In this paper, a novel chance-constrained programming model has been proposed for handling uncertainties in green closed loop supply chain network design. addition to locating the facilities and establishing flow between them, also determines transportation mode facilities. The objective functions are applied minimize expected value variance of total cost CO 2 released is controlled by providin...

In a robust parameter design (RPD) problem, the experimenter is interested to determine the values of con-trol factors such that responses will be robust or insensitive to variability of the noise factors. Response sur-face methodology (RSM) is one of the effective methods that can be employed for this purpose. Since quality of products or processes is usually evaluated through several quality ...

Optimization of multi response surface (MRS) in robust designs is applied to determine optimum characteristics of a process in a satisfactory region and reduce variation of responses. In this paper, a methodology is proposed for optimizing multi response surface in robust designs, which optimizes mean and variance simultaneously by applying fuzzy set theory. At first, a method is proposed to co...

Urbanization has become a main challenge all over developing countries in the 21st Century. However, decision making should take into account the different national situations with their complex factors to achieve sustainable development. As standards of living have risen in urban areas, local/neighbor urbanization has become a coming trend in China. With this in mind, the paper focuses on the ...

We address the no-wait k-stage flexible flowshop scheduling problem where there are m identical machines at each stage. The objectives are to schedule the available n jobs so that makespan and mean tardiness of n jobs are minimized. Sequence-dependent setup times are treated in this problem as one of the prominent practical assumptions. This problem is NP-hard, and therefore we present a new mu...

The Minimum Circuit Size Problem (MCSP) asks for the size of the smallest boolean circuit that computes a given truth table. It is a prominent problem in NP that is believed to be hard, but for which no proof of NP-hardness has been found. A significant number of works have demonstrated the central role of this problem and its variations in diverse areas such as cryptography, derandomization, p...

In the Subset Sum problem, we are given n integers a1, . . . , an and a target number t, and are asked to find the subset of the ai’s such that the sum is t. A version of the subset sum problem is the Random Modular Subset Sum problem. In this version, the ai’s are generated randomly in the range [0,M), and we are asked to produce a subset of them such that the sum is t(modM). The hardness of R...

The benefit of integrating product design decisions and supply chain design decisions has been recognized by researchers. Such integration can facilitate better communication between design teams and operations groups. Consequently, potential supply chain risks can be highlighted and addressed before the launch of a new product. Modularization is one of the most critical elements for both produ...