K-Approximate Convexity and Its Applications
Time: 2016-11-14
Published By: Xiaoni Tan
Speaker(s): Professor Ye Lu (City University of Hong Kong)
Time: 14:00-15:00 November 18, 2016
Venue: Room 29, Quan Zhai, BICMR
In
practice, managers face challenges of incomplete demand information and
nonlinear production cost. We develop a new concept named K-approximate
convexity, which is shown to be a generalization of K-convexity, to address
these challenges. The idea is applied to obtain well-structured heuristic
policies for two operations management problems, the joint pricing and inventory
control problem with incomplete demand information and the periodic review
inventory control problem with nonlinear production cost. We establish
worst-case performance bounds on the heuristic policies in both problems. In a
numerical study on a joint pricing and inventory control problem where demand
is driven from real sales data, we find that the average gap between the
profits of our heuristic policy and the optimal policy is only 0.27%, and the
worst gap is 4.6%. In an extensive numerical study that is designed to reflect
a practical inventory control application, the average gap between the costs of
our heuristic policy and the optimal policy is only 0.11%, and the worst gap is
just 1.81%.
