This study exposes a critical weakness of the (0-1) knapsack dynamic programming approach, widely used for optimal allocation\nof resources. The (0-1) knapsack dynamic programming approach could waste resources on insignificant improvements and\nprevent the more efficient use of the resources to achieve maximum benefit. Despite the numerous extensive studies, this critical\nshortcoming of the classical formulation has been overlooked. The main reason is that the standard (0-1) knapsack dynamic\nprogramming approach has been devised to maximise the benefit derived from items filling a space with no intrinsic value.\nWhile this is an appropriate formulation for packing and cargo loading problems, in applications involving capital budgeting,\nthis formulation is deeply flawed. The reason is that budgets do have intrinsic value and their efficient utilisation is just as\nimportant as the maximisation of the benefit derived from the budget allocation.\nAccordingly, a new formulation of the (0-1) knapsack resource allocation model is proposed where the weighted sum of the\nbenefit and the remaining budget is maximised instead of the total benefit. The proposed optimisation model produces solutions\nsuperior to both ââ?¬â?? the standard (0-1) dynamic programming approach and the cost-benefit approach.\nOn the basis of common parallel-series systems, the paper also demonstrates that because of synergistic effects, sets including\nthe same number of identical options could remove different amount of total risk. The existence of synergistic effects does\nnot permit the application of the (0-1) dynamic programming approach. In this case, specific methods for optimal resource\nallocation should be applied. Accordingly, the paper formulates and proves a theorem stating that the maximum amount of\nremoved total risk from operations and systems with parallel-series logical arrangement is achieved by using preferentially\nthe available budget on improving the reliability of operations/components belonging to the same parallel branch. Improving\nthe reliability of randomly selected operations/components not forming a parallel branch leads to a sub-optimal risk reduction.\nThe theorem is a solid basis for achieving a significant risk reduction for systems and processes with parallel-series logical\narrangement.
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