Survey Design

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Survey Design
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The problem

• One company has the certain numbers of products
  to sell to the customers.
• Each customer will receive questions about the
  product he or she has purchased, the number of
  the questions for each customers are between Ci
  and Ci
• For each product j, there must be the between Pj
  and Pj customers asked about each product j.

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Question needed to be solved

• The company would like to collect maximum number
  of the questionnaires from the customers about
  the products.

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Bipartite Matching

• To solve this problem , we need to use Bipartite
  matching with the maximum flow to solve the
  problem (The maximum-flow problem means given a
  flow network , find the a flow of maximum
  possible value).
• (finding the flows of maximum possible value
  satisfy this problem)

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Left node means the customer
, right node means the product

We extend to the corresponding Flow network.
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0,1
Products
customers
Ci,Ci The number or products asking to customers
Pj, Pj The number of the customers asked about
each product
0 means customer wont receive the question from
this product he bought 1 means customer will
receive the question from this product he bought
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• The capacity is 0 or 1
• I use the ford-Fulkerson algorithm (minus the
  minimum flow 1)and see if e1 is 0 and is 0
• If e1 is 0 , we choose the next edge from S..

E2 minus 1
0 or 1
E1 minus 1