The Travelling Purchaser Problem with Budget Constraint

  IJMTT-book-cover
 
International Journal of Mathematics Trends and Technology (IJMTT)
 
© 2020 by IJMTT Journal
Volume-66 Issue-2
Year of Publication : 2020
Authors : Sumathi P, Viswanatha Reddy G, Purusotham Singamsetty
  10.14445/22315373/IJMTT-V66I2P515

MLA

MLA Style:Sumathi P, Viswanatha Reddy G, Purusotham Singamsetty  "The Travelling Purchaser Problem with Budget Constraint" International Journal of Mathematics Trends and Technology 66.2 (2020):126-137. 

APA Style: Sumathi P, Viswanatha Reddy G, Purusotham Singamsetty(2020). The Travelling Purchaser Problem with Budget Constraint International Journal of Mathematics Trends and Technology, 126-137.

Abstract
The traveling purchaser problem (TPP) is an NP-hard problem in the family of combinatorial optimization. The purchaser needs to buy several items with variable demands which are available at different marketplaces. The cost of travelling between different marketplaces and a list of available items together with the price of such item at each marketplace is known. The objective of the TPP is to design an optimal tour such that the purchaser tour starts and ends at a home point/ domicile point, purchases all the required items on travelling through a subset of marketplaces exactly once and which satisfy the budget constraint i.e. the total purchasing cost of the items should not surpass the pre-defined budget threshold. The tour may not necessary contain all the marketplaces. This problem finds interesting applications in machine scheduling, transportation logistics among others. The problem is nicely designed with zero-one integer programming. In order to find optimum solution for this problem, an exact algorithm called Lexi-search algorithm is proposed, it searches feasible solutions systematically and with effective bounding and backtracking strategies quickly moves towards the optimal solution.

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Keywords
Travelling purchaser problem, Lexi-search Algorithm, Budget threshold, Backtracking.