Optimization models and methods in Operations Management

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We study and develop optimization models and methods for decision problems in Operations Management, along five main research directions.***(1) Submodularity and lattices are mathematical structures that arise in fields such as discrete mathematics, operations research, artificial intelligence, microeconomics and game theory. We study the structure of algebraic lattices and submodular optimization problems, and the development of algorithms for partitioning problems with submodular costs. We also investigate computational properties of methods combining discrete convexity and stochastic optimization for scheduling of surgeries in a hospital in the presence of uncertain operations durations***(2) Minimum cuts in graphs and hypergraphs form a special case of such partitioning problems, with applications to various areas of engineering and discrete optimization. We investigate algorithmic consequences of the remarkable structural properties of global minimum cuts, in particular randomized algorithms and the tradeoffs between probability of success and running time. We also study partitioning problems with submodular part costs subject to minimum part size constraints.***(3) In partitioning, clustering and location problems, it is often desirable that the parts (clusters, regions) have “nice shapes”, or at least are “not too odd”. We plan to investigate formulations and properties of such shape constraints, particularly within mixed-integer programming formulations, as well as “dual” optimization problems of finding maximum weight subsets satisfying such constraints.***(4) Surface and underground mine planning and sequencing: in collaborative research projects we study the solution of open pit mine sequencing projects that induce highly structured but huge integer programming models (with tens of millions of variables and constraints); and the use of continuous-space (and continuous-time) infinite-dimensional optimization models as alternatives to these huge discrete models.***(5) Scheduling methods and applications, in particular for weighted sums of completion times objectives. We study the computational complexity of a continuous relaxation, based on mean busy dates, for very general single-stage scheduling environments; and problems that include the scheduling of maintenance activities, during which the machines are not available for processing.******This research program is expected to contribute to fundamental knowledge and, through its applications, to several sectors of the Canadian economy and of the Canadian society, for example by helping to reduce waiting time in the Canadian health care system.**