Resource allocation

This report discusses the problem of the allocation of resources: how should an organisation (such as MOD) invest bearing in mind the long term delay for the realization of investment strategies, and how might this apply in times of increasing budgetary constraints? After making certain simplifying assumptions, the Study Group constructed a prototype model based on the method of Optimal Control. This allows the decision maker to investigate the impact of particular investment strategies over a period of years, the impact being measured in terms of “quality” or “capability”. Interventions can be designed so that “quality” (Q) is maximized at a particular time, or so that the average quality over a given time interval is maximized. Both of these approaches are explored. This model shows reasonable behaviour when tested over a parameter set. It could be used as part of a systems approach to the defence budget as a whole, but the method itself is scalable to smaller (or larger) resourcing conundrums

Replica Placement on Bounded Treewidth Graphs

We consider the replica placement problem: given a graph with clients and nodes, place replicas on a minimum set of nodes to serve all the clients; each client is associated with a request and maximum distance that it can travel to get served and there is a maximum limit (capacity) on the amount of request a replica can serve. The problem falls under the general framework of capacitated set covering. It admits an O(\log n)-approximation and it is NP-hard to approximate within a factor of $o(\log n)$. We study the problem in terms of the treewidth $t$ of the graph and present an O(t)-approximation algorithm.Comment: An abridged version of this paper is to appear in the proceedings of WADS'1

A transaction-based method for allocation of transmission grid cost and losses

The problem of grid cost and losses allocation may be divided into independent subproblems: allocation of branch flow and losses to transactions, definition of these transactions and cost allocation to transactions. From this final allocation, the charges to participants in transactions may be made straightforwardly. A differential, slack-invariant method for the allocation of flow and losses to transactions that makes use of the AC load flow equation is presented here. The definition of transactions must be addressed using a non-discriminatory rule in pool systems. There are many possible options for this definition, and the choice made has great influence on the results. Cost allocation, on the other hand, may be made in different ways, as well. The paper presents an allocation process that addresses all these issues. Results for the IEEE-RTS96 test system are obtained and discussed.Publicad

On the Ramified Optimal Allocation Problem

This paper proposes an optimal allocation problem with ramified transport technology in a spatial economy. Ramified transportation is used to model the transport economy of scale in group transportation observed widely in both nature and efficiently designed transport systems of branching structures. The ramified allocation problem aims at finding an optimal allocation plan as well as an associated optimal allocation path to minimize overall cost of transporting commodity from factories to households. This problem differentiates itself from existing ramified transportation literature in that the distribution of production among factories is not fixed but endogenously determined as observed in many allocation practices. It's shown that due to the transport economy of scale in ramified transportation, each optimal allocation plan corresponds equivalently to an optimal assignment map from households to factories. This optimal assignment map provides a natural partition of both households and allocation paths. We develop methods of marginal transportation analysis and projectional analysis to study properties of optimal assignment maps. These properties are then related to the search for an optimal assignment map in the context of state matrix.Comment: 36 pages, 8 figure

Pareto-Optimal Allocation of Indivisible Goods with Connectivity Constraints

We study the problem of allocating indivisible items to agents with additive valuations, under the additional constraint that bundles must be connected in an underlying item graph. Previous work has considered the existence and complexity of fair allocations. We study the problem of finding an allocation that is Pareto-optimal. While it is easy to find an efficient allocation when the underlying graph is a path or a star, the problem is NP-hard for many other graph topologies, even for trees of bounded pathwidth or of maximum degree 3. We show that on a path, there are instances where no Pareto-optimal allocation satisfies envy-freeness up to one good, and that it is NP-hard to decide whether such an allocation exists, even for binary valuations. We also show that, for a path, it is NP-hard to find a Pareto-optimal allocation that satisfies maximin share, but show that a moving-knife algorithm can find such an allocation when agents have binary valuations that have a non-nested interval structure.Comment: 21 pages, full version of paper at AAAI-201

Fair task allocation in transportation

Task allocation problems have traditionally focused on cost optimization. However, more and more attention is being given to cases in which cost should not always be the sole or major consideration. In this paper we study a fair task allocation problem in transportation where an optimal allocation not only has low cost but more importantly, it distributes tasks as even as possible among heterogeneous participants who have different capacities and costs to execute tasks. To tackle this fair minimum cost allocation problem we analyze and solve it in two parts using two novel polynomial-time algorithms. We show that despite the new fairness criterion, the proposed algorithms can solve the fair minimum cost allocation problem optimally in polynomial time. In addition, we conduct an extensive set of experiments to investigate the trade-off between cost minimization and fairness. Our experimental results demonstrate the benefit of factoring fairness into task allocation. Among the majority of test instances, fairness comes with a very small price in terms of cost