Y. C. E. Lee

Closed-Loop Supply Chain Network under Oligopolistic Competition with Multiproducts, Uncertain Demands, and Returns

We develop an equilibrium model of a closed-loop supply chain (CLSC) network with multiproducts, uncertain demands, and returns. This model belongs to the context of oligopolistic firms that compete noncooperatively in a Cournot-Nash framework under a stochastic environment. To satisfy the demands, we use two different channels: manufacturing new products and remanufacturing returned products through recycling used components. Since both the demands and product returns are uncertain, we consider two types of risks: overstocking and understocking of multiproducts in the forward supply chain. Then we set up the Cournot-Nash equilibrium conditions of the CLSC network whereby we maximize every oligopolistic firms expected profit by deciding the production quantities of each new product as well as the path flows of each product on the forward supply chain. Furthermore, we formulate the Cournot-Nash equilibrium conditions of the CLSC network as a variational inequality and prove the existence and the monotonicity of the variational inequality. Finally, numerical examples are presented to illustrate the efficiency of our model.

Intelligent Optimization Algorithms: A Stochastic Closed-Loop Supply Chain Network Problem Involving Oligopolistic Competition for Multiproducts and Their Product Flow Routings

Recently, the first oligopolistic competition model of the closed-loop supply chain network involving uncertain demand and return has been established. This model belongs to the context of oligopolistic firms that compete noncooperatively in a Cournot-Nash framework. In this paper, we modify the above model in two different directions. (i) For each returned product from demand market to firm in the reverse logistics, we calculate the percentage of its optimal product flows in each individual path connecting the demand market to the firm. This modification provides the optimal product flow routings for each product in the supply chain and increases the optimal profit of each firm at the Cournot-Nash equilibrium. (ii) Our model extends the method of finding the Cournot-Nash equilibrium involving smooth objective functions to problems involving nondifferentiable objective functions. This modification caters for more real-life applications as a lot of supply chain problems involve nonsmooth functions. Existence of the Cournot-Nash equilibrium is established without the assumption of differentiability of the given functions. Intelligent algorithms, such as the particle swarm optimization algorithm and the genetic algorithm, are applied to find the Cournot-Nash equilibrium for such nonsmooth problems. Numerical examples are solved to illustrate the efficiency of these algorithms.

Optimal control solutions to the maximum volume isoperimetric pillars problem

This paper extends the isoperimetric problem. The problem is to find an enclosed cross-sectional/base region of a pillar defined by a simple closed curve of fixed perimeter such that the volume of the constructed pillar, bounded above by a relatively smooth ceiling, is maximized. Greens Theorem is applied in the formulation of the problem such that the problem can be transformed into canonical form handled by MISER3. For the case of multiple pillars, a novel elliptic separation technique is developed for multiple pillars constructions. This technique is used to ensure that the cross-sectional regions of any pillars are separated. Illustrative examples are provided to demonstrate the effectiveness of the technique developed.

A Computational Optimal Control Approach to the Design of a Flexible Rotating Beam With Active Constrained Layer Damping

In this paper, a computational approach is adopted to solve the optimal control and optimal parameter selection problems of a rotating flexible beam fully covered with active constrained layer damping (ACLD) treatment. The beam rotates in a vertical plane under the gravitational effect with variable angular velocity and carries an end mass. Tangent coordinate system and the moving coordinate system are used in the system modeling. Due to the highly nonlinear and coupled characteristics of the system, a relative description method is used to represent the motion of the beam and the motion equations are set up by using relative motion variables. Finite element shape functions of a cantilever beam [1] are used as the displacement shape functions in this study. Lagrangian formulation and Raleigh-Ritz approach [2] are employed to derive the governing equations of motion of the nonlinear time-varying system. The problem is posed as a continuous-time optimal control problem. The control function parameters are the control gains. The two system parameters are the thickness of the constraining layer and the viscoelastic material layer. The software package MISER3.2, which is based on the Control Parametrization and the Control Parametrization Enhancing Transform (CPET) techniques is used to solve the combined problems. The optimal solution takes the end deflection, control voltage and the total weight into account. Results show that substantial improvements are obtained with ACLD as compared to the passive constrained layer damping (PCLD) treatment.Copyright