∂νu = 0, on ∂Ω, where ν denotes a unit vector field normal to ∂Ω and where ε λ ∈ R corresponds to the Lagrange multiplier associated to the constraint V (u) = c0 |Ω|. One can also ignore the volume constraint, in which case a critical point would satisfy equation (1.1) with λ = 0. Since classical methods of the calculus of variation apply, there is no difficulty in finding minimizers of Eε. The...

In this paper, a new general scalarization technique for solving multiobjective optimization problems is presented. After studying the properties of this formulation, two problems as special cases of this general formula are considered. It is shown that some well-known methods such as the weighted sum method, the -constraint method, the Benson method, the hybrid method and the elastic -constrai...

This paper presents a novel bi-objective multi-product capacitated vehicle routing problem with uncertainty in demand of retailers and volume of products (UCVRP) and heterogeneous vehicle fleets. The first of two conflict fuzzy objective functions is to minimize the cost of the used vehicles, fuel consumption for full loaded vehicles and shortage of products. The second ...

This paper considers a scheduling problem of a set of independent jobs on unrelated parallel machines (UPMs) that minimizesthe maximum completion time (i.e., makespan or ), maximum earliness ( ), and maximum tardiness ( ) simultaneously. Jobs have non-identical due dates, sequence-dependent setup times and machine-dependentprocessing times. A multi-objective mixed-integer linear programmi...

In this paper, a bi-objective mixed-integer linear optimization model for Closed-loop Supply Chain Network Design Problem (CLSCND) is developed. The proposed model includes both the forward and reverse directions and includes different types of facilities, namely, manufacturing/remanufacturing centers, warehouses, and disassembly centers. The first objective function tried to minimize the total...

Generally, human resources play an important role in manufacturing systems as they can affect the work environment. One of the most important factors affecting the human resources is being an interactional interest among the workers in the workshops. If the workers in a manufacturing cell have the highest surface of the interactional interest level, it causes a significant raise in coordination...

in this research, efficiency of iranian forest and rangeland decision making unit was assessed using non-parametric method. inputs and outputs determined by field research and with applying a delphi method the final input and output variables selected. forty five wood-producing units (forestry plans) in three northern iranian province were studied using data envelopment analysis. the efficiency...