## Contributed Session Wed.1.MA 144

#### Wednesday, 10:30 - 12:00 h, Room: MA 144

**Cluster 22: Stochastic optimization** [...]

### Scheduling, control and moment problems

**Chair: Mariya Naumova**

**Wednesday, 10:30 - 10:55 h, Room: MA 144, Talk 1**

**Meggie von Haartman**

Probabilistic realization resource scheduler with active learning

**Coauthor: Wolf Kohn**

**Abstract:**

Many resource-scheduling applications require the construction of a model with predictive capabilities. The model is used to generate demand information as a function of historic data, resource constraints, sensory data, and other elements. Our research is directed towards the online construction and tuning of a semi-Markov model representing a stochastic process of demand. An optimization algorithm based on the optimal conditional probability measure associated with the stochastic process drives the construction. The conditional sequential residual entropy associated with the historic data gives the criterion: Maximization of residual entropy.

The conditional probability measure associated with this model represents the demand at the current time, given the state information at the previous interval. The unique features of our approach are that a realization process in which the conditional probability is updated every time new information becomes available constructs the conditional probability. Another unique feature is that there is no apriori assumptions made about the associated probability space. This space is constructed and tuned as new information becomes available.

**Wednesday, 11:00 - 11:25 h, Room: MA 144, Talk 2**

**Regina Hildenbrandt**

Partitions-requirements-matrices as optimal Markov kernels of special stochastic dynamic distance optimal partitioning problems

**Abstract:**

The stochastic dynamic distance optimal partitioning problem (SDDP problem) is a complex Operations Research problem. The SDDP problem is based on a problem in industry, which contains an optimal conversion of machines.

Partitions of integers as states of these stochastic dynamic programming problems involves combinatorial aspects of SDDP problems. Under the assumption of identical "basic costs'' (in other words of "unit distances'') and independent and identically distributed requirements we will show (in many cases) by means of combinatorial ideas that decisions for feasible states with least square sums of their parts are optimal solutions. Corresponding Markov kernels are called partitions-Requirements-Matrices (PRMs).

Optimal decisions of such problems can be used as approximate

solutions of corresponding SDDP problems, in which the basic costs differ only slightly from each other or as starting decisions if corresponding SDDP problems are solved by iterative methods, such as the Howard algorithm.

**Wednesday, 11:30 - 11:55 h, Room: MA 144, Talk 3**

**Mariya Naumova**

Univariate discrete moment problem for new classes of objective function and its applications

**Coauthor: Andras Prekopa**

**Abstract:**

We characterize the dual feasible bases, in connection with univariate discrete moment problem for classes of objective function not dealt with until now, e.g., step functions with finite number of values. Formulas for the optimum value and dual type algorithmic solutions will be presented. Applications will be mentioned to engineering design and finance.