Survey Design

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 P’j customers asked about each product j.

Question needed to be solved

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

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)

•

Left node means the customer

, right node means the product

We extend to the corresponding Flow network.

Ci,Ci’The number or products asking to customers

Pj, P’jThe number of the customers asked about each product

customers Products

0,1

0 means customer won’t receive the question from this product he bought1 means customer will receive the question from this product he bought

• The capacity is 0 or 1• I use the ford-Fulkers

on 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..

0 or 1

E1 minus 1

E2 minus 1