Optimal Control of a Brownian Storage System
Abstract
Consider a storage system (such as an inventory or bank account) whose content fluctuates as a Brownian Motion X = (X(t), t> or = 0) in the absence of any control. Let Y = (Y(t), t > or = 0) and Z = (Z(T), 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 X(t) + Y(t) - Z(t) > 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 inventory/production control and stochastic cash management are discussed.
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1976
- Accession Number
- ADA030650
Entities
People
- Allison J. Taylor
- J. M. Harrison
Organizations
- Stanford University