The traveling purchaser problem (TPP) is an
NP-hard problem studied in
theoretical computer science
computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory.
It is difficult to circumscribe the ...
. Given a list of marketplaces, the cost of travelling between different marketplaces, and a list of available goods together with the price of each such good at each marketplace, the task is to find, for a given list of articles, the route with the minimum combined cost of purchases and traveling. The
traveling salesman problem
The travelling salesman problem (also called the travelling salesperson problem or TSP) asks the following question: "Given a list of cities and the distances between each pair of cities, what is the shortest possible route that visits each cit ...
(TSP) is a
special case
In logic, especially as applied in mathematics, concept is a special case or specialization of concept precisely if every instance of is also an instance of but not vice versa, or equivalently, if is a generalization of . A limiting case i ...
of this problem.
Relation to traveling salesman problem (TSP)
The problem can be seen as a generalization of the traveling salesman problem, which can be viewed as the special case of TPP where each article is available at one market only and each market sells only one item. Since TSP is NP-hard, TPP is NP-hard.
Solving TPP
Approaches for solving the traveling purchaser problem include
dynamic programming
Dynamic programming is both a mathematical optimization method and a computer programming method. The method was developed by Richard Bellman in the 1950s and has found applications in numerous fields, from aerospace engineering to economics. ...
and
tabu search Tabu search is a metaheuristic search method employing local search methods used for mathematical optimization. It was created by Fred W. Glover in 1986
and formalized in 1989.
Local (neighborhood) searches take a potential solution to a pro ...
algorithms.
A Tabu Search Approach for solving the Travelling Purchase Problem
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See also
* Vehicle routing problem
The vehicle routing problem (VRP) is a combinatorial optimization and integer programming problem which asks "What is the optimal set of routes for a fleet of vehicles to traverse in order to deliver to a given set of customers?" It generalises ...
References
NP-complete problems
Travelling salesman problem