A one-dimensional search with traveling cost

A one-dimensional search with traveling cost

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Article ID: iaor1992970
Country: Japan
Volume: 33
Issue: 3
Start Page Number: 262
End Page Number: 276
Publication Date: Sep 1990
Journal: Journal of the Operations Research Society of Japan
Authors:
Keywords: programming: dynamic
Abstract:

There are 2n+1 neighboring cells in a straight line. An object is in one of all cells except for the cell which locates at the center of all cells, according to a known probability distribution which is assumed to be symmetric with respect to the cell at the center. A searcher is at the cell which locates at the center of all cells at the beginning of the search, and after choosing an ordering of the 2n labels attached to the 2n cells, the searcher examines each cell in that order. An ordering is considered to be optimal when the expected cost of the search is minimized. The cost comprises a traveling cost dependent on the distance from the last cell examined and a fixed examination cost. After basic observations on the present model are made the Bellman’s Principle of Optimality is applied to it. There is then the optimal equation, from which some properties are derived. Approximately optimal search strategies are defined and analyzed. Several discussions are provided.

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