Selection of vendors—a mixed-integer programming approach
CIE '96 Proceedings of the 19th international conference on Computers and industrial engineering
Theory and Practice of Uncertain Programming
Theory and Practice of Uncertain Programming
A fuzzy goal programming approach for vendor selection problem in a supply chain
Computers and Industrial Engineering
Fuzzy programming with recourse
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Material Requirement Planning with fuzzy constraints and fuzzy coefficients
Fuzzy Sets and Systems
A steady-state genetic algorithm for multi-product supply chain network design
Computers and Industrial Engineering
A discrete particle swarm optimization algorithm for scheduling parallel machines
Computers and Industrial Engineering
Analyzing the evolutionary stability of the vendor-managed inventory supply chains
Computers and Industrial Engineering
An application of swarm optimization to nonlinear programming
Computers & Mathematics with Applications
Expected value of fuzzy variable and fuzzy expected value models
IEEE Transactions on Fuzzy Systems
Convergent results about the use of fuzzy simulation in fuzzy optimization problems
IEEE Transactions on Fuzzy Systems
A multi-period stochastic production planning and sourcing problem with discrete demand distribution
ICSI'11 Proceedings of the Second international conference on Advances in swarm intelligence - Volume Part II
A bilevel fuzzy principal-agent model for optimal nonlinear taxation problems
Fuzzy Optimization and Decision Making
Minimum risk criterion for uncertain production planning problems
Computers and Industrial Engineering
Computers and Industrial Engineering
On the correlations between fuzzy variables
ICSI'10 Proceedings of the First international conference on Advances in Swarm Intelligence - Volume Part II
A class of fuzzy portfolio optimization problems: E-S models
ICSI'10 Proceedings of the First international conference on Advances in Swarm Intelligence - Volume Part II
Computers and Industrial Engineering
A fuzzy supply chain contract problem with pricing and warranty
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
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This paper presents a new class of two-stage fuzzy material procurement planning (MPP) models with minimum-risk criteria, in which the material demand, the spot market material unit price and the spot market material supply quantity are uncertain and assumed to be fuzzy variables with known possibility distributions. We formulate the two-stage MPP model with the objective of maximizing the credibility of the total material procurement costs less than a given allowable investment level, and the credibility can be regarded as the material procurement risk criteria in a fuzzy environment. Since the fuzzy material demand, the fuzzy spot market material unit price and the fuzzy spot market material supply quantity are usually continuous fuzzy variables with infinite supports, the proposed MPP model belongs to an infinite-dimensional optimization problem that cannot be solved directly. To avoid this difficulty, we apply an approximation approach (AA) to the proposed two-stage fuzzy MPP model, and turn it into an approximating finite-dimensional optimization one. The convergence about the objective function of the approximating two-stage MPP model to that of the original two-stage MPP one is also discussed. Since the exact analytical expression for the objective function in the approximating fuzzy MPP model is unavailable, and the approximating MPP model is a mixed-integer program that is neither linear nor convex, traditional optimization algorithms cannot be used to solve it. Therefore, we develop two heuristic algorithms to solve the approximating MPP model. The first is a particle swarm optimization (PSO) algorithm based on the AA, and the second is a hybrid PSO algorithm which based on the AA and a neural network (NN). Finally, we provide an actual optimization problem about the fuel procurement to compare the effectiveness of the designed algorithms.