Yan-Kui Liu

Stochastic p-hub center problem with discrete time distributions

This paper considers a stochastic p-hub center problem, in which travel time is characterized by discrete random vector. The objective of the problem is to minimize the efficient time point of total travel time. For Poisson travel time, the problem is equivalent to a deterministic programming problem by finding the quantiles of the related probability distribution functions. For general discrete distributed travel time, the proposed problem is equivalent to a deterministic mixed-integer linear programming problem. So, we can employ conventional optimization algorithms such as branch-and-bound method to solve the deterministic programming problem. Finally, one numerical example is presented to demonstrate the validity of the proposed model and the effectiveness of the solution method.

Fuzzy generalized assignment problem with credibility constraints

In this paper, we firstly discuss some properties with respect to the credibility constraints. After that, we construct a new class of fuzzy generalized assignment problem with credibility constraints, in which the cost and time are uncertain and assumed to be characterized by fuzzy variables with known possibility distributions. The problem is a very changeable combinational optimization and it is always different to solve the programming problems using the classical algorithms. In some special cases, we can transform the objective and the credibility constraints into the equivalent linear form by means of the results that we deduce. As a consequence, we can solve it with standard software. Finally, we present one application example encountered by the Canadian Department of Transportation to demonstrate the proposed method.

The variance formulas for triangular fuzzy random variables

Fuzzy random variable is a measurable mapping from a probability space to a collection of fuzzy variables. The variance is a fundamental concept for fuzzy random variables. Due to the difficulties involved in computing variance, we usually focus on searching for good approximation and simulation methods to solve a complex model. Based on the definition of the variance of a fuzzy random variable, this paper first presents precision formulas for the variances of triangular fuzzy random variables, which can be applied to fuzzy random optimization problems as we design algorithms to solve fuzzy random programming. Then, to apply the variance formulas, we provide two numerical examples.

Two-Stage Fuzzy Optimization of an MPMP Production Planning Model

Based on credibility theory and two-stage fuzzy optimization method, this paper presents a class of multi-product multi-period (MPMP) production planning problem. Some basic properties about the two-stage production-planning model are discussed. In addition, a heuristic algorithm, which combines fuzzy simulations and genetic algorithm (GA), is designed to solve the production planning problem, and a numerical example about the three-product three-period production planning problem is given to show the feasibility of the algorithm

On the independence of fuzzy vectors

Fuzzy variable is a function from a possibility space to the real line. By analogy of the independence of random variables, there are similar terms for fuzzy variables such as unrelated fuzzy variables, noninteractive fuzzy variables, and independent fuzzy variables. The purpose of this work is to discuss the relations among these terms. Toward this end, the work first defines the marginal possibility distributions of a fuzzy vector, and then gives a simple approach to define the independent fuzzy variables. After that, the equivalence of unrelated, noninteractive, and independent fuzzy variables are proved in the framework of possibility theory.

A multiperiod fuzzy production planning and sourcing problem with service level constraints

In this paper, we consider a multiperiod fuzzy production and sourcing problem that a manufacturer has a number of plants and subcontractors. The manufacturer has to meet the products demand according to the service level requirements set by its customers. The demand for each product in each period is assumed to be a fuzzy variable. Since the proposed model is too complex that the conventional optimization methods cannot be used. To solve the problem, a heuristic solution method, which combines approximation method, genetic algorithm (GA) and neural network (NN), is proposed. We provide a numerical example to illustrate the feasibility and effectiveness of the designed algorithm.

Fuzzy two-stage mathematical programming problems

In this paper, a new class of fuzzy programming problems, called fuzzy two-stage programming, is first presented. Then some basic properties of the two-stage model are discussed. In addition, three solution concepts, wait-and-see solution, here-and-now solution and expected value solution are defined for fuzzy programming. After that, two important indexes, the expected value of perfect information (EVPI) and the value of fuzzy solution (VFS), are introduced, and their relations are illustrated via numerical examples.

Fuzzy Two-Stage Supply Chain Problem and Its Intelligent Algorithm

This paper presents a new class of fuzzy two-stage supply chain problems, in which transportation costs and demands are characterized by fuzzy variables with known possibility distributions. Since fuzzy parameters are often with infinite supports, the conventional optimization algorithms cannot be used to solve the proposed supply chain problem directly. To avoid this difficulty, an approximation method is developed to turn the original supply chain problem into a finite dimensional one. Generally, the approximating supply chain problem is neither convex nor linear. So, to solve the approximating supply chain problem, we design a hybrid algorithm by integrating approximation method, neural network (NN) and particle swarm optimization (PSO). Finally, one numerical example is presented to demonstrate the effectiveness of the designed algorithm.

The Properties of Two-Stage Fuzzy Random Programming

Based on fuzzy random theory, a new class of two-stage fuzzy random model is studied in this paper. In case of general recourse matrix, some fundamental properties of two-stage fuzzy random programming are discussed, including the convexity of feasible set as well as convexity of objective function.

Two-Stage Fuzzy Optimization of a Fuzzy Production Game Model

Based on credibility theory and two-stage optimization method, this paper presents a new class of production games in the fuzzy setting and some basic properties about the two-stage production games model are discussed. In additional, a hybrid algorithm, which combines the approximating method, neural network (NN) and genetic algorithm (GA), is designed to solve the production games problem, and a numerical example about distribution games is given to show the feasibility of the algorithm.