Contributed Session Mon.2.MA 141

Monday, 13:15 - 14:45 h, Room: MA 141

Cluster 22: Stochastic optimization [...]

Applications in natural resources


Chair: Ralf Lenz



Monday, 13:15 - 13:40 h, Room: MA 141, Talk 1

Gankhuyag Danzan
Regional economical mathematical models considering ecological factors

Coauthors: Buyantogtokh Danzan, Khajidsuren Navaandamba


Mongolia is experiencing rapid economic development attributable to
growth in the mining sector. Exploration by major national and
international mining companies has identified substantial reserves
of coal, copper and other minerals. Exploitation of these reserves
is under way with production expected to grow significantly in the
next five years. \ However, while the nation is experiencing
significant GDP growth, the exploitation of mineral reserves is
having a negative impact on the environment. Natural resources are
being depleted, chemicals are entering atmosphere, water is being
polluted with toxic metals, pasture land is being destroyed and the
incidence of sickness among the local population is ever increasing.
\  There is now a growing demand for the development of
mathematical models and related software to analyze the impact of
and the inter-relationship of different factors on the regional
economies affected by the mining industry. Statistical and dynamical
models have been developed, defined and solved using multi-extremals
and stochastic programming problems.



Monday, 13:45 - 14:10 h, Room: MA 141, Talk 2

Ralf Lenz
Optimization of water network operation under uncertainties

Coauthors: Frédérik Blank, Guido Dr. Sand, Martin Dr. Weiser


Water utilities operate their water networks in a very conservative manner. To be able to satisfy a volatile demand, the current operation procedure focuses on maintaining high water levels in the reservoirs. This results in higher operation costs due to inefficiencies regarding pressure levels and pump energy consumption.
While common approaches available in literature and as software packages use deterministic water demand predictions as a base, the focus of this talk considers uncertainties in the water demands prediction.
We present a methodology, which targets on lowering the minimum water storage level bounds without increasing the risk of running out of water. This is done by modeling uncertainties in water demand and applying stochastic programming techniques. Controlling the water storage levels allows the decrease of the artificial high bounds.
Reducing water storage levels implies a reduction of pumping costs, as pumps do not have to work against these high heads.
Finally we present the results by means of a small practical problem.
%This is a joint work together with ABB AG Corporate Research Center.



Monday, 14:15 - 14:40 h, Room: MA 141, Talk 3

Adriana Piazza
The optimal harvesting problem under price uncertainty

Coauthor: Bernardo K. Pagnoncelli


We study the exploitation of a one species forest plantation when timber price is governed by a stochastic process. The work focuses on providing closed expressions for the optimal harvesting policy in terms of the parameters of the price process and the discount factor. We assume that harvest is restricted to mature trees older than a certain age and neglect natural mortality and growth after maturity. We use stochastic dynamic programming techniques to characterize the optimal policy for two important cases: (i) when prices follow a geometric Brownian motion we completely characterize the optimal policy, (ii) if prices are governed by a mean reverting (Ornstein-Uhlenbeck) process we provide sufficient conditions, based on explicit expressions for reservation prices, assuring that harvesting everything available is optimal. For the Ornstein-Uhlenbeck process, we propose a policy based on a reservation price that performs well in numerical simulations. In both cases we solve the problem for every initial condition and the best policy is obtained without imposing any ad hoc restrictions such as maximum sustained yield or convergence to a predefined final state.


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