A Continuous-time Inventory Model with Procurement from Spot Market
Not only the amount of product demand but also the prices of the product have a strong impact on a manufacturers revenue. In this paper we consider a continuous-time inventory model where the spot price of the product stochastically fluctuates according to a Brownian motion. Should information of the spot price be available, the manufacturer wishes to buy the product from the spot market if profitable. The purpose of this paper is to find an optimal procurement policy so as to minimize the total expected discounted costs over an infinite planning horizon. We extend Sulem(1986) model into the one in which not only demand but also the market price of the product follows geometric Brownian motions. Then we obtain the optimal cost as the solution of Quasivariational inequality, and show that there exists an optimal procurement policy as (s, S) policy.We shall clarify the dependence of such optimal (s, S) policy on the spot price at the procurement epoch. These values of (s, S) policy can be used and revised in the succeeding ordering cycles.Finally, some numerical examples are provided to investigate analytical properties of the expected cost function as well as of the optimal policy.
Inventory control Stochastic model Quasi-variational inequality
Kimitoshi Sato Katsushige Sawaki
Graduate School of Mathematical Sciences and Information Engineering, Nanzan University, 27 Seirei-c Graduate School of Business Administration, Nanzan University, 18 Yamazato-cho, Showa-ku, Nagoya 466
国际会议
The Seventh International Symposium(ISORA08)(第七届国际效力研究及其应用学术会议)
云南丽江
英文
282-291
2008-10-31（万方平台首次上网日期，不代表论文的发表时间）