CORAL og DORS inviterer til foredrag med Peter Berling:

Title: Optimal Inventory Policies when Purchase Price and Demand are Stochastic

Time: May 19, 2009

Place: Aarhus School of Business M323

Abstract

In this paper we consider the problem of a form that faces a stochastic demand (Poisson)

and must replenish from a market in which prices fluctuate, such as a commodity

market. We describe the price evolution as a continuous stochastic process and we focus

on commonly used processes suggested by the financial literature, such as the Geometric

Brownian Motion and the Ornstein-Uhlenbeck process. It is well-known that under

variable purchase price, a price-dependent base-stock policy is optimal. Using the singleunit

decomposition approach, we explicitly characterize the optimal base-stock level

using a series of threshold prices. We show that the base-stock level is first nondecreasing

and then non-increasing in the current purchase price. We provide a

procedure for calculating the thresholds, which yields closed-form solutions when price

follows a Geometric Brownian Motion and implicit solutions under the Ornstein-Uhlenbeck

price model. In addition, our numerical study shows that the optimal policy performs

much better than inventory policies that ignore future price evolution, because it tends

to place larger orders when prices are expected to increase.