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