Optimal mine design and scheduling

In this paper, novel integer programming formulations are developed for solving the optimal scheduling of patients waiting for radiotherapy treatment. In this specific clinical domain, the suitable management and control of a patients’ waiting list strongly affect both the quality of the therapeutical outcome, in terms of effectiveness, and the cost-saving use of the overall therapeutical resources, in terms of efficiency. The proposed models allow the best scheduling strategy to be devised by taking into account the quality of the health care service offered to the patient as well as the status and the preferences of the patient. The computational experiments, carried out on realistic scenarios and considering real data, are very promising and show the efficiency and robustness of the proposed models to address the problem under consideration.

Musician’s behavior-inspired harmony search (HS) algorithm was first applied to the optimal operation scheduling of a multiple dam system. The HS model tackled a popular benchmark system with four dams. Results showed that the HS model found five different global optimal solutions with identical maximum benefit from hydropower generation and irrigation, while enhanced GA model (real-value coding, tournament selection, uniform crossover, and modified uniform mutation) found only near-optimal solutions under the same number of function evaluations. Furthermore, the HS model arrived at the global optima without performing any sensitivity analysis of algorithm parameters whereas the GA model required tedious sensitivity analysis.

We study the problem of scheduling n jobs on two identical parallel processors or machines where an optimal schedule is defined as one with the shortest total weighted flowtime (i.e., the sum of the weighted completion time of all jobs), among the set of schedules with minimum makespan (i.e., the completion time of the last job finished). We present a two phase non-linear Integer Programming formulation for its solution, admittedly not to be practical or useful in most cases, but theoretically interesting since it models the problem. Thus, as an alternative, we propose an optimization algorithm, for small problems, and a heuristic, for large problems, to find optimal or near optimal solutions. Furthermore, we perform a computational study to evaluate and compare the effectiveness of the two proposed methods.

The paper presents a performance model that can be used to optimally schedule arbitrary tasks on a network of heterogeneous computers when there is an upper bound on the size of the task that can be solved by each computer. We formulate a problem of partitioning of an n-element set over p heterogeneous processors using this advanced performance model and give its efficient solution of the complexity O(p3 × log2 n).