This study examines a resource-sharing problem involving multiple parties that agree to use a set of capacities together. We start with modeling the whole problem as a mathematical program, where all parties are required to exchange information to obtain the optimal objective function value. This information bears private data from each party in terms of coefficients used in the mathematical program. Moreover, the parties also consider the individual optimal solutions as private. In this setting, the concern for the parties is the privacy of their data and their optimal allocations. We propose a two-step approach to meet the privacy requirements of the parties. In the first step, we obtain a reformulated model that is amenable to a decomposition scheme. Although this scheme eliminates almost all data exchanges, it does not provide a formal privacy guarantee. In the second step, we provide this guarantee with a locally differentially private algorithm, which does not need a trusted aggregator, at the expense of deviating slightly from the optimality. We provide bounds on this deviation and discuss the consequences of these theoretical results. We also propose a novel modification to increase the efficiency of the algorithm in terms of reducing the theoretical optimality gap. The study ends with a numerical experiment on a planning problem that demonstrates an application of the proposed approach. As we work with a general linear optimization model, our analysis and discussion can be used in different application areas including production planning, logistics, and revenue management.

翻译：本研究探讨了多方同意共同使用一组容量的资源共享问题。我们首先将整个问题建模为一个数学规划，其中所有各方需要交换信息以获得最优目标函数值。这些信息包含各方在数学规划中使用的系数形式的私有数据。此外，各方还将各自的最优解视为私有信息。在此情境下，各方关注的是其数据及最优分配的隐私保护。我们提出了一种两步方法以满足各方的隐私需求。第一步，我们获得了适用于分解方案的重构模型。尽管该方案几乎消除了所有数据交换，但并未提供形式化的隐私保证。第二步，我们通过一种无需可信聚合器的本地差分隐私算法提供了这种保证，但以略微偏离最优性为代价。我们给出了这种偏离的界限，并讨论了这些理论结果的影响。我们还提出了一种改进算法效率的新颖修正方法，以缩小理论最优性差距。研究最后以一个规划问题的数值实验展示了所提方法的应用。由于我们处理的是通用线性优化模型，我们的分析与讨论可应用于包括生产规划、物流和收益管理在内的不同领域。