sohrab effati

In this paper, necessary optimality conditions for a class of optimal control problems containing time-varying delays in control and state variables are discussed. There is an important aspect of these problems in that time-varying delays are applied to both state and control variables. Also, the cost functional of problems is influenced by the time-varying delays in state and control. We prove necessary optimality conditions in this study. A key aspect of the proof is calculating the variations of control and state variables when there are time-dependent delays. we make use of appropriate changing variables to derive these variations. In order to illustrate the use of these conditions, several examples are solved and numerical results are presented. At the end, some conclusions are drawn.

Finished products and manufacturing plants are some elements of the production system in the supply chain, and there are other manufacturing plants. They produce work in process and finished products and hold them in warehouses. So, they need to plan and control production and inventories. Isolated planning and control by different manufacturers increase inventories in them, and then they must plan and control integratory. This paper presents an iterative approach for solving the optimal control problem with bounded control variables. The projection function constructs ‎the iterative method to approximate the control law. Employing the approximation of control law, the approximation of state and the co-state variables are obtained. For this purpose, we apply the Hamiltonian of the optimal control problem. From the Hamiltonian, the approximation of control law and then the approximation of state law is obtained. A simple example is given to compare the results with another published paper. Also, a case study on production planning in a three-stock reverse logistics system with deteriorating items is derived to show the method's performance.

In this paper, as an extension of Pareto optimality concepts for multi objective programming problems to fuzzy multi objective linear programming (FMOLP) problems, different types of Pareto optimal solutions (POSs), namely, weakly, strictly, and properly POSs are defined on the basis of α-cuts of fuzzy numbers. Then a method for solving FMOLP problems is proposed to obtain them. It is shown that they can be obtained by solving some non fuzzy multi objective linear programming problems. A numerical example is solved to illustrate the method.

We apply a new method to solve fractional partial differential equations (FPDEs) with proportional delays. The method is based on expanding the unknown solution of FPDEs with proportional delays by the basis of Bernstein polynomials with unknown control points and uses operational matrices with the least-squares method to convert the FPDEs with proportional de lays to an algebraic system in terms of Bernstein coefficients (control points) approximating the solution of FPDEs. We use the Caputo derivatives of de gree 0 < α ≤ 1 as the fractional derivatives in our work. The main advantage of using this technique is that the method can easily be employed to a variety of FPDEs with or without proportional delays, and also the method offers a very simple and flexible framework for direct approximating of the solution of FPDEs with proportional delays. The convergence analysis of the present method is discussed. We show the effectiveness and superiority of the method by comparing the results obtained by our method with the results of some available methods in two numerical examples.

The optimal allocation of natural gas resources to various uses such as final and intermediate consumption, injection into oil fields, and exports can help policymakers to use this kind of resources efficiently. Empirical evidence support using hyperbolic discount rates instead of fixed discount rates in the economic literature. The purpose of this study is to maximize the social welfare function and analyze the optimal paths of different uses of natural gas over the next three decades based on a nonlinear dynamic programming model using a hyperbolic discount rate. The results show that in the current situation, gas exports do not maximize social welfare, but by expanding Iran's natural gas production, exports will lead to maximizing social welfare.