numbers. Applications to inventoryproduction control and stochastic cash management are discussed.

# Descriptors:

# Subject Categories:

- Statistics and Probability
- Operations Research
- Computer Hardware