Affiliation:
1. Queen’s University Belfast, Northern Ireland, United Kingdom
2. The Hong Kong University of Science and Technology, Kowloon, Hong Kong
Abstract
In many commercial campaigns, we observe that there exists a tradeoff between the number of customers satisfied by the company and the profit gained. Merely satisfying as many customers as possible or maximizing the profit is not desirable. To this end, in this article, we propose a new problem called
k
-
<underline>S</underline>atisfiability <underline>A</underline>ssignment for <underline>M</underline>aximizing the <underline>P</underline>rofit
(
k
-SAMP), where
k
is a user parameter and a non-negative integer. Given a set
P
of products and a set
O
of customers,
k
-SAMP is to find an assignment between
P
and
O
such that at least
k
customers are satisfied in the assignment and the profit incurred by this assignment is maximized. Although we find that this problem is closely related to two classic computer science problems, namely maximum weight matching and maximum matching, the techniques developed for these classic problems cannot be adapted to our
k
-SAMP problem. In this work, we design a novel algorithm called
Adjust
for the
k
-SAMP problem. Given an assignment
A
,
Adjust
iteratively increases the profit of
A
by
adjusting
some appropriate matches in
A
while keeping at least
k
customers satisfied in
A
. We prove that
Adjust
returns a global optimum. Extensive experiments were conducted that verified the efficiency of
Adjust
.
Publisher
Association for Computing Machinery (ACM)
Cited by
8 articles.
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