POSSIBLE APPLICATIONS OF THE BELLMAN'S VECTOR OPTIMALITY PRINCIPLE IN MINERAL DEPOSIT MANAGEMENT

Decision problems in mineral deposit management and in mining management can be solved with the aid of mathematical techniques. Accomplishment of geological-mining projects is usually long-term and expensive as well as it proceeds in uncertainty conditions and it is burdened by the considerable risk. Moreover the necessity of examination of many objective functions about different character should be taken into consideration e.g.: economic, ecological or social. These criterions are usually contradictory and seeking the compromise decision becomes necessary. Such problems can be solved with the aid of multi-criteria optimisation. Application of the Bellman's vector optimality principle on the copper-silver mine example was presented. This Bellman's principle takes into consideration a time factor, and decision making is not made one-time but repeatedly. Therefore, a multistage object function shall be applied. Apart from the set of acceptable decisions, being a subset of the decision-making space comparing of vectors as an elements of criterion space is integral. Solving a decision-making problem begins from seeking the solution for the last stage, next moving back, the solutions of earlier stages up to initial one are being found. A hypothetical problem of the optimal allocation of financial means serving the purpose of production results improvement in six mining divisions was taken. Maximisation of twenty-four hour production output as well as incomes at simultaneous minimising losses was the purpose of optimisation. Exploitation divisions differential in the quality of ore and in the geological-mining conditions enable to achieve different exploitation capacity and generate different incomes. Task was solved as a three-criterion decision problem in 3 stages: 4) maximisation of production output at simultaneous minimising of exploitation losses, 5) maximisation of incomes at simultaneous minimising of exploitation losses, 6) maximisation of production output and incomes at simultaneous minimising of exploitation losses. In the run of the optimisation process not-dominated vectors of assessment were enumerated for mine divisions also the maximum vectors and efficient solutions of the model were found. Solutions enabled to fix the sequence of optimal decisions constituting the optimal strategy in the scope of allocating of financial means.