Optimal investment under operational flexibility, risk aversion, and uncertainty

Traditional real options analysis addresses the problem of investment under uncertainty assuming a risk-neutral decision maker and complete markets. In reality, however, decision makers are often risk averse and markets are incomplete. We confirm that risk aversion lowers the probability of investment and demonstrate how this effect can be mitigated by incorporating operational flexibility in the form of embedded suspension and resumption options. Although such options facilitate investment, we find that the likelihood of investing is still lower compared to the risk-neutral case. Risk aversion also increases the likelihood that the project will be abandoned, although this effect is less pronounced. Finally, we illustrate the impact of risk aversion on the optimal suspension and resumption thresholds and the interaction among risk aversion, volatility, and optimal decision thresholds under complete operational flexibility.     

Pricing swing options with regime switching

Gasoline price is highly volatile and exhibits Markov regime-switching process. In the electricity and the natural gas markets, “swing” options, which can provide some protection against day-to-day price fluctuations, are used to incorporate flexibility in delivering acquired energy. We propose a framework for pricing swing options for an underlying variable that follows a regime-switching process. We study the proposed framework in the gasoline industry for pricing swing options under price uncertainty by extracting the gasoline market information, estimating the parameters of the regime-switching process, and then presenting different numerical examples.     

An MINLP retrofit approach for improving the flexibility of heat exchanger networks

A mixed integer nonlinear programming (MINLP) model for the retrofit of heat exchanger networks (HENs) in order to improve their flexibility is presented in this paper. As stream flowrates and inlet temperatures and/or heat transfer coefficients are allowed to vary within either specified ranges or discrete sets, a multiperiod hyperstructure network representation is developed based on critical operating conditions (i.e. periods of operation) that limit the network's flexibility. This multiperiod hyperstructure includes all possible network configurations. Structural modifications, such as new stream matches, exchanger reassignments, splitting and mixing of streams are explicitly modeled either considering one-to-one or one-to-many assignment of heat exchangers to stream matches. Energy recovery and utility consumption are not predetermined but are optimized as part of a total annualized cost along with the structural modification cost in the objective function. Thus, trade-offs between operating and retrofit investment costs to improve the flexibility of a HEN are accounted for. The resulting large scale MINLP is solved with the application of the Generalized Benders Decomposition. The proposed multiperiod retrofit model can be included in a general framework to improve the operability of heat exchanger networks.     

An attribute approach to the measurement of machine-group flexibility

Researchers have emphasized that different factors have to be considered when discussing the flexibility of a single machine and that of a group of machines. The present research focuses on proposing methods for measuring machine-group flexibility, which is an extension of the model for measuring single machine flexibility. The measurement of machine-group flexibility needs to take into account at least the following three attributes, namely efficiency, versatility and redundancy. Measurement models for each of these three attributes are demonstrated, and a combined measurement approach for machine-group flexibility is suggested. The entropy approach, which states that the greater the number of available options, the larger the entropy value, is applied to the measurement of versatility and redundancy. Finally, an example illustrates the application of the flexibility measurement models developed in this research.     

An Integrated Market for Electricity and Natural Gas Systems with Stochastic Power Producers

In energy systems with high shares of weather-driven renewable power sources, gas-fired power plants can serve as a back-up technology to ensure security of supply and provide short-term flexibility. Therefore, a tighter coordination between electricity and natural gas networks is foreseen. In this work, we examine different levels of coordination in terms of system integration and time coupling of trading floors. We propose an integrated operational model for electricity and natural gas systems under uncertain power supply by applying two-stage stochastic programming. This formulation co-optimizes day-ahead and real-time dispatch of both energy systems and aims at minimizing the total expected cost. Additionally, two deterministic models, one of an integrated energy system and one that treats the two systems independently, are presented. We utilize a formulation that considers the linepack of the natural gas system, while it results in a tractable mixed-integer linear programming (MILP) model. Our analysis demonstrates the effectiveness of the proposed model in accommodating high shares of renewables and the importance of proper natural gas system modeling in short-term operations to reveal valuable flexibility of the natural gas system. Moreover, we identify the coordination parameters between the two markets and show their impact on the system’s operation and dispatch.     

FINITE-TIME H_∞ CONTROL FOR A CLASS OF MARKOVIAN JUMPING NEURAL NETWORKS WITH DISTRIBUTED TIME VARYING DELAYS-LMI APPROACH

In this article, we investigates finite-time H_∞ control problem of Markovian jumping neural networks of neutral type with distributed time varying delays. The mathematical model of the Markovian jumping neural networks with distributed delays is established in which a set of neural networks are used as individual subsystems. Finite time stability analysis for such neural networks is addressed based on the linear matrix inequality approach.Numerical examples are given to illustrate the usefulness of our proposed method. The results obtained are compared with the results in the literature to show the conservativeness.     

Penalized least squares estimation with weakly dependent data

In statistics and machine learning communities, the last fifteen years have witnessed a surge of high-dimensional models backed by penalized methods and other state-of-the-art variable selection techniques. The high-dimensional models we refer to differ from conventional models in that the number of all parameters p and number of significant parameters s are both allowed to grow with the sample size T. When the field-specific knowledge is preliminary and in view of recent and potential affluence of data from genetics, finance and on-line social networks, etc., such (s, T, p)-triply diverging models enjoy ultimate flexibility in terms of modeling, and they can be used as a data-guided first step of investigation. However, model selection consistency and other theoretical properties were addressed only for independent data, leaving time series largely uncovered. On a simple linear regression model endowed with a weakly dependent sequence, this paper applies a penalized least squares (PLS) approach. Under regularity conditions, we show sign consistency, derive finite sample bound with high probability for estimation error, and prove that PLS estimate is consistent in L ₂ norm with rate \(\sqrt {s\log s/T}\).     

A fuzzy approach to R&D project portfolio selection

A major advance in the development of project selection tools came with the application of options reasoning in the field of Research and Development (R&D). The options approach to project evaluation seeks to correct the deficiencies of traditional methods of valuation through the recognition that managerial flexibility can bring significant value to projects. Our main concern is how to deal with non-statistical imprecision we encounter when judging or estimating future cash flows. In this paper, we develop a methodology for valuing options on R&D projects, when future cash flows are estimated by trapezoidal fuzzy numbers. In particular, we present a fuzzy mixed integer programming model for the R&D optimal portfolio selection problem, and discuss how our methodology can be used to build decision support tools for optimal R&D project selection in a corporate environment.     

Combinatorial flexibility problems and their computational complexity

The concept of flexibility—originated in the context of heat exchanger networks—is associated with a substructure which guarantees the performance of the original structure, in a given range of possible states. We extend this concept to combinatorial optimization problems, and prove several computational complexity results in this new framework.Under some monotonicity conditions, we prove that a combinatorial optimization problem polynomially transforms to its associated flexibility problem, but that the converse need not be true.In order to obtain polynomial flexibility problems, we have to restrict ourselves to combinatorial optimization problems on matroids. We also prove that, when relaxing in different ways the matroid structure, the flexibility problems become NP-complete. This fact is shown by proving the NP-completeness of the flexibility problems associated with the Shortest Path, Minimum Cut and Weighted Matching problems.     

Managing capacity flexibility in make-to-order production environments

This paper addresses the problem of managing flexible production capacity in a make-to-order (MTO) manufacturing environment. We present a multi-period capacity management model where we distinguish between process flexibility (the ability to produce multiple products on multiple production lines) and operational flexibility (the ability to dynamically change capacity allocations among different product families over time). For operational flexibility, we consider two polices: a fixed allocation policy where the capacity allocations are fixed throughout the planning horizon and a dynamic allocation policy where the capacity allocations change from period to period. The former approach is modeled as a single-stage stochastic program and solved using a cutting-plane method. The latter approach is modeled as a multi-stage stochastic program and a sampling-based decomposition method is presented to identify a feasible policy and assess the quality of that policy. A computational experiment quantifies the benefits of operational flexibility and demonstrates that it is most beneficial when the demand and capacity are well-balanced and the demand variability is high. Additionally, our results reveal that myopic operating policies may lead a firm to adopt more process flexibility and form denser flexibility configuration chains. That is, process flexibility may be over-valued in the literature since it is assumed that a firm will operate optimally after the process flexibility decision. We also show that the value of process flexibility increases with the number of periods in the planning horizon if an optimal operating policy is employed. This result is reversed if a myopic allocation policy is adopted instead.     

A hybrid macroscopic-based model for traffic flow in road networks

Recently, the unquestionable growth of interest to increase the operational efficiency and capability of transportation systems led to the development of a large number of traffic modeling theories. One of the major operational issues when developing a transportation system management model lies in the selection of the appropriate methodological approach with respect to several decisions, such as the selection of the type of input and output data as well as the qualitative representation and the computational power of the model. Despite the considerable effort in the area, there is still not an approach which per se models effectively the various dynamically evolving features of traffic in road networks. The present paper addresses this issue by introducing a new hybrid approach which combines the complementary features and capabilities of both continuum mathematical models e.g. 1, 6, 23 and 26 and knowledge-based models e.g. 7, 22 and 28 in order to describe effectively traffic flow in road networks.     

Investment in electric energy storage under uncertainty: a real options approach

In this paper we develop a real options approach to evaluate the profitability of investing in a battery bank. The approach determines the optimal investment timing under conditions of uncertain future revenues and investment cost. It includes time arbitrage of the spot price and profits by providing ancillary services. Current studies of battery banks are limited, because they do not consider the uncertainty and the possibility of operating in both markets at the same time. We confirm previous research in the sense that when a battery bank participates in the spot market alone, the revenues are not sufficient to cover the initial investment cost. However, under the condition that the battery bank also can receive revenues from the balancing market, both the net present value (NPV) and the real options value are positive. The real options value is higher than the NPV, confirming the value of flexible investment timing when both revenues and investment cost are uncertain.     

Semi-Lagrangean approach for price discovery in markets with non-convexities

From standard economic theory, the market clearing price for a commodity is set where the demand and supply curves intersect. Convexity is a property that economic models require for a competitive equilibrium, which is efficient and well-behaved and provides equilibrium prices. However, some markets present non-convexities due to their cost structure or due to some operational constraints that need to be addressed. This is the case for electricity markets where the electricity producers incur costs for shutting down a generating unit and then bringing it back on. Non-convex cost structures can be a challenge for the price discovery process, since the supply and demand curves may not intersect, or if they intersect, the price found may not be high enough to cover the total cost of production. We apply a Semi-Lagrangean approach to find a price that can be applied in the electricity pool markets where a central system operator decides who produces and how much they should produce. By applying the model to an example from the literature, we found prices that are high enough to cover the producer’s total costs, and follows the optimal solution for achieving mining cost in production. The prices are an alternative solution to the price discovery problem in non-convexities economies; in addition, they provide nonnegative profits to all the generators without the use of side-payments or up-lifts, and closes the integrality gap.     

Valuing the flexibility of investing in security process innovations

In this paper, we develop a decision model of a firm’s optimal strategy for investment in security process innovations (SPIs) when confronted with a sequence of malicious attacks. The model incorporates real options as a methodology to capture the flexibility embedded in such investment decisions. SPIs, when seamlessly integrated with the organization’s overall business dynamics, induce organizational learning and provide the flexibility of switching to more suitable technologies as the environment of malicious attacks changes. The theoretical contribution of this paper is a mathematical model of the invest-to-learn and switching options generated upon early investment in flexible SPIs. The practical significance of the paper is the application of a binomial lattice model to approximate the continuous-time model, resulting in an easy to use decision aid for managers.     

Well-Posedness of a Problem of Propagation of Nonlinear Acoustic-Gravity Waves in the Atmosphere Generated by Surface Pressure Variations

Currently there are many international microbarograph networks for high-resolution recording of wave pressure variations on the Earth’s surface. This arouses interest in wave propagation in the atmosphere generated by atmospheric pressure variations. A full system of nonlinear hydrodynamic equations for atmospheric gases with lower boundary conditions in the form of wavelike pressure variations on the Earth’s surface is considered. Since the wave amplitudes near the Earth’s surface are small, linearized equations are used in the analysis of well-posedness of the problem. With the help of a wave energy functional method, it is shown that in the non-dissipative case the solution to the boundary value problem is uniquely determined by the variable pressure field on the Earth’s surface. The corresponding dissipative problem is well-posed if, in addition to the pressure field, appropriate conditions on the velocity and temperature on the Earth’s surface are given. In the case of an isothermal atmosphere, the problem admits analytical solutions that are harmonic in the variables x and t. A good agreement between the numerical and analytical solutions is obtained. The study shows that the temperature and density can rapidly vary at the lower boundary of the boundary value problem. An example of solving the three-dimensional problem with variable pressure on the Earth’s surface taken from experimental observations is given. The developed algorithms and computer programs can be used to simulate atmospheric waves generated by pressure variations on the Earth’s surface.     

Exponential stability of non-linear hyperbolic distributed complex-valued parameter systems: The linear fuzzy operator inequality approach

In this work, exponential stability of non-linear hyperbolic distributed complex-valued parameter systems has been addressed. Using a linear fuzzy operator inequality approach, which is a novel notion proposed for the first time in this work, delay-dependent sufficient conditions for the exponential stability in complex Hilbert spaces are established in terms of linear matrix inequalities (LMIs). Finally, numerical computation illustrates our result.     

On extracting information implied in options

Options are financial instruments with a payoff depending on future states of the underlying asset. Therefore option markets contain information about expectations of the market participants about market conditions, e.g. current uncertainty on the market and corresponding risk. A standard measure of risk calculated from plain vanilla options is the implied volatility (IV). IV can be understood as an estimate of the volatility of returns in future period. Another concept based on the option markets is the state-price density (SPD) that is a density of the future states of the underlying asset. From raw data we can recover the IV function by nonparametric smoothing methods. Smoothed IV estimated by standard techniques may lead to a non-positive SPD which violates no arbitrage criteria. In this paper, we combine the IV smoothing with SPD estimation in order to correct these problems. We propose to use the local polynomial smoothing technique. The elegance of this approach is that it yields all quantities needed to calculate the corresponding SPD. Our approach operates only on the IVs—a major improvement comparing to the earlier multi-step approaches moving through the Black–Scholes formula from the prices to IVs and vice-versa.     

Long term capacity decisions in uncertain markets for advanced manufacturing systems incorporating scope economies

By examining the literature in the field of manufacturing flexibility many researchers have located several form of flexibility by distinguishing them into strategic and operational flexibility forms. Furthermore, many measures and design methods have been proposed for flexible manufacturing systems. Surely scope economies are one of the most important strategic form of flexibility in manufacturing systems and their strategic impact has been acknowledged by the very beginning of the flexible manufacturing era. However, despite several researches are available to address scope economies measurement and design methodologies, very few researches investigate their economic convenience in front of dedicated manufacturing systems depending on the competitive market conditions.This paper proposes a theoretical model whose main aim is the general understanding of the convenience conditions of scope economies-based manufacturing systems. The results of the theoretical model are very interesting, because they locate market conditions that make scope economies manufacturing systems less profitable than dedicated manufacturing ones; moreover, the proposed model sets some general criteria to guide the entrepreneur in making right investment decision regarding this kind of manufacturing investments. Such results can explain the reason of many failures of flexible manufacturing systems and it suggests the use of this kind of approach to investigate other flexibility forms of manufacturing systems. The ultimate goal of this research is the construction of a Decision Support System for supporting the entrepreneur in making decision on Advanced Manufacturing Systems investment decisions.     

Exponential stability of delayed fuzzy cellular neural networks with diffusion

The exponential stability of delayed fuzzy cellular neural networks (FCNN) with diffusion is investigated. Exponential stability, significant for applications of neural networks, is obtained under conditions that are easily verified by a new approach. Earlier results on the exponential stability of FCNN with time-dependent delay, a special case of the model studied in this paper, are improved without using the time-varying term condition: dτ(t)/dt < μ.     

Data envelopment analysis with imprecise data

In original data envelopment analysis (DEA) models, inputs and outputs are measured by exact values on a ratio scale. Cooper et al. [Management Science, 45 (1999) 597–607] recently addressed the problem of imprecise data in DEA, in its general form. We develop in this paper an alternative approach for dealing with imprecise data in DEA. Our approach is to transform a non-linear DEA model to a linear programming equivalent, on the basis of the original data set, by applying transformations only on the variables. Upper and lower bounds for the efficiency scores of the units are then defined as natural outcomes of our formulations. It is our specific formulation that enables us to proceed further in discriminating among the efficient units by means of a post-DEA model and the endurance indices. We then proceed still further in formulating another post-DEA model for determining input thresholds that turn an inefficient unit to an efficient one.