Testing integer knapsacks for feasibility

Article Abstract:

A new method for determining whether there are nonnegative integers x1, x2,....,xn, satisfying a1x1 + a2x2 + ... + anxn = b, where a1 < a2 < ... < an and b are nonnegative integers, is presented. Its worst case time complexity is O(a superscript 2; subscript 1) + n and its space complexity is O(a1). One important feature of the new algorithm is that its feasibility can be tested for an additional right hand side in O(1) time, i.e. the work requiring O(a superscript 2; subscript 1 + n) time is independent of b.

Models, Integer programming, Dynamic programming

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New polynomial bounds for matroidal knapsacks

Article Abstract:

The matroidal knapsack problem with the objective function of maximizing the weight basis for a given matroid under a knapsack constraint is considered. Specifically, a relaxation procedure for deriving an upper bound on the optimal value of the matroidal knapsack problem in polynomial time is introduced. The procedure is applicable to both the multiple choice knapsack and the capacitated minimal spanning tree problems.

Operations research, Research, Management science, Case studies, Relaxation methods (Mathematics)

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Heuristic method for a mixed capacitated arc routing problem: Aa refucse collection application

Article Abstract:

A new heuristic method that provides viable solutions for a mixed arc routing problem for household refuce collection on mixed graphs is presented. The results of the method indicate us to fix the service direction.

Portugal, Refuse systems, Solid Waste Collection, Methods, Analysis, Reports, Graphic methods, Sanitation services, Heuristic programming, Refuse collection

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