scholarly journals Optimal Search and Discovery

2021 ◽  
Author(s):  
Rafael P. Greminger
Keyword(s):  
Optimal Policy ◽  
Purchase Decision ◽  
Search Problem ◽  
Directed Search ◽  
Optimal Search

This paper studies a search problem in which a consumer is initially aware of only a few products. At every point in time, the consumer then decides between searching among alternatives of which he is already aware and discovering more products. I show that the optimal policy for this search and discovery problem is fully characterized by tractable reservation values. Moreover, I prove that a predetermined index fully specifies the purchase decision of a consumer following the optimal search policy. Finally, a comparison highlights differences to classical random and directed search. This paper was accepted by Dmitri Kuksov, marketing.

scholarly journals Optimal Search for a Moving Target

1995 ◽  
Vol 9 (2) ◽  
pp. 159-182 ◽  
Author(s):  
I. M. MacPhee ◽  
B. P. Jordan
Keyword(s):  
Markov Chain ◽  
Optimal Policy ◽  
Average Cost ◽  
Large Range ◽  
Moving Target ◽  
Optimal Search ◽  
Threshold Probability

Consider the problem of searching for a leprechaun that moves randomly between two sites. The movement is modelled with a two-state Markov chain. One of the sites is searched at each time t = 1,2,…, until the leprechaun is found. Associated with each search of site i is an overlook probability αi and a cost Ci Our aim is to determine the policy that will find the leprechaun with the minimal average cost. Let p denote the probability that the leprechaun is at site 1. Ross conjectured that an optimal policy can be defined in terms of a threshold probability P* such that site 1 is searched if and only if p ≥ P*. We show this conjecture to be correct (i) when α1 = α2 and C1 = C2, (ii) for general Ci when the overlook probabilities α, are small, and (iii) for general αi and Ci for a large range of transition laws for the movement. We also derive some properties of the optimal policy for the problem on n sites in the no-overlook case and for the case where each site has the same αi, and Ci.

Part Selection From a Federated Catalog

1995 ◽  
Author(s):  
Ling Jiang ◽  
Don R. Brown ◽  
Kuo-Yen Hwang
Keyword(s):  
Experimental System ◽  
Data Retrieval ◽  
Excessive Amount ◽  
Search Problem ◽  
Selection System ◽  
Optimal Search ◽  
Data Problem ◽  
Key Issues ◽  
Part Selection

Abstract This paper discusses issues related to a network-based catalog part selection system. Some of the key issues are: the optimal search problem, the burden imposed on the server of a network-based catalog or the time spent in data retrieval, identical parts in different vendor catalogs, and the excessive amount of data in a database of component information. The paper addresses the problem of network “burden,” the problem of identical parts, and the excessive data problem. The authors employ a “Configuration-decomposition” strategy in the approach to the excessive data problem. As an example of applying this approach, the implementation of the authors’ experimental system for part selection is discussed.

scholarly journals Informational Complementarity

2020 ◽  
Vol 66 (8) ◽  
pp. 3699-3716
Author(s):  
T. Tony Ke ◽  
Song Lin
Keyword(s):  
Search Strategy ◽  
Equilibrium Price ◽  
Lower Price ◽  
Search Problem ◽  
Product Attributes ◽  
Optimal Search ◽  
Complementarity Effect ◽  
Wide Range ◽  
Search For Information

Many products have similar or common attributes and are thus correlated. We show that, when these attributes are uncertain for consumers, a complementarity effect can arise among competing products in the sense that the lower price of one product may increase the demands for the others. This effect occurs when consumers sequentially search for information about both common and idiosyncratic product attributes before purchase. We characterize the optimal search strategy for the correlated search problem, provide the conditions for the existence of the complementarity effect, and show that the effect is robust under a wide range of alternative assumptions. We further explore the implications of the effect for pricing. When firms compete in price, although product correlation may weaken differentiation between the firms, the complementarity effect owing to correlated search may raise equilibrium price and profit. This paper was accepted by Matthew Shum, marketing.

Optimal search for a randomly moving object

1986 ◽  
Vol 23 (3) ◽  
pp. 708-717 ◽  
Author(s):  
R. R. Weber
Keyword(s):  
Markov Process ◽  
Optimal Policy ◽  
Moving Object ◽  
The Other ◽  
Optimal Search ◽  
Expected Cost

It is desired to minimize the expected cost of finding an object which moves back and forth between two locations according to an unobservable Markov process. When the object is in location i (i = 1, 2) it resides there for a time which is exponentially distributed with parameter λ1 and then moves to the other location. The location of the object is not known and at each instant until it is found exactly one of the two locations must be searched. Searching location i for time δ costs ciδ and conditional on the object being in location i there is a probability αiδ + o(δ) that this search will find it. The probability that the object starts in location 1 is known to bé p1(0). The location to be searched at time t is to be chosen on the basis of the value of p1(t), the probability that the object is in location 1, given that it has not yet been discovered. We prove that there exists a threshold Π such that the optimal policy may be described as: search location 1 if and only if the probability that the object is in location 1 is greater than Π. Expressions for the threshold Π are given in terms of the parameters of the model.

An Optimal Search Problem

SIAM Review ◽  
1965 ◽  
Vol 7 (4) ◽  
pp. 562-562 ◽  
Author(s):  
Wallace Franck
Keyword(s):  
Search Problem ◽  
Optimal Search

Optimal search for a randomly moving object

1986 ◽  
Vol 23 (03) ◽  
pp. 708-717 ◽  
Author(s):  
R. R. Weber
Keyword(s):  
Markov Process ◽  
Optimal Policy ◽  
Moving Object ◽  
The Other ◽  
Optimal Search ◽  
Expected Cost

It is desired to minimize the expected cost of finding an object which moves back and forth between two locations according to an unobservable Markov process. When the object is in location i (i = 1, 2) it resides there for a time which is exponentially distributed with parameter λ1 and then moves to the other location. The location of the object is not known and at each instant until it is found exactly one of the two locations must be searched. Searching location i for time δ costs ciδ and conditional on the object being in location i there is a probability α i δ + o(δ) that this search will find it. The probability that the object starts in location 1 is known to bé p 1(0). The location to be searched at time t is to be chosen on the basis of the value of p 1(t), the probability that the object is in location 1, given that it has not yet been discovered. We prove that there exists a threshold Π such that the optimal policy may be described as: search location 1 if and only if the probability that the object is in location 1 is greater than Π. Expressions for the threshold Π are given in terms of the parameters of the model.

scholarly journals Transition probabilities in generalized quantum search Hamiltonian evolutions

2019 ◽  
Vol 17 (01) ◽  
pp. 2050006 ◽  
Author(s):  
Steven Gassner ◽  
Carlo Cafaro ◽  
Salvatore Capozziello
Keyword(s):  
Transition Probability ◽  
Success Probability ◽  
Search Time ◽  
Search Algorithms ◽  
Search Problem ◽  
Quantum Search ◽  
Optimal Search ◽  
Target State ◽  
Special Cases ◽  
Source State

A relevant problem in quantum computing concerns how fast a source state can be driven into a target state according to Schrödinger’s quantum mechanical evolution specified by a suitable driving Hamiltonian. In this paper, we study in detail the computational aspects necessary to calculate the transition probability from a source state to a target state in a continuous time quantum search problem defined by a multiparameter generalized time-independent Hamiltonian. In particular, quantifying the performance of a quantum search in terms of speed (minimum search time) and fidelity (maximum success probability), we consider a variety of special cases that emerge from the generalized Hamiltonian. In the context of optimal quantum search, we find it is possible to outperform, in terms of minimum search time, the well-known Farhi–Gutmann analog quantum search algorithm. In the context of nearly optimal quantum search, instead, we show it is possible to identify sub-optimal search algorithms capable of outperforming optimal search algorithms if only a sufficiently high success probability is sought. Finally, we briefly discuss the relevance of a tradeoff between speed and fidelity with emphasis on issues of both theoretical and practical importance to quantum information processing.

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