This paper develops a mathematical model using differential equations and considers a bullwhip effect in a supply chain network with multiple retailers and distributors. To ensure the stability of the entire system and reduce the bullwhip effect, a robust control method and an inventory replenishment policy are proposed. This shows that the choice of the output matrix may reduce the bullwhip effect. It has also observed in the inventory replenishment mechanism may be a negative impact on the robustness of the bullwhip effect. However, the inventory replenishment behavior may lead to the bullwhip effect on the presented model. This means that the complex supply relationships may have a significant role in controlling or reducing the bullwhip effect of fluctuations. تفاصيل المقالة

In this paper, a mixed-integer linearized programming (MINLP) model is presented to design a group layout (GL) of a cellular manufacturing system (CMS) in a dynamic environment with considering production planning (PP) decisions. This model incorporates with an extensive coverage of important manufacturing features used in the design of CMSs. There are also some features that make the presented model different from the previous studies. These include: 1) the variable number of cells, 2) machine depot keeping idle machines, and 3) integration of cell formation (CF), GL and PP decisions in a dynamic environment. The objective is to minimize the total costs (i.e., costs of intra-cell and inter-cell material handling, machine relocation, machine purchase, machine overhead, machine processing, forming cells, outsourcing and inventory holding). Two numerical examples are solved by the GAMS software to illustrate the results obtained by the incorporated features. Since the problem is NP-hard, an efficient simulated annealing (SA) algorithm is developed to solve the presented model. It is then tested using several test problems with different sizes and settings to verify the computational efficiency of the developed algorithm in compare to the GAMS software. The obtained results show that the quality of the solutions obtained by SA is entirely satisfactory in compare to GAMS software based on the objective value and computational time, especially for large-sized problems. تفاصيل المقالة

In this paper, a closed-loop supply chain is modeled to obtain the best allocation and location of retailers including production centers, retailers' centers, probabilistic customers, collection and disposal centers. In this study, by considering electric conversion of CO2 to O2 in vehicles, the amount of environmental pollution is minimized. Furthermore, two strategies are considered to find the best places for retailers by focusing on: 1- the type of expected movement (Rectangular, Euclidean, Euclidean Square, and Chebyshev); 2- expected coverage (distance and time). To this end, a bi-objective nonlinear programming model is proposed. This model concurrently compares strategies 1 and 2 and selects the best competitor. Based on the selected strategy, the best allocation is made by employing a heuristic algorithm and the locations of the best retailers are determined. As the proposed model is NP-hard in its nature of the problem, a meta-heuristic, namely, a non-dominated sorting genetic algorithm is employed for the solution process. Eventually, to authenticate and confirm the effectiveness of the suggested model, a numerical example is given and solved utilizing optimization software, and the results are analyzed. تفاصيل المقالة