Finding the nucleolus of any n-person cooperative game by a single linear program

Puerto, Justo; Perea, Federico

doi:10.1016/j.cor.2013.03.011

Cited by 22 publications

(18 citation statements)

References 17 publications

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“…The nucleolus solution can be chosen to allocate the cost to each shipper. Computation of the nucleolus in general is NP-hard; it can be made somewhat more tractable by techniques introduced fairly recently [19,20,[24][25][26]. In any event, its computation could be done after the algorithm described above is completed and all subset cost estimates are available.…”

Section: Allocationmentioning

confidence: 99%

Sharing Loading Costs for Multi Compartment Vehicles

Hartman

2018

Games

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Supply chains for goods that must be kept cool-cold chains-are of increasing importance in world trade. The goods must be kept within well-defined temperature limits to preserve their quality. One technique for reducing logistics costs is to load cold items into multiple compartment vehicles (MCVs), which have several spaces within that can be set for different temperature ranges. These vehicles allow better consolidation of loads. However, constructing the optimal load is a difficult problem, requiring heuristics for solution. In addition, the cost determined must be allocated to the different items being shipped, most often with different owners who need to pay, and this should be done in a stable manner so that firms will continue to combine loads. We outline the basic structure of the MCV loading problem, and offer the view that the optimization and cost allocation problems must be solved together. Doing so presents the opportunity to solve the problem inductively, reducing the size of the feasible set using constraints generated inductively from the inductive construction of minimal balanced collections of subsets. These limits may help the heuristics find a good result faster than optimizing first and allocating later.

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Section: Allocationmentioning

confidence: 99%

Sharing Loading Costs for Multi Compartment Vehicles

Hartman

2018

Games

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“…Recently, Puerto and Perea (2013) develop an approach to compute the nucleolus by solving only one LP, though of much larger dimension than the LPs in the sequential approach. They also point out the computation may be affected by numerical precision issues and propose a procedure to avoid them.…”

Section: Computational Aspectsmentioning

confidence: 99%

Common Mistakes in Computing the Nucleolus

Guajardo

Jørnsten

2014

SSRN Journal

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Despite linear programming and duality have correctly been incorporated in algorithms to compute the nucleolus, we have found mistakes in how these have been used in a broad range of applications. Overlooking the fact that a linear program can have multiple optimal solutions and neglecting the relevance of duality appear to be crucial sources of mistakes in computing the nucleolus. We discuss these issues and illustrate them in mistaken examples collected from a variety of literature sources. The purpose of this note is to prevent these mistakes propagate longer by clarifying how linear programming and duality can be correctly used for computing the nucleolus.

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“…The computational complexity of Policy 5 increases exponentially with the number of entities O(2 n ). Policy 6 is the most complex policy, computed by solving a sequence of at most |N | number of linear programming (LP) problems of decreasing dimension [Maschler et al 1979] or a single large-scale LP problem with O(4 n ) constraints [Puerto and Perea 2013]. The complexity of Policy 7 is O(2 n ) due to two steps: (1) the calculation of LSP using Equation 9 involves iterating over the 2 n coalitions, and (2) a maximum of |N | operations are performed by the algorithm to compute LSN.…”

Section: Computational Complexitymentioning

confidence: 99%

Fairness and Incentive Considerations in Energy Apportionment Policies

Vergara

Nadjm‐Tehrani

Asplund

2016

ACM Trans. Model. Perform. Eval. Comput. Syst.

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The energy consumption of a system is determined by the system component usage patterns and interactions between the coexisting entities and resources. Energy accounting plays an essential role to reveal the contribution of each entity to the total consumption and for energy management. Unfortunately, energy accounting inherits the apportionment problem of accounting in general, which does not have a general single best solution. In this paper we leverage cooperative game theory commonly used in cost allocation problems to study the energy apportionment problem, i.e., the problem of prescribing the actual energy consumption of a system to the consuming entities (e.g., applications, processes or users of the system).We identify five relevant fairness properties for energy apportionment and present a detailed categorisation and analysis of eight previously proposed energy apportionment policies from different fields in computer and communication systems. In addition, we propose two novel energy apportionment policies based on cooperative game theory which provide strong fairness notion and a rich incentive structure. Our comparative analysis in terms of the identified five fairness properties as well as information requirement and computational complexity shows that there is a trade-off between fairness and the other evaluation criteria. We provide guidelines to select an energy apportionment policy depending on the purpose of the apportionment and the characteristics of the system.

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Finding the nucleolus of any n-person cooperative game by a single linear program

Cited by 22 publications

References 17 publications

Sharing Loading Costs for Multi Compartment Vehicles

Sharing Loading Costs for Multi Compartment Vehicles

Common Mistakes in Computing the Nucleolus

Fairness and Incentive Considerations in Energy Apportionment Policies

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