As a well-developed optimization problem, the knapsack problem has been broadly applied in various fields involving resource allocations, especially production planning. In this paper, we propose a target-based distributionally robust knapsack problem (TDRKP), considering both uncertain profit and capacity, as well as the impact of a given target for profit. Based on a shortfall risk measure and piecewise utility function, the violation risk of the target is investigated. To solve the model efficiently, TDRKP is reformulated into computationally tractable form as a second-order conic program. Through a series of numerical experiments, we verify that the proposed TDRKP formulation performs better than both the sample average approximation model and the minimizing violation probabilities model.
We study a two-stage resource pooling problem with multiple resources and customers. The central decision-maker decides the capacity level of the resources within a total budget before the realization of uncertain demand. Then, the fulfillment policy is determined by individual service-level requirements. We use a robust satisficing framework to formulate the problem and allow ambiguity in the distribution of demand. Moreover, we introduce a new utility-based probability distance allowing the model to be solved exactly using a column and constraint generation algorithm. We also provide a more efficient solution method for some special cases. Finally, we conduct experiments for a process flexibility problem, which is an example of the resource pooling problem. We show the advantage of our model over some benchmark approaches, and show the impact of the flexibility structure and correlation between demands.
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