Balancing the profit and capacity under uncertainties: a target‐based distributionally robust knapsack problem

Abstract

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.

Study of Enterprise Resource Optimization Scheme from the Perspective of Knapsack Problems

“…Rooderkerk and van Heerde [43] analyzed product assortment optimization for retailers from the 0-1 knapsack problem perspective. A target-based distributionally robust knapsack problem was proposed by considering both uncertain profit and capacity, as well as the impact of a given target for profit [44].…”