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The performance of such solvers depends crucially on four types of in built heuristics: primal, improvement, branching, and cut separation or, more generally, bounding heuristics. However, such heuristics have, until recently, not exploited structure in integer linear programs beyond the recognition of certain types of single row constraints.Many alternative approaches to integer linear programming can be cast in the following, novel framework. “Structure” in any integer linear program is a class of equivalence among triples of algorithms: deriving combinatorial objects from the input, adapting them, and transforming the adapted object to solutions of the original integer linear program.

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After the pharmacy observations were completed, five pharmacists and twelve support staff interviews were held to discuss professional perspectives of MURs.The findings from this study suggest that the MUR service is a modern and developing service but one that remains unestablished. Patient awareness of MURs was poor and nearly all MURs were initiated by the pharmacist; no patients were referred from the GP. Pharmacy staff did not actively seek to recruit patients who may benefit most from an MUR and the majority were invited in ad hoc manner.

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