PRODUCTION SMOOTHING WITH STOCHASTIC DEMAND AND RELATED INVENTORY PROBLEMS.
Abstract
The dynamic single product inventory problems treated here have costs that depend on changes in production rates as well as on the rates themselves and on inventory levels. All but one of the models have stochastic demand and backorder excess demand. A discrete time model in which smoothing costs are proportional to the difference between production rates in successive periods is shown to have an optimal policy in which production decreases as inventory increases; uniform bounds are given for the optimal policy parameter values. The model generalizes to one in which employment level and production rate are separate variables. A generalized stationary analysis is given for the simpler case. When units are made sequentially in time and demand is a renewal process, the presence of smoothing costs leads to optimal policies for the minimization of average cost per unit time which are based on only two parameters and which are easily administered. Analogous results are obtained for a similar discrete time model and the resulting stationary distributions of state variables is given for the cases of demand being a Poisson process and either constant or exponentially distributed production times. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Aug 17, 1967
- Accession Number
- AD0659993
Entities
People
- Matthew J. Sobel
Organizations
- Stanford University