Vangelis F. Magirou

An algorithm for the multiprocessor assignment problem

An exhaustive search algorithm is presented for the assignment of tasks to processors in a distributed processing system so that the sum of execution and communication costs is minimized. The algorithm relies on an efficient lower bound generated by reducing the original task graph to a tree, for which the optimization problem is polynomially solvable. It is also pointed out that the problem is NP-complete even in the case of 3 processors.

Stockpiling under price uncertainty and storage capacity constraints

Abstract A model is presented for the operation of an agent whose responsibility is to purchase and perhaps stockpile sufficient quantities of a certain commodity in order to satisfy an exogenous constant demand per time period. This is the situation faced by a state agency which is responsible for the purchasing of oil products to satisfy the demand of a country in which demand for energy has stabilized at a certain level. An important feature of the model is that the price of the commodity is described by a stochastic process. This reflects the volatility of prices of oil products. Furthermore, the model takes storage capacity constraints explicitly into account, and thus can help to assess the optimal level of storage capacity expansion. The relevant stochastic dynamic programming equations are derived and solved for the least cost function, which turns out to be piecewise linear in the inventory level. The storage capacity enters only in the computation of the constant term of the value function. The solution of the dynamic programming equation leads also to the optimal purchasing strategy of agencies with different levels of flexibility in their policy: in the model, an agency can be allowed or not to resell from the stock and it can have finite or infinite storage capacity.

A Graph-Theoretic Approach to Default Logic

A network representation of propositional seminormal disjunction-free default theories is presented, leading to a graph-theoretic approach to their analysis. The problem of finding an extension is proved to be equivalent to that of determining a kernel for a corresponding graph, allowing stronger complexity results as well as new conditions for the existence of extensions.

On kernels, defaults and even graphs

Extensions in prerequisite‐free, disjunction‐free default theories have been shown to be in direct correspondence with kernels of directed graphs; hence default theories without odd cycles always have a “standard” kind of an extension. We show that, although all “standard” extensions can be enumerated explicitly, several other problems remain intractable for such theories: Telling whether a non‐standard extension exists, enumerating all extensions, and finding the minimal standard extension. We also present a new graph‐theoretic algorithm, based on vertex feedback sets, for enumerating all extensions of a general prerequisite‐free, disjunction‐free default theory (possibly with odd cycles). The algorithm empirically performs well for quite large theories.

On the optimal level of a small country's strategic petroleum reserve

Abstract Decisions relating to a countrys strategic petroleum reserve must take into account the level of risk inherent in its petroleum imports, the cost resulting from any shortfall in the import level, the cost of storage, and finally the effects of stockpiling transactions on the sensitive spot oil markets. Of course, small countries need not take into account their effect on the global market, a fact that drastically simplifies their decision problem. We present such a simple decision model for a small countrys petroleum reserve which in addition to the above factors take into account the uncertainty of the countrys refining capacity. A complete analytical treatment is feasible for this model, and a specific numerical example is presented for the case of Greece.

A Lagrangian relaxation algorithm for sparse quadratic assignment problems

The Task Assignment Problem (TAP) arises in distributed computing environments and is a relaxed version of the Quadratic Assignment Problem (QAP). In this paper we present a new approach to the QAP which relies on the relationship between the two problems. First, by using the TAP, Lagrangian relaxation lower bounds are obtained for QAPs whose underlying flow graph is a k-tree, a generalization of ordinary trees. Second, for QAPs on arbitrary flow graphs the TAP solution is combined with the well-known Gilmore-Lawler procedure to get an improved bound. Methods to speed-up the branch and bound search are presented, based on the sequence in which the machines are examined and on the use of the linear assignment problem. Finally, we report on our computational results.

Switching away from oil: A game-theoretic approach

Abstract The reluctance of many national administrations to undertake extensive energy conservation and fuel switching programmes can be viewed as yet another occurrence of the Prisoners Dilemma paradigm of the Theory of Games. This is demonstrated through the analysis of a simple non-zero sum, non-cooperative game describing the process of national decision making with respect to energy saving and fuel switching programmes.

Problem Decomposition in Distributed Problem-Solving Systems

Distributed Problem Solving (DPS) is defined as the cooperative solution of problems by a decentralized and loosely coupled collection of problem solvers (agents), each of them knowing how to execute only some of the necessary tasks. This approach considers the problem-solving process as occurring in three phases: problem decomposition, subproblem solution, and answer synthesis. In the problem decomposition phase, one has to determine which tasks will be executed by each agent and when. One of the key research questions in the problem decomposition process is how to decompose a problem in order to minimize the cost of resources needed for its solution. In this article, we construct mathematical programming models in order to describe the decomposition process under the above criterion, study its complexity, and present exact and heuristic algorithms for its solution. Our work was motivated by the operation of an actual system that can be considered as a distributed problem solver for the assessment of irrigation projects design.

On the optimal allocation of grants to energy conservation investments

A criterion is presented for the allocation of grants by a state agency to energy conservation investments which maximizes the expected value of the resulting energy savings, subject to a constraint on the total expenditure for these grants. The allocation formula that follows from the application of the above criterion has certain properties that do not depend on the precise value of the relevant parameters and which are a desirable feature of any grant allocation scheme.

On certain optimal gas storage policies

A gas distribution company must satisfy at every instant of time an exogenous demand. In order to meet the peak demand in the most economic way, it can resort to storage and peak shaving techniques. For the case of a local distribution company linked to a national gas grid through a connection of bounded transmission capacity, we derive a schedule of drawing gas from the national grid that minimizes the storage capacity required under the assumption of deterministic demand. The storage minimizing schedule is derived through both elementary and optimal control methods. An extension is possible for the case of stochastic demand.