Fractile Model Research Articles

ALLOCATION OF CAPITAL INVESTMENTS OF AN OIL COMPANY BASED ON INDEPENDENT OPPORTUNITY INFORMATION

To solve the problem of investment allocation with optimization of the total level of return on investment for projects under conditions of risk associated with uncertainty of project income, a linear combination with non-negative coefficients of two loss-making models was used: the model of the usual minimax loss-making and the model of the minimax loss-making level. The problem of probabilistic programming obtained as a result of this combination, provided that the probabilistic variables characterizing the profitability of investments in projects are independent (unrelated), is reduced to a linear programming problem. The solution of this problem by the simplex method gives a vector of the equity distribution of investments that determine the total return of investments by the criterion of the minimum of the loss function. On the basis of the proposed approach to the optimal solution of the problem of investment allocation, an algorithm for project investment planning has been developed using a database of invested and returned funds for projects in previous planning periods, according to which distributions of possible investment returns are modeled. The numerical implementation of the algorithm is illustrated by the example of investment planning in an oil company for oil and gas production projects. Keywords: probability programming, investments, investment portfolio, minimax criterion, loss-making function, return on investment, income, concentrated distribution, probability distribution, measure of opportunity, measure of necessity, fractile model, probability variable, fuzzy variable membership function.

Decision making for electricity retailers in fractile model from multiple markets with rational responses of consumers

This paper presents a new decision-making model that enables a retailer to optimise a portfolio reflecting his or her risk attitude in the non-convex decision-making problem. In the proposed model, the responses of consumers to selling prices offered by the retailer are integrated with three types of electricity transactions. In our model, we deal with the three types of electricity transactions, i.e., forward contracts, day-ahead market transactions, and real-time market transactions, and consumers optimise the electricity consumption schedules in response to the time-of-use (TOU) selling prices offered by the retailer. In this paper, in order to examine behavior of the retailers with various risk attitudes effectively, we employ the fractile model that can find the preferred solution in the proposed non-convex decision-making model. Through the computational experiments, we demonstrate the validity of the proposed model for examining the retailer's actions in the deregulated electricity market.

Decision making for electricity retailers in fractile model from multiple markets with rational responses of consumers

Decision making for electricity retailers in fractile model from multiple markets with rational responses of consumers

Interactive fuzzy stochastic multiobjective purchase and transportation planning for food retailing

This paper considers purchase and transportation planning for food retailing in Japan where the food retailer deals with vegetables and fruits which are purchased at the central wholesale markets in several cities, and transports them by truck from each of the central wholesaler markets to the food retailer's storehouse. From a stochastic perspective, by carefully reviewing parameters in our original problem formulation, through the introduction of stochastic parameters, multiobjective linear stochastic programming problems are introduced. By using the typical stochastic models including the expectation model, the fractile model, the probability model together with chance constrained programming, the formulated multiobjective linear stochastic programming problems are transformed into deterministic ones. Assuming the decision maker has the fuzzy goal for each of the objective functions, several interactive fuzzy satisficing methods are presented for deriving a satisficing solution for the decision maker by updating the reference membership levels.

機会制約付き最適化問題におけるFractile modelを用いた市場価格変動リスクを考慮した小売業者の電力調達問題

This paper presents a stochastic decision making framework of the retailer for the power procurement in the deregulated electricity market taking into account the risk induced by the volatile market prices. Unlike conventional related literature, the paper incorporates the three types of trades, which are a forward contract, a spot market, and a real-time market for adjusting the imbalance, in the transaction model with rational responses of the consumers to the selling prices offered by the retailer. For the risk hedge using the forward contract, it is quite significant to reflect the risk attitude of the retailer on decision making in market transactions. In the literature, the weighting method is often used to formulate the retailer's decision making for the power procurement. In the weighting method, however, it is difficult to determine both the weighting coefficients and the confidential level associated with the risk so as to reflect the risk attitude of the retailer adequately, particularly in the bi-level programming problem. In this paper, in order to naturally model the retailer's decision making, we employ the fractile model in which the target variable is maximized subject to the probability that the profit is not less than the target variable exceeds a given assured level given by the retailer according to the risk attitude. Through the computational experiments, we demonstrate the retailer's behavior with satisfactory level for the profit and risk in the deregulated electricity market.

An Inexact Probabilistic–Possibilistic Optimization Framework for Flood Management in a Hybrid Uncertain Environment

Flooding is one of the leading causes of loss due to natural catastrophes, and at least one third of all losses due to natural forces can be attributed to flooding. Flood management systems involve a variety of complexities, such as multiple uncertainties, dynamic variations, and policy implications. This paper presents an inexact probabilistic–possibilistic programming with fuzzy random coefficients (IPP-FRC) model for flood management in a hybrid uncertain environment. IPP-FRC is capable not only of tackling multiple uncertainties in the form of intervals with fuzzy random boundaries but of addressing the dynamic complexity through capacity expansion planning within a multi-region, multi-flood-level, and multi-option context. The possibility and necessity measures used in IPP-FRC are suitable for risk-seeking and risk-averse decision making, respectively. A case study is used to demonstrate the applicability of the proposed methodology for facilitating flood management. The results indicate that the inexact degrees of possibility and necessity would decrease with increased probabilities of occurrence, implying a potential tradeoff between fulfillment of objectives and associated risks. A number of decision alternatives can be obtained under different policy scenarios. They are helpful for decision makers to formulate the appropriate flood management policy according to practical situations. The performance of IPP-FRC is analyzed and compared with a possibility-based fractile model.

Fuzzy random non-cooperative two-level linear programming through fractile models with possibility and necessity

In this article, assuming non-cooperative behaviour of the decision makers, solution methods for decision making problems in hierarchical organizations under fuzzy random environments are presented. Taking into account hte vagueness of judgments by decision makers, fuzzy goals are introduced into the formulated fuzzy random two-level linear programming problems. Considering the possibility and necessity measures that each objective function fulfils the corresponding fuzzy goal, the fuzzy random two-level linear programming problems to minimize each objective function with fuzzy random variables are transformed into stochastic two-level programming problems to maximize the degree of possibility and necessity that each fuzzy goal is fulfilled. Through the fractile criterion optimization model, or Kataoka's model in stochastic programming, the transformed stochastic two-level programming problems can be reduced to deterministic two-level programming problems. For the transformed problems, extended concepts of Stackelberg solutions are introduced and computational methods are also presented. A numerical example is provided to illustrate the proposed methods.

Random fuzzy bilevel linear programming through possibility-based fractile model

This paper focuses on random fuzzy noncooperative bilevel linear programming problems. Considering the probabilities that the decision makers’ objective function values are smaller than or equal to target variables, fuzzy goals of the decision makers are introduced. Using the fractile model to optimize the target variables under the condition that the degrees of possibility with respect to the attained probabilities are greater than or equal to certain permissible levels, the original random fuzzy bilevel programming problems are reduced to deterministic ones. Extended concepts of Stackelberg solutions are introduced and computational methods are also presented. A numerical example is provided to illustrate the proposed method.

Interactive fuzzy programming for random fuzzy two-level programming problems through possibility-based fractile model

This paper focuses on interactive decision making methods for random fuzzy two-level linear programming problems. Considering the probabilities that the decision makers’ objective function values are smaller than or equal to target variables, fuzzy goals of the decision makers are introduced. Using the fractile model to optimize the target variables under the condition that the degrees of possibility with respect to the attained probabilities are greater than or equal to certain permissible levels, the original random fuzzy two-level programming problems are reduced to deterministic ones. Interactive fuzzy nonlinear programming to obtain a satisfactory solution for the decision maker at the upper level in consideration of the cooperative relation between decision makers is presented. An illustrative numerical example demonstrates the feasibility and efficiency of the proposed method.

Communications to the Editor—Comment on the Fractile Approach to Linear Programming under Risk

Sengupta and Portillo-Campbell have recently proposed a fractile decision criterion for risk situations as an alternative to the expected value and E-V criteria [Sengupta, J. K., J. H. Portillo-Campbell. 1970. A fractile approach to linear programming under risk. Management Sci. 16(5, January) 298–308.]. The fractile model seems to add little to the current literature on risk programming models under normality assumptions except to provide a direct solution procedure for identification of a specific solution in a Baumol efficient E-L set.