Markovian networks in labour markets

In labour theory, equilibrium is described in terms of mean variables, which is limited and can be misleading. In this article, we model the labour market as a closed Markovian network and find the steady state distribution of unemployment and advertised vacancies. We determine the stochastic equilibrium distribution for two different types of matching functions and allow for both unemployed and on the job search. In general cases, where probabilities cannot be analytically computed, we find restrictions that must hold for all matching processes. Our modelling is applicable to most economic markets with frictions.     

The management of high seas fisheries

The intergovernmental United Nations Conference on Highly Migratory and Straddling Stocks, initiated in 1993 and finished in 1995, addressed the conservation and management of fishery resources located both within the coastal state 200 mile Exclusive Economic Zone (EEZ) and the adjacent high seas. These types of marine resources continue to be a source for international conflicts and debates. The original United Nations Law of the Sea of 1982 failed to address transboundary fisheries in a proper way. In particular, the agreement did not recognize the emergence of the complicated straddling stock issue. In the new United Nations Law of the Sea agreement of 1995, a consensus was reached that the management of the straddling and highly migratory fish stocks should be carried out through regional fisheries management organizations. We present a review of the straddling stock issues in the international agreement emerging from the negotiations within the United Nations. The review is contrasted with and clarified by game theoretic analyses. We also discuss one international fishery exemplifying the case, the Norwegian springspawning herring. The main conclusion is that the local problems, faced during the stage of setting up regional fisheries organizations for the management of straddling and highly migratory fish stocks, are expected to be much more complicated and difficult to solve as compared to the cases of shared fish stocks. In the current paper, we present two reasons for this increased complexity. The first is the larger number of players as compared to the case of shared fish stocks and the second is the possibility of new members entering the regional fisheries organizations.     

Mid-term bio-economic optimization of multi-species fisheries

In this paper, we analyze the dynamics of a multi-species fisheries system in the presence of harvesting. We solve the problem of finding the optimal harvesting strategy for a mid-term horizon with a fixed final stock of each species, while maximizing the expected present value of total revenues. The problem is formulated as an optimal control problem. For its solution, we combine techniques derived from Pontryagin’s Maximum Principle, cyclic coordinate descent and the shooting method. The algorithm we develop can solve problems both with inter-species competition and with predator–prey behaviors. Several numerical examples are presented to illustrate the different possibilities of the method and a study of the dependence of the behavior on some parameters is performed.     

A model of rational equilibrium in quota-regulated multiple-species fisheries

This paper derives rational ecological–economic equilibrium outcomes—capital and variable input allocations, harvests, discards, revenue, costs, and stock abundances—in a spatially heterogeneous, multispecies fishery that is regulated with individual fishing quotas (IFQs). The production setting is decentralized; a manager chooses species-specific, seasonal, and spatially nondelineated quotas. Industry controls all aspects of harvesting operations. We present a solution concept and computational algorithm to solve for equilibrium harvests, discards, and profits across species, space, and time (within the regulatory cycle). The rational equilibrium mapping that we derive, used recursively, can be used to implement management-preferred bioeconomic outcomes. The model offers an essential IFQ regulation-to-outcome mapping that enables more precise implementation of management goals in multiple-species and heterogeneous fishery settings. Recommendations for Resource Managers Knowing where and when individual tradeable fishing quotas will be utilized across heterogeneous space and time in multiple-species fisheries is essential for effective fisheries management. Ad hoc models, while simple, contribute to “implementation uncertainty” whereby predicted mortality, discards, cost, and rent outcomes across fish species, space, and time are poorly matched to the realized outcomes that are implemented by resource users. A model of rational equilibrium mortality, discards, costs, and rent across space and time offers and powerful tool to improve the management of quota-regulated fisheries.     

Optimization of power production and costs in microgrids

This paper proposes a mathematical formulation for energy management in a connected microgrid. The aim is determining the optimal operating strategy for energy storage, to fulfil a time-varying energy demand and operational constraints while achieving a tradeoff between microgrid running costs and energy storage system life. The microgrid is composed by various renewable power production plants, storage devices and controllable loads, and has the ability to increase energy efficiency and reduce costs for energy purchasing from the main grid. The problem is formulated as a mixed-integer linear optimization problem. The optimization is aimed at minimizing the overall cost function of the system while satisfying the customer demand and safety of the electrical network. A case study of an existing microgrid is investigated: the microgrid consists of a photovoltaic and a hydroelectric power plant, a battery storage, an office building and an industrial facility. The optimization problem is solved in an efficient way by using commercial software. Simulation results show the feasibility and the effectiveness of the proposed approach to satisfy the load and reduce total costs.     

Joint insurance and capitalization costs

This paper studies the underpinnings of three related issues that arise in joint insurance. These are: capitalization, premium payments and relevance (or irrelevance) of insolvency. Principally, a dynamical model is constructed and investigated in terms of the impact of the policies a joint insurance firm may follow. A discussion relating to agency costs and re-capitalization in joint insurance, as well as a specific case are treated in detail.     

Average search and update costs in skip lists

Skip lists, introduced by Pugh, provide an alternative to search trees, although a precise analysis of their behaviour had been elusive. The exact value of the expected cost for the search of themth element in a skip list ofn elements is derived first in terms of previously studied functions, and secondly as an asymptotic expression. The latter suggests that Pugh's upper bound of the expected search cost is fairly tight for the interesting cases. Assuming a uniform query distribution, the exact and an asymptotic value of the average (over allm) expected search cost in a skip list ofn elements is also derived. Finally, all insert and delete costs are obtained.This research was supported in part by the Natural Science and Engineering Research Council of Canada under grant No. A-8237, the Information Technology Research Centre of Ontario, and FON-DECYT (Chile) under grant 91-1252.     

Minimizing earliness and tardiness costs in stochastic scheduling

We address the single-machine stochastic scheduling problem with an objective of minimizing total expected earliness and tardiness costs, assuming that processing times follow normal distributions and due dates are decisions. We develop a branch and bound algorithm to find optimal solutions to this problem and report the results of computational experiments. We also test some heuristic procedures and find that surprisingly good performance can be achieved by a list schedule followed by an adjacent pairwise interchange procedure.     

Search costs in quadtrees and singularity perturbation asymptotics

Quadtrees constitute a classical data structure for storing and accessing collections of points in multidimensional space. It is proved that, in any dimension, the cost of a random search in a randomly grown quadtree has logarithmic mean and variance and is asymptotically ditributed as a normal variable. The limit distribution property extends to quadtrees of all dimensions a result only known so far to hold for binary search trees. The analysis is based on a technique of singularity perturbation that appears to be of some generality. For quadtrees, this technique is applied to linear differential equations satisfied by interventing bivariate generating functions This work was partly supported by the ESPRIT Basic Research Action No. 7141 (ALCOM II).     

Transaction costs and efficiency of portfolio strategies

Some recent results for frictionless economies show that popular dynamic portfolio strategies such as stop-loss and lock-in are inefficient. I.e for each of these strategies there exists an alternative portfolio strategy that gives the same final payoff distribution at lower initial costs. However, the alternative strategies require considerably more active trading than the simple strategies. The results rely heavily on the assumption of no transaction costs. Under this assumption the initial investment required is a linear function of the prices of the contingent claims that build the final payoff distribution. In this paper we demonstrate that, even for modest levels of transaction costs, the efficient strategies are more costly than the simple strategies, i.e. a strategy that replicates the final payoff distribution of an efficient strategy is excessively costly due to the transaction costs and the heavy trading involved. Since the initial investment is no longer a linear function of the contingent claims, the optimization problems to find the most efficient strategy are complicated combinatorial optimization problems which can only be solved for trees with a small number of steps. In a world without transaction costs, options are redundant instruments, since all payoff distributions can be replicated by trading in stocks and bonds. In the second half of this paper we show that the use of options in a world with transaction costs enables investors to realize final value distributions at lower initial costs than would be possible with trades in stocks an bonds only. Hence, although in theory options do not give rise to other portfolio strategies, they do in a more restrictive setting with transaction costs.     

Fuzzy costs in quadratic programming problems

Although quadratic programming problems are a special class of nonlinear programming, they can also be seen as general linear programming problems. These quadratic problems are of the utmost importance in an increasing variety of practical fields. As, in addition, ambiguity and vagueness are natural and ever-present in real-life situations requiring operative solutions, it makes perfect sense to address them using fuzzy concepts formulated as quadratic programming problems with uncertainty, i.e., as Fuzzy Quadratic Programming problems. This work proposes two novel fuzzy-sets-based methods to solve a particular class of Fuzzy Quadratic Programming problems which have vagueness coefficients in the objective function. Moreover, two other linear approaches are extended to solve the quadratic case. Finally, it is shown that the solutions reached from the extended approaches may be obtained from two proposed parametric multiobjective approaches.     

Optimization of moves and measurements in networks with stochastic costs

Summary The optimal routing of a decision maker in a network is considered. Some branches of the network can take on a finite or an infinite cost with a given probability. The costs of the stochastic branches which depart from a node become known to the decision maker whenever he visits the node. Without visiting the node, information on a stochastic branch can also be acquired under the payment of an observation cost.The decision rule which gives the optimal moves and measurements can be found by introducing an augmented graph, by means of which position in the network and information state can be considered from a unified point of view. A dynamic programming approach is presented and simplified methods for special networks are discussed.

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Zusammenfassung Es wird der optimale Weg eines Entscheidungsträgers durch ein Netz betrachtet. Einige Zweige des Netzes können mit einer bestimmten Wahrscheinlichkeit endliche oder unendliche Kosten annehmen. Die Kosten der stochastischen Zweige, die von einer Ecke abzweigen, werden dem Entscheidungsträger beim Erreichen der Ecke jeweils bekannt. Ohne dieses Erreichen kann die Information über einen Zweig auch durch die Einzahlung von Messungskosten erworben werden.Die Entscheidungsregel, die die optimalen Bewegungen und Messungen ergibt, kann durch die Einführung eines vergrößerten Graphen gefunden werden, der die Betrachtung der Lage im Netz und des Informationszustandes von einem gemeinsamen Gesichtspunkt ermöglicht. Es werden eine auf dem Dynamischen Programmieren aufbauende Lösung und vereinfachte Methoden für Spezialfälle entwickelt und diskutiert.

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This work has been supported by the National Council of Research of Italy (C.N.R.).     

Take back costs and product durability

Extended Producer Responsibility (EPR) initiatives may require a manufacturer to be responsible in the future for taking back the products it produces today. A ramification of EPR is that take back costs may influence firms’ decisions regarding product durability. In the absence of EPR, prior literature has shown that a firm may intentionally lower durability, yielding planned obsolescence. We use a two period model to examine the impact of take back costs on a manufacturer’s product durability and pricing decisions, under both selling and leasing scenarios. We show that compared to selling, leasing provides a greater incentive to raise durability, thus extending a classic insight to a setting with product take backs. Interestingly, we also show that it is possible for the optimal product durability to decrease if the stipulated take back fraction increases. In such situations, were the take back fraction tied to durability rather than a fixed fraction, we demonstrate durability can increase. We explore the impact of take backs on profits and surplus by alternatively considering products for which take back costs are either increasing or decreasing functions of durability. When increasing durability implies higher take back costs, our results demonstrate that leasing can increase durability, profits, and surplus significantly compared to selling. In contrast, when increasing durability implies a lower take back cost, there is a built-in incentive for the firm to increase durability, which can make selling more efficient (i.e., surplus enhancing) than leasing.     

Entropy control costs and entropic equilibria

Strategic errors may occur because of player trembles or because of noise in the communication channels. Suppose that the probability distribution of potential errors can be influenced at a cost proportional to the entropy reduction. This modified strategic-form game involves the choice of a probability distribution over strategies and a probability distribution over potential errors with weight on the latter. Each modified game has a Nash Equilibrium (NE), and any limit as 0 is called an -entropic equilibrium, -entropic equilibria always exist and constitute a subset of trembling-hand-perfect equilibria, but otherwise -EE are independent of other refinements such as Proper NE.The author is grateful to Larry Samuelson and an anonymous referee for helpful comments, but retains sole responsibility for any error.     

Demand dispersion and logistics costs in one-to-many distribution systems

When an organization decides on which groups of consumers it should target, the locations of these target consumers often play a role. Methods from the field of market segmentation are able to identify target groups with high benefit levels, but the expected costs of supplying products to the target groups are less well understood. These costs can play a large role if the locations of the customers, the demand locations, are geographically widely dispersed. This paper focuses on one-to-many distribution systems in which a central facility serves all demand points. We derive accurate logistics cost estimates from the dispersion of demand points for such systems, enabling a comparison of the expected logistics costs of different candidate target groups. The most accurate measure combines the average distance from the demand locations to a central location and the mutual distances between neighboring demand locations. The average of the distances between all pairs of locations forms a good alternative measure.