/
/
/
Application of Coordinate Transformation with Close-Form Exact Algorithm for Minimizing Maximum Processing Time in the Unbounded Knapsack Problem

Application of Coordinate Transformation With Close-Form Exact Algorithm for Minimizing Maximum Processing Time in the Unbounded Knapsack Problem

Original Research ArticleNov 12, 2018Vol. 5 No. 1 (2005)

Abstract

We address a variant of the unbounded knapsack problem (UKP) into which the processing time of each item is also put and considered, referred as MMPTUKP problem. The problem is a decision of allocating amount of n items such that the maximum processing time of the selected items is minimized and the total profit is gained as at least as determined without exceeding capacity of knapsack (budget). In this paper, we proposed the new modified exact algorithm for this problem, CTCFMMPTUKP algorithms. It applied the coordinate transformation with CFMMPTUKP algorithm, close-form exact algorithm. We present computational experiments with 4 different type of problems for which data were generated to validate our ideas and demonstrate the efficiency of the proposed algorithms. It can be concluded that, for most types of problems, the proposed CTCFMMPTUKP algorithms performs in term of solution time faster than the 5 other algorithms.

Keywords:  Linear programming, Simplex method, Integer linear programming, Branch and bound algorithm, Unbounded and bounded knapsack problem, Processing time.

Corresponding author: E-mail: chanin_sri@yahoo.com

How to Cite

Srisuwannapa*, C. ., & Chansethikul, P. . (2018). Application of Coordinate Transformation with Close-Form Exact Algorithm for Minimizing Maximum Processing Time in the Unbounded Knapsack Problem. CURRENT APPLIED SCIENCE AND TECHNOLOGY, 366-378.

References

  • P.toth (2000), Optimization engineering techniques for the exact solution of NP-hard combination optimization problem, European Journal of Operation Research, vol 125, pp. 222-238.
  • S. Martello, D. Psinger, P. Toth (1999), Dynamic programming and strong bounds for the 0-1 knapsack problem, Management Science, vol. 45, pp 414-424.
  • A. Freville, G. Plateau (1986), Heuristics and reduction methods for multiple constrains Linear Programming, European Journal of Operations Research, vol 24, pp. 206-215.
  • D. Psinger (1999), An exact algorithm for large multiple knapsack problem, European Journal of Operations Research, vol 114, pp. 528-541.
  • S. Martello, P. Toth (1981), A branch-and- bound algorithm for the zero-one knapsack problem, Discrete Applied Mathematics, vol 3, pp.275-288.

Author Information

Chanin Srisuwannapa*

Department of Applied Statistics, Faculty of Science, King Mongkut’s Institute of Technology Ladkrabang, Bangkok, Thailand

Peerayuth Chansethikul

Department of Industrial Engineering, Faculty of Engineering, Kasetsart University, Bangkok, Thailand

About this Article

Journal

Vol. 5 No. 1 (2005)

Type of Manuscript

Original Research Article

Keywords

Linear programming, Simplex method, Integer linear programming, Branch and bound algorithm, Unbounded and bounded knapsack problem, Processing time.

Published

12 November 2018