Location problems on a sphere

This paper reviews recent developments in facility location with geodesic distances. Geodesic distances are becoming more important as industrial, defence and energy networks become progressively more global. Discussed are the minisum or Weber problem, the minimax or Rawls problem, and the maximin or obnoxious facility problem. These problems are basic to location theory on the plane; they become more complex on the sphere than on the plane because of the topological nature of the surface of a sphere. Extensions and variations are discussed.     

Rectangular input-output tables, multiplier analysis and entropy maximising principles: A new methodology

A new approach to input output multiplier methods relevant in situations using rectangular input output tables (situations where a sector product distinction can be made) is introduced. The method makes use of entropy maximising principles, using constraints expressing basic technologies of production and taking base year intersectoral transactions as prior values for the expected future values of those transactions. In contrast to existing rectangular input output multiplier models, the present approach requires just one set of input output coefficients (in particular, it does not require any ‘make’ matrix coefficients) and has an immediate flexibility to incorporate any further assumptions or information that may be available.     

A theory of formal conceptual definitions: developing theory-building measurement instruments

This study develops the need for formal conceptual definitions (sometimes called nominal definitions) and how to develop better measurement instruments for theory-building. It develops the underlying theory for ‘good’ formal conceptual definitions by defining terms, demonstrating that formal conceptual definitions are needed for all theory-building empirical research, explains how and why ‘good’ formal conceptual definitions are used to develop properties and their measures, and last, it logically explains that good formal conceptual definitions are necessary conditions for construct validity (content validity, criterion validity, convergent validity, and discriminant validity) while statistical tests are sufficient conditions for validity. This theory development explains why formal conceptual definitions are necessary before any traditional statistical empirical validity tests are performed. This study suggests that any statistical validity tests are not meaningful if the concept is not formally defined.In short, the theory of formal conceptual definitions provides a structure to develop ‘good’ measures of the formal theory that leads to ‘good’ empirical theory-building.     

Highway traffic flow and the uneconomic region of production

In this paper highway traffic flow is formulated as a short-run production function in which traffic volume is the output and traffic density is the variable input. Given this formulation, the ‘uneconomic’ region of production is relevant. Often it is the case that traffic density will exceed the point at which traffic volume is at a maximum; i.e., the marginal product of the variable input is negative.     

A note on comparative statics and stochastic dominance

This is a bibliographical note which points out the applicability of some existing results to the development of a sort of Stochastic Dominance ‘algebra’. The ‘more risk averse’ relation of Ross (1981) is established within a general framework.     

The Delphi technique as a forecasting tool: issues and analysis

This paper systematically reviews empirical studies looking at the effectiveness of the Delphi technique, and provides a critique of this research. Findings suggest that Delphi groups outperform statistical groups (by 12 studies to two with two ‘ties’) and standard interacting groups (by five studies to one with two ‘ties’), although there is no consistent evidence that the technique outperforms other structured group procedures. However, important differences exist between the typical laboratory version of the technique and the original concept of Delphi, which make generalisations about ‘Delphi’ per se difficult. These differences derive from a lack of control of important group, task, and technique characteristics (such as the relative level of panellist expertise and the nature of feedback used). Indeed, there are theoretical and empirical reasons to believe that a Delphi conducted according to ‘ideal’ specifications might perform better than the standard laboratory interpretations. It is concluded that a different focus of research is required to answer questions on Delphi effectiveness, focusing on an analysis of the process of judgment change within nominal groups.     

高速公路环境下区域物流节点选址规划模型

通过分析高速公路对物流发展的影响,引进阻尼系数对区域物流节点的选址模型进行改进,并利用CFLP(capacitated facility location problem)法进行计算,为高速公路环境下区域物流节点选址提供理论依据,并且通过算例分析对理论模型进行验证。     

Self-organized criticality in evolutionary systems with local interaction

This paper studies a stylized model of local interaction where agents choose from an ever increasing set of vertically ranked actions, e.g. technologies. The driving forces of the model are infrequent upward shifts (‘updates’), followed by a rapid process of local imitation (‘diffusion’). Our main focus is on the regularities displayed by the long-run distribution of diffusion waves and their implication on the performance of the system. By integrating analytical techniques and numerical simulations, we come to the following two main conclusions. (1) If non-coordination costs are sufficiently high, the system behaves critically, in the sense customarily used in physics. (2) The performance of the system is optimal at the frontier of the critical region. Heuristically, this may be interpreted as an indication that (performance-sensitive) evolutionary forces induce the system to be placed ‘at the edge of order and chaos’.     

Theoretical tests of the rational expectations hypothesis in economic dynamical models

This paper examines different theoretical stability tests of infinite-horizon rational expectations equilibria. These ‘tests’ have different status: two of them express that the considered equilibrium is ‘isolated’ [neither (non-sunspot) equilibria (test 1) nor (well-behaved) sunspot equilibria exist in a neighbourhood (test 2)] and two of them are learning criteria [either standard ‘evolutive learning’ (test 3) or game-theoretical ‘eductive’ learning (test 4)]. Surprisingly, these four tests select the same steady state equilibria in the class of one-dimensional one-step-forward looking economic models. The extension of this equivalence theorem to n-dimensional and then more complex systems is discussed.     

Planning horizon results for the dynamic warehouse location problem

In the last decade, a number of models for the dynamic facility location problem have been proposed. The various models contain differing assumptions regarding the revenues and costs realized in the opening, operation, and closure of a facility as well as considering which of the facility sites are candidates for acquisition or disposal at the beginning of a time period. Since the problem becomes extremely large for practical applications, much of the research has been directed toward developing efficient solution techniques. Most of the models and solutions assume that the facilities will be disposed of at the end of the time horizon since distant future conditions usually can't be forecasted with any reasonable degree of accuracy. The problem with this approach is that the “optimal” solution is optimal for only one hypothesized post horizon facility configuration and may become nonoptimal under a different configuration. Post-optimality analysis is needed to assure management that the “optimal” decision to open or close a facility at a given point in time won't prove to be “nonoptimal” when the planning horizon is extended or when design parameters in subsequent time periods change. If management has some guarantee that the decision to open or close a facility in a given time period won't change, it can safely direct attention to the accuracy of the design parameters within that time period.This paper proposes a mixed integer linear programming model to determine which of a finite set of warehouse sites will be operating in each time period of a finite planning horizon. The model is general in the sense that it can reflect a number of acquisition alternatives—purchase, lease or rent. The principal assumptions of the model are: a) Warehouses are assumed to have infinite capacity in meeting customer demand, b) In each time period, any non-operating warehouse is a candidate for becoming operational, and likewise any operating warehouse is a candidate for disposal, c) During a given time period, the fixed costs of becoming operational at a site are greater than the disposal value at that site to reflect the nonrecoverable costs involved in operating a warehouse. These costs are separate from the acquisition and liquidation values of the site. d) During a time period the operation of a warehouse incurs overhead and maintenance costs as well as a depreciation in the disposal value.To solve the model, it is first simplified and a partial optimal solution is obtained by the iterative examination by both lower and upper bounds on the savings realized if a site is opened in a given time period. An attempt is made to fix each warehouse open or closed in each time period. The bounds are based on the delta and omega tests proposed by Efroymson and Ray (1966) and Khumawala (1972) with adjustment for changes in the value of the warehouse between the beginning and end of a time period. A complete optimal solution is obtained by solving the reduced model with Benders' decomposition procedure. The optimal solution is then tested to determine which time periods contain “tentative” decisions that may be affected by post horizon data by analyzing the relationship between the lower (or upper) bounds used in the model simplification time period. If the warehouse decisions made in a time period satisfy these relationships and are thus unaffected by data changes in subsequent time periods, then the decisions made in earlier time periods will also be unaffected by future changes.     

Myopic utility functions on sequential economies

In Brown and Lewis (1981) continuity in the Mackey topology of (l^∞, l¹) is related to myopic (or impatient) economic behavior. They also show that finer (locally convex) topologies admit continuous non-myopic utility functions. In that work the space of bounded sequences, l^∞, is interpreted as all time sequences of bounded consumption plans. In Brown (1981) the analysis is extended to study the theory of interest on related sequence spaces.This note applies our simple technique for ‘computing’ Mackey continuity of real-valued functions defined on l^∞. Our first result is motivated by Bewley's (1972, app. II) theorem, but extends it in several important ways (on sequential economies). First, Beweley's examples (specialized to the sequential setting) are all ‘temporally separable’,that is, consumption in one time period does not affect indifference sets in another. We give new explicit examples of Cobb-Douglass-like utility functions and show that the ‘obvious’ infinite-dimensional Cobb-Douglass functions are non-myopic. Known equilibrium theory [from Bewley (1972), but pre-dating him in the sequential case] applies to these new examples. Second, we remove the assumptions of concavity and monotony from the proof of continuity.Our second result shows that some of the ‘stationary’ utility functions studied by Koopmans, Diamond and Williamson (1964) are also myopic in the sense of Brown and Lewis. In general their work is based on the finer uniform topology.Finally, we show how to transform our technique so that it applies to Brown's more general sequential economies. A change of variables transfers our examples to these spaces.     

The latin model of welfare: Do ‘insertion contracts’ reduce long-term dependence?

This paper aims to present an assessment of the welfare policies implemented in most South European countries. Welfare programs in these countries try to combine a basic level of economic protection and measures favoring life and labor skills (‘insertion benefits’) of low-income households. We focus on a specific program set up with the twofold strategy of cash and ‘insertion benefits’ (Madrid's IMI) and, more precisely, on the so-called ‘insertion projects’, consisting in a gradual mix of job search assistance, training and subsidized jobs. We evaluate the effects of these ‘insertion projects’ on welfare recidivism and the duration of off-welfare spells using propensity score-matching methods. Our results suggest that propensity score estimators appear to reduce selectivity due to non-random participation. Both recidivism rates as well as the duration of off-welfare spells suggest potentially successful interventions.     

Restricted houseswapping games

Restricted houseswapping games (RHGs) are a generalization of ‘one-sided matching games’, in which we specify a class II* of ‘allowable’ simple trading cycles. The cores of such games may be empty. Given II*, all possible closed RHGs have non-empty cores of II* is ‘strongly balanced’. Examples include the one-sided matching markets (^{Shapley and Scarf. Journal of Mathematical Economics 1974. 1. 23–37}. ^{Tijs et al., OR Spektrum 1984, 6, 119–123}; ^{Quinzii, International Journal of Game Theory 1984, 13, 41–60}) and the two-sided matching markets (^{Gale and Shapley. American Mathematical Monthly 1962. 69, 9–16}; ^{Shapley and Shubik, International Journal of Game Theory 1972, 1, 111–130}: and ^{Demange and Gale Econometrica 1985, 53, 873–888}).We then consider the subclass of RHGs in which there is no transferable resource. In this case, a weaker condition on II*, called ‘weak balancedness’, is sufficient to guarantee core non-emptiness. In addition, if II* is not weakly balanced, then there exists a preference profile such that the strict core of the resultant game is empty.Several other examples are given of II* that are (a) strongly balanced: (b) weakly balanced but not strongly balanced: and (c) not even weakly balanced.Finally, we discuss the issues of equilibrium definition, existence, and core-equilibrium allocation equivalence in RHGs.     

Siting a facility in continuous space to maximize coverage of a region

Siting facilities in continuous space such that continuously distributed demand within a region is optimally served is a challenging location problem. This problem is further complicated by the non-convexity of regions typically encountered in practice. In this paper a model for maximizing the service coverage of continuously distributed demand through the location of a single service facility in continuous space is proposed. To address this problem, theoretical conditions are established and associated methods are proposed for optimally siting a service facility in a region (convex or non-convex) with uniformly distributed demand. Through the use of geographic information systems (GIS), the developed approach is applied to identify facility sites that maximize regional coverage provided limitations on facility service ability.     

When does coordination pay?

In a continuous-time model of two symmetric open economies, with a floating exchange rate, we find that the pay-off to macroeconomic policy coordination depends systematically on how heterogeneous is their inflation experience. While monetary policy coordination improves welfare in handling a common rate of underlying inflation, it exacerbates the ‘time consistency’ problem arising when there are differences (as is illustrated diagrammatically). Since the principle of ‘certainty equivalence’ applies to time-consistent policy in linear quadratic models, we are also able to give a stochastic interpretation of the deterministic results.     

Economic dynamics of reservoir sedimentation management: Optimal control with singularly perturbed equations of motion

We analyze the economic dynamics of reservoir sedimentation management using the hydrosuction-dredging sediment-removal system. System dynamics depend on two interdependent hydraulic processes evolving at different rates. The accumulation of water impounded in the reservoir evolves on a ‘fast’ time scale, while the loss of water storage capacity to trapped sediments evolves on a ‘slow’ time scale. We formulate a multidimensional optimal control problem with singularly perturbed equations of motion to accommodate the disparate time scales. We apply singular perturbation methods to approximate (via polynomial series expansion) a ‘slow’ manifold reducing multi-dimensional solution space to the single-dimensional subspace confining long-term dynamics.     

Age-specific dynamic labor demand and human capital investment

To study the optimal age-specific labor demand and human capital investment at the firm level we extend the standard dynamic labor demand model by introducing ‘age’ as a second dynamic variable and distinguish between two types of workers: ‘low skilled’ and ‘high skilled’. Applying an age-structured optimal control model we derive qualitative features of the optimal age-specific hiring and training effort. For the case of a linear revenue and production function we prove that firms do not anticipate changes in adjustment costs in their optimal decisions. This result no longer holds if a nonlinear revenue or production function is considered.     

Management of a capital stock by Strotz's naive planner

The capital management problem posed by R.H. Strotz is analyzed for the case of the ‘naive’ planner who fails to anticipate changes in his own preferences. By imposing progressively stronger restrictions on the primitives of the problem – namely, the discounting function, the utility index function, and the investment technology – the planner's behavior is characterized first as the solution to an ordinary differential equation and then via explicit formulae. Inasmuch as these characterizations leave the discounting function essentially unrestricted, the theory can accommodate, in particular, decision makers who discount time according to the hyperbolic and ‘quasi-hyperbolic’ curves used in applied work and said to be supported by psychological studies. Comparative statics of the model are discussed, as are extensions of the analysis to allow for credit constraints, limited foresight, and partial commitment.     

Dynamic programming for non-additive stochastic objectives

We derive the existence of an optimum and the techniques of dynamic programming for non-additive stochastic objectives. Our key assumption for non-negative objectives is that asymptotic impatience exceeds asymptotic ‘mean’ growth, where ‘mean’ growth is derived not only from intertemporal inelasticity and the random return on investment but also from the curvature of the non-additive stochastic aggregator (i.e. the ‘certainty equivalent’). We provide broad families of new, interesting, and tractable examples. They illustrate that ‘mean’ growth can exist even when the distribution of returns has unbounded support, that power discounting often implies infinite asymptotic impatience, and that non-positive objectives are easily handled with few restrictions on growth.     

A continuity property for local price adjustment mechanisms

This paper makes a case that a (local) continuity property is a reasonable one for any local price adjustment mechanism. This property means that if the starting points (i.e., initial prices) of the adjustment process are ‘close' to one another, and if the characteristics of the economies are ‘close' to one another, then, given any price adjustment mechanism, agents should compute equilibria that are ‘close' to one another. Under preferences which satisfy a ‘surjectivity hypothesis', it is shown that the tâtonnement process satisfies this continuity property on a nice subset of the space of all economies. A characterization of these economies for which the tâtonnement process is locally stable is given. Chart logic is a useful way to think about the path dependent property of implied volatility and about the relationship between implied volatility and historical volatility.