Spring 2002

ME/IE 8773-8774

FILL RATES OF SINGLE-STAGE AND MULTI-STAGE SUPPLY SYSTEMS

by

Matthew J. Sobel
Professor of Operations
William E. Umstattd Professorof Leadership and Enterprise Development
Chair, Department of Operations
Weatherhead School of Management
Case Western Reserve University

Wednesday, April 10, 2002
3:30-4:30 p.m.
Room 108 ME
Broadcast on UNITE Channel A
Coffee and cookies will be available in 125 ME following the seminar

The fill rate of a supply system is the average fraction of demand that is met from on-hand inventory. This talk presents formulas and bounds for the fill rate of periodic review supply systems with demands that are independent and identically distributed nonnegative random variables. The first part of the talk concerns a single-stage system and contains fill rate formulas for general distributions of demand. When demand is normally distributed, a good fill rate approximation uses only the standard normal distribution function and an exact expression uses only the normal loss table. The second part of the talk concerns a serial system with buffer inventories between stages that is operated with a modified base-stock level policy. Such systems describe supply chains and multi-stage manufacturing. It is easy to calculate the fill rate and easier to calculate bounds on it when demand has an empirical discrete distribution. A byproduct of the analysis is the conclusion that shorter supply chains have higher fill rates.

Dr. Matthew Sobel's research concerns the integration of operations with marketing and finance, optimization of stochastic models, economics of industrial organization, and environmental management. He is the William E. Umstattd Professor at Case Western Reserve University where he is Professor and Chair in the Department of Operations, and Professor of Electrical Engineering and Computer Science. He was previously on the faculties of the State University of New York at Stony Brook, Georgia Institute of Technology, and Yale University and he worked in industry and government. He has degrees in liberal arts, mathematical statistics, industrial engineering, and operations research from Columbia and Stanford Universities.

Informal Faculty Luncheon: Wednesday, April 10, 2002, 12:00 noon Prof. Sobel will be able to attend.