Sharing delay costs in stochastic scheduling problems with delays

Abstract

An important problem in project management is determining ways to distribute amongst activities the costs that are incurred when a project is delayed because some activities end later than expected. In this study, we address this problem in stochastic projects, where the durations of activities are unknown but their corresponding probability distributions are known. We propose and characterise an allocation rule based on the Shapley value, illustrate its behaviour by using examples, and analyse features of its calculation for large problems.

ProjectManagement: an R Package for Managing Projects

“…Next, we introduce a generalization of the model and the rules described above. It follows the results in Gonçalves-Dosantos et al (2020a). If instead of x 0 i , the planned duration of activity i ∈ N , we consider the non-negative random variable X 0 i describing the duration of i, we can define a stochastic project SP as tuple SP = G, X 0 .…”

Anonymity in sharing the revenues from broadcasting sports leagues

“…Other well known instances to which the literature has paid attention are: airport problems (e.g., Littlechild and Owen, 1973), bankruptcy problems (e.g., O'Neill, 1982;Thomson, 2019a), telecommunications problems (e.g., van den Nouweland et al, 1996), minimum cost spanning tree problems (e.g., Bergantiños and Vidal-Puga, 2021), transport problems (e.g., Algaba et al 2019;Estañ et al 2021), inventory problems (e.g., Guardiola et al, 2021), liability problems with rooted tree networks (e.g. Oishi et al, 2023), knapsack problems (e.g., Arribillaga and Bergantiños 2023), pooling games (Schlicher et al 2020), m-attribute games (Özen et al, 2022), urban consolidation centers (Hezarkhani et al, 2019), and scheduling problems with delays (Gonçalves-Dosantos et al, 2020) .…”