Abstract We study a problem in which independent project managers cooperate to generate additional revenue by reallocating their resources. This additional revenue equals the increase in the direct return of a project minus the resource transfer cost. For each project, its direct return is closely related to its duration, which is mainly determined by the amount of resources available. In practice, the relationship between direct return and resources can be very complex. We study the situation that all projects use one same type of continuously divisible renewable resource and require some other types of discrete renewable resources. The activity processing rate of a project depends on its continuous resource and can be linear, strictly concave, or convex. The direct return of a project is linear over time. Based on results reported in the literature, we first show that it is not uncommon for the direct return of a project to be concave in relation to the amount of resources. Then, we formulate the resource transfer problem (RTP) as a convex programming problem and derive interesting properties. Furthermore, we design a revenue sharing scheme, which is in the core of a corresponding cooperative game. Finally, we conduct numerical experiments to show the value of cooperation, examine the efficiency of the proposed additional revenue sharing scheme, and evaluate the effects of the transfer cost, the unit time reward/penalty, and the amount of initial resource.

中文翻译：

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项目间资源转移的收益分享

摘要 我们研究了一个问题，在这个问题中，独立的项目经理通过重新分配他们的资源来合作以产生额外的收入。这种额外收入等于项目直接回报的增加减去资源转移成本。对于每个项目，其直接收益与其工期密切相关，主要由可用资源量决定。在实践中，直接回报和资源之间的关系可能非常复杂。我们研究了所有项目都使用一种相同类型的连续可分割可再生资源并需要一些其他类型的离散可再生资源的情况。项目的活动处理率取决于其连续资源，可以是线性的、严格的凹面或凸面。一个项目的直接回报随着时间的推移是线性的。根据文献报道的结果，我们首先表明，一个项目的直接回报相对于资源量呈凹形的情况并不少见。然后，我们将资源转移问题 (RTP) 公式化为凸规划问题并推导出有趣的属性。此外，我们设计了一个收益分享方案，这是相应合作游戏的核心。最后，我们进行了数值实验来展示合作的价值，检查所提出的额外收益分享方案的效率，并评估转移成本、单位时间奖励/惩罚和初始资源量的影响。我们将资源转移问题 (RTP) 表述为凸规划问题，并推导出有趣的属性。此外，我们设计了一个收益分享方案，这是相应合作游戏的核心。最后，我们进行了数值实验来展示合作的价值，检查所提出的额外收益分享方案的效率，并评估转移成本、单位时间奖励/惩罚和初始资源量的影响。我们将资源转移问题 (RTP) 表述为凸规划问题，并推导出有趣的属性。此外，我们设计了一个收益分享方案，这是相应合作游戏的核心。最后，我们进行了数值实验来展示合作的价值，检查所提出的额外收益分享方案的效率，并评估转移成本、单位时间奖励/惩罚和初始资源量的影响。