A Diffusion Model of Inventory and Production Control.
Abstract
We consider the diffusion limits of several closely related production planning problems. Each involves a make-to-stock producer who faces IID demands over a sequence of future periods. In the simplest formulation, a production capacity or workforce level must be fixed at time zero, and thereafter the actual production rate is adjusted dynamically in response to inventory fluctuations. The capacity decision fixes certain operating costs and constrains subsequent decisions regarding production rates. Fixing the demand process, we consider a sequence of cost structures in which the total inventory carrying cost approaches zero. (This requires that both the physical cost of carrying inventory and the interest rate earned on external investment vanish). Under this condition, the production planning problem approaches a two-stage optimal control problem for Brownian motion. The first stage of the limiting problem involves drift rate selection for a Brownian motion, and its second stage is the instantaneous control problem formulated and solved by Harrison-Taylor (1977). With small holding costs, we find that an optimal capacity decision calls for near equality of the average production and demand rates, which in turn justifies a diffusion approximation for the subsequent problem of inventory control through production rate adjustment.
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 01, 1982
- Accession Number
- ADA120645
Entities
People
- J. Michael Harrison
Organizations
- Stanford University