The design of economic policy under model uncertainty

This paper examines how considerations of model uncertainty can affect policy design. Without such considerations one may expect that choice of policy control rules for a macroeconomic model would depend on some welfare criterion based on the model as given. However if there is uncertainty in the structure of the model or in the values of particular model parameters then it is argued that choice of policy should take this into account.We introduce and define some measures ofrobustness which describe how well a particular control rule performs when the model is uncertain. These can only be evaluated using Monte-Carlo simulations; in that sense they are ex post. Then we define a number of indicators which may be of use in predicting robustness, and which do not require simulations to calculate. In that sense they are ex ante.Lastly we evaluate the ex ante indicators on a small macromodel by comparing their predictions with the actual robustness outturn for the range of possible control rules. We find that use of the indicators in choosing rules yields some improvement on the ordinary welfare criterion, especially when the shocks hitting the system are unknown.     

Handling uncertainty in economic nonlinear model predictive control: A comparative case study

In the last years, the use of an economic cost function for model predictive control (MPC) has been widely discussed in the literature. The main motivation for this choice is that often the real goal of control is to maximize the profit or the efficiency of a certain system, rather than tracking a predefined set-point as done in the typical MPC approaches, which can be even counter-productive. Since the economic optimal operation of a system resulting from the application of an economic model predictive control approach drives the system to the constraints, the explicit consideration of the uncertainties becomes crucial in order to avoid constraint violations. Although robust MPC has been studied during the past years, little attention has yet been devoted to this topic in the context of economic nonlinear model predictive control, especially when analyzing the performance of the different MPC approaches. In this work, we present the use of multi-stage scenario-based nonlinear model predictive control as a promising strategy to deal with uncertainties in the context of economic NMPC. We make a comparison based on simulations of the advantages of the proposed approach with an open-loop NMPC controller in which no feedback is introduced in the prediction and with an NMPC controller which optimizes over affine control policies. The approach is efficiently implemented using CasADi, which makes it possible to achieve real-time computations for an industrial batch polymerization reactor model provided by BASF SE. Finally, a novel algorithm inspired by tube-based MPC is proposed in order to achieve a trade-off between the variability of the controlled system and the economic performance under uncertainty. Simulations results show that a closed-loop approach for robust NMPC increases the performance and that enforcing low variability under uncertainty of the controlled system might result in a big performance loss.     

Optimal bus scheduling and fleet selection: A programming approach

A set of nonlinear programming models is developed here to determine an optimal vehicle-mix and fleet selection. The institutional framework assumed is as follows: a given number of n vehicles is available for dispatch from some source to serve passengers along fixed routes; the arriving passengers follow a simple queueing process, i.e. if a passenger cannot be served in a given time interval i, he has to wait until the next interval, thus forming a queue. One wishes to choose the number of buses n_i, to assign in interval i (i = 1, 2, …, 9) so as to optimize a criterion function, which includes such components as costs of operating the fleet, gross returns per vehicle per trip and the implicit cost of passengers' waiting time. Stochastic aspects of travel demand are handled through some formulations of stochastic programming. It is shown that under suitable simplifying assumptions, stochastic linear programming methods could provide good approximations to the more general nonlinear programming models.     

Optimal economic stabilization policies under decentralized control and conflicting objectives

This paper derives methods for the calculation of optimal stabilization policies under the assumption that monetary and fiscal control are exercised by separate authorities who may have different objectives. Each authority minimizes its own quadratic cost functional subject to the constraint of a linear econometric model. Nash solution strategies are calculated for this discrete-time differential game, both in the context of open-loop and closed-loop behavior (in the closed-loop framework each authority can continually revise his policy in response to the evolving strategy of the other authority). The results are applied to a small econometric model, and show how the degree of fiscal or monetary, control depends on the particular conflict situation, and how conflicting policies are "suboptimal" in comparison with coordinated policies.     

Optimal control problems treated with algorithms of linear and nonlinear programming

Algorithms solving optimal control problems for linear discrete systems and linear continuous systems (without discretization) are discussed. The algorithms are based on a new approach to solving linear programming problems worked out in Minsk (USSR). A new method for solving nonlinear programming problems is justified. It uses the network interpretation of nonlinear functions and special network operations. Results of numerical experiment (on geometric programming problems) are given. In conclusion an algorithm of solving optimal control problem for the system with nonlinear input is described.     

An introduction to nonlinear programming—II: The linear programming problem

Linear programming problems represent the most thoroughly analyzed and widely solved class of parameter optimization problems. In Part II, we shall restrict our attention to this general class of problems. The characteristics of the admissible region are investigated and established. The Kuhn-Tucker conditions developed in Part I are applied to establish necessary and sufficient conditions that must be satisfied at a minimum. Included in the discussion is a consideration of dual linear programming problems. Then, we direct our attention to the question of determining the solution of specific problems. A general algorithm known as the Simplex Method is described and applied to several examples.     

Optimal investment policy: An example of a control problem in economic theory

A problem in mathematical economics concerning the optimal investment of resources is solved via the techniques of optimal control theory. Interesting theoretical complications include the simultaneous presence of interdependent control variable inequality constraints, state variable inequality constraints, and singularity conditions. Economic implications of the results are briefly discussed.     

Optimal fixed rules and simple feedback laws in the design of economic policy

The constancy parameter of fixed-rate-of-growth rules and the parameters of simple feedback laws, linking policy instruments to specified endogenous variables, can be determined optimally within a policy optimization framework. An approach for doing this is described along with results using the National Institute of Economic and Social Research nonlinear econometric model of the U.K. The framework is also extended to rational expectations. The effect of an optimal fixed-rate-of-growth monetarist rule is illustrated in an example incorporating the credible announcement of monetary targets. This is evaluated against a strategy derived without the assumption of announcement effects. The use of indicators is also discussed to provide an empirical example for parametrized optimal feedback laws. Exchange rate indicators are derived and compared with open-loop policies. Robust control extensions are suggested and Monte Carlo simulations are used to test the behaviour of the policies in the presence of stochastic disturbances.     

A policy model for income growth and distribution using econometric and programming techniques: the Taiwan case

A computable general equilibrium model is developed by means of an extended input-output model under realistic constraints at two levels: sectoral and aggregative. Econometric estimates of sectoral production functions and a linear programming test that imposes resource and other constraints are performed for the economy of Taiwan to evaluate the trade-off between income growth and income equality, which is otherwise known as Kuznets hypothesis. Several policy scenarios, such as export promotion and import substitution as well as shortages of foreign exchange, are examined to evaluate their impact on the economy, its growth and the income distribution pattern.

The simulated profiles and linear programming experiments appear not to support the so-called Kuznets hypothesis for Taiwan in her drive towards industrial growth in recent years. This inference is upheld even when capital-labour substitution is econometrically estimated for each sector and then integrated with the input-output model     

Identification of filter management strategy in fluid power systems under uncertainty: an interval-fuzzy parameter integer nonlinear programming method

An interval-fuzzy integer nonlinear programming (IFINP) method is developed for the identification of filter allocation and replacement strategies in a fluid power system (FPS) under uncertainty. It can handle uncertainties expressed as interval-fuzzy values that exist in the left- and right-hand sides of constraints as well as in the objective function. The developed method is applied to a case of planning filter allocation and replacement strategies under uncertainty for a FPS with a single circuit. A piecewise linearisation approach is used to convert the nonlinear problem of FPS into a linear one. The generated fuzzy solutions will be used to analyse and interpret the multiple decision alternatives under various system conditions, and thus help decision-makers to make a compromise among the system contamination level, system cost, satisfaction degrees and system-failure risks under different contaminant ingression/generation rates. The results demonstrate that the suction and return filters can effectively reduce the contamination level associated with a low system cost, but the FPS will take lots of failure risk when the contaminant ingression/generation rate is high; and the combination of suction and pressure filters can bring the lowest system cost with more security instead. Furthermore, comparisons for the optimised solutions are made among IFINP, interval-parameter integer nonlinear programming and deterministic linear programming also. Generally, the IFINP method can effectively reduce the total design and operation cost of the filtration system when contaminants ingression/generation rate is high, and it could be extended to the lubricating system.     

Supporting decision making and action selection under time pressure and uncertainty: the case of in-flight icing

Operators in high-risk domains such as aviation often need to make decisions under time pressure and uncertainty. One way to support them in this task is through the introduction of decision support systems (DSSs). The present study examined the effectiveness of two different DSS implementations: status and command displays. Twenty-seven pilots (9 pilots each in a baseline, status, and command group) flew 20 simulated approaches involving icing encounters. Accuracy of the decision aid (a smart icing system), familiarity with the icing condition, timing of icing onset, and autopilot usage were varied within subjects. Accurate information from either decision aid led to improved handling of the icing encounter. However, when inaccurate information was presented, performance dropped below that of the baseline condition. The cost of inaccurate information was particularly high for command displays and in the case of unfamiliar icing conditions. Our findings suggest that unless perfect reliability of a decision aid can be assumed, status displays may be preferable to command displays in high-risk domains (e.g., space flight, medicine, and process control), as the former yield more robust performance benefits and appear less vulnerable to automation biases.     

Optimal control of grinding mill circuit using model predictive static programming: A new nonlinear MPC paradigm

The recently developed reference-command tracking version of model predictive static programming (MPSP) is successfully applied to a single-stage closed grinding mill circuit. MPSP is an innovative optimal control technique that combines the philosophies of model predictive control (MPC) and approximate dynamic programming. The performance of the proposed MPSP control technique, which can be viewed as a ‘new paradigm’ under the nonlinear MPC philosophy, is compared to the performance of a standard nonlinear MPC technique applied to the same plant for the same conditions. Results show that the MPSP control technique is more than capable of tracking the desired set-point in the presence of model-plant mismatch, disturbances and measurement noise. The performance of MPSP and nonlinear MPC compare very well, with definite advantages offered by MPSP. The computational speed of MPSP is increased through a sequence of innovations such as the conversion of the dynamic optimization problem to a low-dimensional static optimization problem, the recursive computation of sensitivity matrices and using a closed form expression to update the control. To alleviate the burden on the optimization procedure in standard MPC, the control horizon is normally restricted. However, in the MPSP technique the control horizon is extended to the prediction horizon with a minor increase in the computational time. Furthermore, the MPSP technique generally takes only a couple of iterations to converge, even when input constraints are applied. Therefore, MPSP can be regarded as a potential candidate for online applications of the nonlinear MPC philosophy to real-world industrial process plants.     

Control theory and economic policy: Balance and perspectives

This paper provides a selective survey of applications of control theory to the analysis of economic policy problems. We discuss applications of closed-loop control and of optimum control theory, including deterministic, stochastic and decentralized optimum control. Promising areas of mutual cooperation between control theorists and economists such as robust control and dynamic game theory are identified. A critical evaluation is given of different control theory approaches to an empirically useful theory of economic policy.     

Optimal linear regulators: The discrete-time case

In this paper the optimal discrete-time linear-quadratic regulator problem is carefully presented and the basic results are reviewed. Dynamic programming is used to determine the optimization equations. Special attention is given to problems unique to the discrete-time case; this includes, for example, the possibility of a singular system matrix and a singular control-effort weighting matrix. Some problems associated with sampled-data systems are also summarized, e.g., sensitivity to sampling time, and loss of controllability due to sampling. Computational methods for the solution of the optimization equations are outlined and a simple example is included to illustrate the various computational approaches.     

Optimal design modifications by geometric programming and constrained stochastic network models

A new class of constrained stochastic network models is formulated in a manner that can be used to support a variety of analyses of optimal design modifications for special weapons systems under budgetary and other constraints. Alternative expressions in terms of geometric programming are also explored. These, however, are far more inconvenient to compute or manipulate especially as the model size increases. Component modifications to the B52G system are considered in a prototype example.     

The economic impact of a transportation bottleneck: an integrated input-output and linear programming approach

A transport-constrained input-output and linear programming (IO/LP) model is proposed for the purpose of studying the impact of a transportation bottleneck in an economy. This removes the implicit assumption of no capacity constraints that characterizes the traditional demand-driven input-output model. Data for Taiwan are used for empirical experiments, and results from these experiments indicate the kinds of policy implications that might be drawn.     

Optimal economic production quantity policy for randomly failing process with minimal repair,backorder and preventive maintenance

This study examines the feasibility of using an economic production quantity (EPQ) model incorporating maintenance and production programs to model an imperfect process involving a deteriorating production system. In response to failure, defective parts were produced and minimal repairs performed to create an in-control state. The conditions are studied in the case of the EPQ model undergoing a backorder owing to rejection of defective parts after a failure. Following production run period, two types of periodic preventive maintenance (PM) exist: imperfect and perfect. The probability of perfect PM being performed depends on the number of imperfect PM performed since the last renewal cycle. For the EPQ model, the optimal run time for minimising the total cost is discussed. Various special cases are considered, including the PM learning effect. Finally, this investigation presents a numerical example to illustrate the effects of PM ability, repair cost and defect number on total costs and production period. This study finds that enhancing maintenance ability reduces production related costs. The product system can be produced more efficiently using a PM program.     

A modular Decision Support System for optimum investment selection in presence of uncertainty: Combination of fuzzy mathematical programming and fuzzy rule based system

In this paper, we have developed a modular Decision Support System (DSS) in order to select an optimum portfolio of several chances for investments in presence of uncertainty. The investments are considered as the projects so as their initial investment costs, profits, resource requirement, and total available budget are assumed to be uncertain. This uncertainty has been modeled using fuzzy concepts. The proposed DSS has two main modules. The first one is a fuzzy binary programming model which represents the mathematical model of the associated fuzzy capital-budgeting problem. It involves finding optimum combination of investment portfolio considering a multi-objective measurement function and subject to several set of constraints. The results of optimistic and pessimistic analysis of the aforementioned fuzzy binary programming model plus a managerial Confidence Level (CL) value are treated as input of a fuzzy rule based system which is the second module of the proposed DSS. Although some projects are simple to make a decision about at the final step of the first module but the unique output of the second module of the proposed DSS is Risk of Investment (ROI) for all remained project. The logic relations between precedence parts of the rules as well as CL value will work in favor of computational efforts in second module through diminishing some unessential rules. This will help to define a complete set of fuzzy IF-THEN rules more efficiently. The proposed DSS can help the decision makers to select an optimum investment portfolio with minimum risk in a complete ambiguous condition.     

A nonlinear galerkin method: The two-level fourier-collocation case

In this article we study the implementation of the Nonlinear Galerkin method as a multiresolution method when a two-level Fourier-collocation discretization is used. The set of collocation points with an even number of points is considered as the fine grid and decomposed into two coarse grids containing half as many points. Using these two grids we decompose the unknown into the sum of a large scale component containing only low frequency modes and based on one of the coarse grids and a small scale component containing only high frequency modes and based on the other coarse grid. This produces interesting connections between the physical space and the Fourier space representations of the function. A nonlinear Galerkin scheme is then applied to the Burgers equation; finally, implementation issues are discussed showing the advantages of the method.