The paper "The Price of Robustness" by Bertsimas and Sim (2004) addresses the issue of over-conservatism in robust optimization. It introduces a new robust approach to linear optimization problems where data uncertainty is present. The paper focuses on the zero-one knapsack problem, a discrete optimization problem where the goal is to maximize the total value of goods that can be loaded onto a cargo with weight restrictions. The weights of the items are uncertain and follow a symmetric distribution. The paper proposes a robust version of the knapsack problem that accounts for uncertainty in the weights. The robustness of the solution is controlled by a parameter, Gamma, which determines how much protection is provided against constraint violations. A higher Gamma value leads to a more robust solution, but at the cost of a lower objective function value. The robust knapsack problem is formulated as a mixed-integer linear program (MILP). The solution approach uses strong duality to transform the problem into a linear program, which can be solved efficiently. The paper also presents a case study where the robust knapsack problem is applied to maximize the total value of goods under a constraint on the probability of violating the weight limit. The results show that the robust approach reduces the "price of robustness," meaning it does not heavily penalize the objective function value while still protecting against constraint violations. The paper concludes that the proposed robust approach is effective in reducing the price of robustness, providing a balance between robustness and optimality. The results demonstrate that the robust knapsack formulation can achieve a desired level of protection against constraint violations while maintaining a high objective function value.The paper "The Price of Robustness" by Bertsimas and Sim (2004) addresses the issue of over-conservatism in robust optimization. It introduces a new robust approach to linear optimization problems where data uncertainty is present. The paper focuses on the zero-one knapsack problem, a discrete optimization problem where the goal is to maximize the total value of goods that can be loaded onto a cargo with weight restrictions. The weights of the items are uncertain and follow a symmetric distribution. The paper proposes a robust version of the knapsack problem that accounts for uncertainty in the weights. The robustness of the solution is controlled by a parameter, Gamma, which determines how much protection is provided against constraint violations. A higher Gamma value leads to a more robust solution, but at the cost of a lower objective function value. The robust knapsack problem is formulated as a mixed-integer linear program (MILP). The solution approach uses strong duality to transform the problem into a linear program, which can be solved efficiently. The paper also presents a case study where the robust knapsack problem is applied to maximize the total value of goods under a constraint on the probability of violating the weight limit. The results show that the robust approach reduces the "price of robustness," meaning it does not heavily penalize the objective function value while still protecting against constraint violations. The paper concludes that the proposed robust approach is effective in reducing the price of robustness, providing a balance between robustness and optimality. The results demonstrate that the robust knapsack formulation can achieve a desired level of protection against constraint violations while maintaining a high objective function value.