| 1. |
- Amankwah, Henry, et al.
(författare)
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Open-pit mining with uncertainty : A conditional value-at-risk approach
- 2013
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Ingår i: Optimization Theory, Decision Making, and Operations Research Applications. - New York : Springer. - 9781461451334 - 9781461451341 ; , s. 117-139
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Konferensbidrag (refereegranskat)abstract
- The selection of a mine design is based on estimating net present values of all possible, technically feasible mine plans so as to select the one with the maximum value. It is a hard task to know with certainty the quantity and quality of ore in the ground. This geological uncertainty and also the future market behavior of metal prices and foreign exchange rates, which are always uncertain, make mining a high risk business. Value-at-Risk (VaR) is a measure that is used in financial decisions to minimize the loss caused by inadequate monitoring of risk. This measure does, however, have certain drawbacks such as lack of consistency, nonconvexity, and nondifferentiability. Rockafellar and Uryasev [J. Risk 2, 21-41 (2000)] introduce the Conditional Value-at-Risk (CVaR) measure as an alternative to the VaR measure. The CVaR measure gives rise to a convex optimization problem. An optimization model that maximizes expected return while minimizing risk is important for the mining sector as this will help make better decisions on the blocks of ore to mine at a particular point in time. We present a CVaR approach to the uncertainty involved in open-pit mining. We formulate investment and design models for the open-pit mine and also give a nested pit scheduling model based on CVaR. Several numerical results based on our models are presented by using scenarios from simulated geological and market uncertainties.
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| 2. |
- Quttineh, Nils-Hassan, 1979-, et al.
(författare)
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Effect Oriented Planning of Joint Attacks
- 2013
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Ingår i: Optimization Theory, Decision Making, and Operations Research Applications. - New York, NY : Springer-Verlag New York. - 9781461451334 - 9781461451341 ; , s. 49-70
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Konferensbidrag (refereegranskat)abstract
- We consider tactical planning of a military operation on a large target scene where a number of specific targets of interest are positioned, using a given number of resources which can be, for example, fighter aircraft, unmanned aerial vehicles, or missiles. The targets could be radar stations or other surveillance equipment, with or without defensive capabilities, which the attacker wishes to destroy. Further, some of the targets are defended, by, for example, Surface-to-Air Missile units, and this defense capability can be used to protect also other targets. The attacker has knowledge about the positions of all the targets and also a reward associated with each target. We consider the problem of the attacker, who has the objective to maximize the expected outcome of a joint attack against the enemy. The decisions that can be taken by the attacker concern the allocation of the resources to the targets and what tactics to use against each target. We present a mathematical model for the attacker’s problem. The model is similar to a generalized assignment problem, but with a complex objective function that makes it intractable for large problem instances. We present approximate models that can be used to provide upper and lower bounds on the optimal value, and also provide heuristic solution approaches that are able to successfully provide near-optimal solutions to a number of scenarios.
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