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Optimal search on a stochastic tree with an application to multi-phased RandD scheduling

Author: Rothblum, U. G. ; Van Der Heyden, LudoINSEAD Area: Technology and Operations Management Series: Working Paper ; 96/05/TM Publisher: Fontainebleau : INSEAD, 1996.Language: EnglishDescription: 42 p.Type of document: INSEAD Working Paper Online Access: Click here Abstract: We consider the problem of determining a path of feasible edges from the root of a directed tree to any one of its endpoints so as to minimize the expected search cost. Each edge in the tree is characterized by an exploration cost and a feasibility probability. When an edge is explored and found infeasible, all paths using this edge become infeasible too, and other paths must be looked for. An algorithm for solving the problem is provided. The obtained solution exhibits the dynamic aspect of searches in this setting. In particular, one may encounter repeated jumping between different parts of the tree. This model was motivated by the problem of determining an optimal schedule for an RandD project presenting several options where each can be decomposed into multiple phases satisfying precedence relationships. The model's solution demonstrates that in such situations the optimal RandD schedule exhibits a parallel, adaptative structure
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We consider the problem of determining a path of feasible edges from the root of a directed tree to any one of its endpoints so as to minimize the expected search cost. Each edge in the tree is characterized by an exploration cost and a feasibility probability. When an edge is explored and found infeasible, all paths using this edge become infeasible too, and other paths must be looked for. An algorithm for solving the problem is provided. The obtained solution exhibits the dynamic aspect of searches in this setting. In particular, one may encounter repeated jumping between different parts of the tree. This model was motivated by the problem of determining an optimal schedule for an RandD project presenting several options where each can be decomposed into multiple phases satisfying precedence relationships. The model's solution demonstrates that in such situations the optimal RandD schedule exhibits a parallel, adaptative structure

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