# Accession Number:

## AD0648410

# Title:

## STOCHASTIC RENTAL INVENTORY MODEL

# Descriptive Note:

## Research rept.

# Corporate Author:

## CALIFORNIA UNIV BERKELEY OPERATIONS RESEARCH CENTER

# Personal Author(s):

# Report Date:

## 1966-10-01

# Pagination or Media Count:

## 104.0

# Abstract:

An inventory of rented equipment is studied. Equipment is withdrawn from the inventory by customers who use it for a length of time and then return it. Decisions about the amount of equipment to rent can be made at certain points in time. This paper describes a policy for making these decisions which minimizes expected costs. A dynamic programming model is formulated to describe the problem. The model is different than the usual ones considered in the literature in three respects. First, the equipment which is withdrawn from the inventory is not consumed it is only used for a certain length of time then it returns to the inventory. The amount of equipment in the inventory, consequently, can fluctuate up or down. Second, all the equipment in the inventory is rented. Thus, when a decision is made about how much equipment is needed, either more or less than currently is on hand can be rented. Third, convexity of the cost function is not important because simple optimal policies can be found when the cost function is nonconvex. The exact form of the optimal policy depends on the specific assumptions made, however, all of the optimal policies have the following generic structure. At the time a decision is to be made two numbers t and u, with t or u, can be computed. If the amount of equipment currently on hand is greater than u less than t then it is optimal to rent u t. If the amount of equipment is in between t and u then, assuming convexity, it is optimal to continue renting the same quantity or, assuming nonconvexity, no general statement can be made about what to do because for each number rented in between t and u there may be a different optimal number to rent.

# Descriptors:

# Subject Categories:

- Forestry
- Operations Research