Han-n Li

A robust optimization model for stochastic logistic problems

The main di

A global approach for general 0–1 fractional programming

culty of a logistic management problem is in the face of uncertainty about the future. Since many logistic models encounter uncertainty and noisy data in which variables or parameters have the probability of occurrence, a highly promising technique of solving stochastic optimization problems is the robust programming proposed by Mulvey et al. (Operations Research 43(2) (1995a) 264}281) and Mulvey and Ruszczynski (Operations Research 43 (3) (1995b) 477}490). However, heavy computational burden has prevented wider applications in practice. In this study, we reformulate a stochastic management problem as a highly e

General fuzzy piecewise regression analysis with automatic change-point detection

cient robust optimization model capable of generating solutions that are progressively less sensitive to the data in the scenario set. The method proposed herein to transform a robust model into a linear program only requires adding n#m variables (where n and m are the number of scenarios and total control constraints, respectively). Whereas, the current robust programming methods proposed by Mulvey et al., Mulvey and Ruszczynski and Bai et al. (Management Science 43 (7)(1997) 895}907) require adding 2n#2m. Two logistic examples, logistic management problems involving a wine company and an airline company, demonstrate the computational e

Approximately global optimization for assortment problems using piecewise linearization techniques

ciency of the proposed model. ( 2000 Elsevier Science B.V. All rights reserved.

A global optimization method for nonconvex separable programming problems

Abstract Current methods of general 0–1 fractional programming (G-FP) can only find the local optimum. This paper proposes a new method of solving G-FP problems by a mixed 0–1 linear program to obtain a global optimum. Given a mixed 0–1 polynomial term xy where x is a 0–1 variable and 0 y ≤ 1, we develop a theorem to transfer the xy term into a set of mixed 0–1 linear inequalities. Based on this theorem, a G-FP problem can be solved by a branch-and-bound method to obtain the global solution.

A Superior Representation Method for Piecewise Linear Functions

Yu et al. (Fuzzy Sets and Systems 105 (1999) 429) performed general piecewise necessity regression analysis based on linear programming (LP) to obtain the necessity area. Their method is the same as that according to data distribution, even if the data are irregular, practitioners must specify the number and the positions of change-points. However, as the sample size increases, the number of change-points increases and the piecewise linear interval model also becomes complex. Therefore, this work devises general fuzzy piecewise regression analysis with automatic change-point detection to simultaneously obtain the fuzzy regression model and the positions of change-points. Fuzzy piecewise possibility and necessity regression models are employed when the function behaves differently in different parts of the range of crisp input variables. As stated, the above problem can be formulated as a mixed-integer programming problem. The proposed fuzzy piecewise regression method has three advantages: (a) Previously specifying the number of change-points, then the positions of change-points and the fuzzy piecewise regression model are obtained simultaneously. (b) It is more robust than conventional fuzzy regression. The conventional regression is sensitive to outliers. In contrast, utilizing piecewise concept, the proposed method can deal with outliers by automatically segmenting the data. (c) By employing the mixed integer programming, the solution is the global optimal rather than local optimal solution. For illustrating more detail, two numerical examples are shown in this paper. By using the proposed method, the fuzzy piecewise regression model with detecting change-points can be derived simultaneously.

A fuzzy ranking method with range reduction techniques

Abstract Recently, Li and Chang proposed an approximate model for assortment problems. Although their model is quite promising to find approximately global solution, too many 0–1 variables are required in their solution process. This paper proposes another way for solving the same problem. The proposed method uses iteratively a technique of piecewise linearization of the quadratic objective function. Numerical examples demonstrate that the proposed method is computationally more efficient than the Li and Chang method.

A fuzzy multiobjective program with quasiconcave membership functions and fuzzy coefficients

Abstract Conventional methods of solving nonconvex separable programming (NSP) problems by mixed integer programming methods requires adding numerous 0–1 variables. In this work, we present a new method of deriving the global optimum of a NSP program using less number of 0–1 variables. A separable function is initially expressed by a piecewise linear function with summation of absolute terms. Linearizing these absolute terms allows us to convert a NSP problem into a linearly mixed 0–1 program solvable for reaching a solution which is extremely close to the global optimum.

An approximately global optimization method for assortment problems

Many nonlinear programs can be piecewisely linearized by adding extra binary variables. For the last four decades, several techniques of formulating a piecewise linear function have been developed. By expressing a piecewise linear function with m + 1 break points, the current method requires us to use m additional binary variables and 4m constraints, which causes heavy computation when m is large. This study proposes a superior way of expressing the same piecewise linear function, where only ⌈ log 2m ⌉ binary variables and 8 + 8 ⌈ log 2m ⌉ additive constraints are used. Various numerical experiments demonstrate that the proposed method is more computationally efficient than current methods.

Comments on “fuzzy programming with nonlinear membership functions...”

For ranking alternatives based on pairwise comparisons, current analytic hierarchy process (AHP) methods are difficult to use to generate useful information to assist decision makers in specifying their preferences. This study proposes a novel method incorporating fuzzy preferences and range reduction techniques. Modified from the concept of data envelopment analysis (DEA), the proposed approach is not only capable of treating incomplete preference matrices but also provides reasonable ranges to help decision makers to rank decision alternatives confidently. 2007 Elsevier B.V. All rights reserved.