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.

Subject Categories:

  • Statistics and Probability
  • Operations Research
  • Computer Hardware

Distribution Statement:

APPROVED FOR PUBLIC RELEASE