Tree Approximations of Dynamic Stochastic Programs

Dynamic multistage stochastic optimization programsoffer a possibility to include uncertainty intooptimization models, providing a contemporary set oftools for modern management sciences with wide rangeof applications.In order to solve realistic real-world stochasticoptimization programs, the approximation of theunderlying stochastic process describing the futureuncertainty is performed. In this work, a tree-baseddiscretization technique utilizing conditionaltransportation distance is considered, as it is wellsuited for the approximation of multi-stagestochastic programming problems. Correspondingconvergence properties are investigated. The relationbetweenthe approximation quality of the probability modeland the quality of the solution is established.An example of application, multistage inventorycontrol, is used to verify theoretical results. Thenumerical solution and the obtained error bounds arecalculated explicitly.

Autorentext

Radoslava Mirkov, PhD: Studies of Mathematics at the University
of Novi Sad, Serbia and at the University of Vienna, Austria.
Research assistant an the University of Vienna, currently working
at the Market Risk Management Department, Bank Austria, UniCredit
Group, Vienna, Austria.

Klappentext

Dynamic multistage stochastic optimization programs
offer a possibility to include uncertainty into
optimization models, providing a contemporary set of
tools for modern management sciences with wide range
of applications.

In order to solve realistic real-world stochastic
optimization programs, the approximation of the
underlying stochastic process describing the future
uncertainty is performed. In this work, a tree-based
discretization technique utilizing conditional
transportation distance is considered, as it is well
suited for the approximation of multi-stage
stochastic programming problems. Corresponding
convergence properties are investigated. The relation
between
the approximation quality of the probability model
and the quality of the solution is established.

An example of application, multistage inventory
control, is used to verify theoretical results. The
numerical solution and the obtained error bounds are
calculated explicitly.