1 research outputs found
Parametric Distributionally Robust Optimisation Models for Budgeted Multi-period Newsvendor Problems
In this paper, we consider a static, multi-period newsvendor model under a
budget constraint. In the case where the true demand distribution is known, we
develop a heuristic algorithm to solve the problem. By comparing this algorithm
with off-the-shelf solvers, we show that it generates near-optimal solutions in
a short time. We then consider a scenario in which limited information on the
demand distribution is available. It is assumed, however, that the true demand
distribution lies within some given family of distributions and that samples
can be obtained from it. We consider the cases of normal and Poisson demands.
For each case, we show that using maximum likelihood estimates in place of the
true parameters can lead to poor estimates of the true cost associated with an
order quantity. Hence, we make use of likelihood inference to develop
confidence sets for the true parameters. These are used as ambiguity sets in a
distributionally robust model, where we enforce that the worst-case
distribution lies in the same family as the true distribution. We solve these
models by discretising the ambiguity set and reformulating them as piecewise
linear models. We show that these models quickly become large as the ambiguity
set grows, resulting in long computation times. To overcome this, we propose a
heuristic cutting surface algorithm that exploits theoretical properties of the
objective function to reduce the size of the ambiguity set. We illustrate that
our cutting surface algorithm solves orders of magnitude faster than the
piecewise linear model, while generating very near-optimal solutions