The hybrid vehicle routing problem is an extension of the green vehicle routing problem where vehicles can use different fuels. In this research, a bi-objective hybrid vehicles routing problem is presented and solved bu considering alternative paths, various lengths and reliabilities. The first objective function minimizes overall system costs and fuel consumption and greenhouse gas emissions, whereas the second objective function maximizes the reliability of the entire system with alternative paths and several reliabilites. The proposed model is formulated as mixed-integer nonlinear programming and a bi-objective simulated annealing (MOSA) algorithm along with the e-constraint method is used as solution strategy. The implementation of the proposed method is presented using some numerical instances.

In recent years, one of the goals of any company is to increase overall production and process reliability. Hereupon supply chain reliability has been gaining growing attention and provides a technical framework for quantifying supply chain risks and uncertainties. In this paper, supply chain reliability was investigated in a two-stage stochastic programming model to design reliable closed-loop green four-echelon forward/backward supply chain networks. The purpose of this model was to maximize the total reliability of the supply chain based on the structural reliability theory. Our proposed model also minimized the cost of the supply chain by definition of recycling centres and the cost of penalizing unauthorized carbon emission and damages. The model optimized the locations of factories, warehouses, and recycling centres considering stochastic modes for demands and carbon price, as well as the flow between different sectors and the optimal orders. As the proposed model was a mixed-integer nonlinear problem, both e-constraint method and the metaheuristic algorithm (NSGA-II) were used in different scales and the sensitivity analysis was performed for critical parameters.

In this paper, an integrated layout model has been considered to incorporate intra and inter-department layout. In the proposed model, the arrangement of facilities within the departments is obtained through the QAP and from the other side the continuous layout problem is implemented to find the position and orientation of rectangular shape departments on the planar area. First, a modified version of QAP with fewer binary variables is presented. Afterward the integrated model is formulated based on the developed QAP. In order to evaluate material handling cost precisely, the actual position of machines within the departments (instead of center of departments) is considered. Moreover, other design factors such as aisle distance, single or multi row intra-department layout and orientation of departments have been considered. The mathematical model is formulated as mixed-integer programming (MIP) to minimize total material handling cost. Also due to the complexity of integrated model a heuristic method has been developed to solve large scale problems in a reasonable computational time. Finally, several illustrative numerical examples are selected from the literature to test the model and evaluate the heuristic.

In this paper, we evaluate the performance of a supply chains (SCs) under uncertainty with different components such as direct costs, operational costs, transaction expenses, order lead time, product flexibility and net profit. Data Envelopment Analysis (DEA) can be used for measuring the performance of supply chain problems. On the other hand, robust optimization approach is a powerful technique for handling problems faced with various environmental uncertainties. This paper combines these two concepts and proposes a method to evaluate SCs performance. The results of the proposed method, under any different environmental situation, show which ranking of SC’s performance is better in a network. The preliminary results of the implementation of a real-world case study indicates that the method could be successfully used for performance measurement.

Formulation and evaluation of strategy play important role in the strategy management. Strength, Weakness, Opportunity and Threats (SWOT) is a famous approach to formulate strategy planning, which relies on external and internal factors. Identifying these factors precisely is very critical for any organization and manager. This study aims at providing a quantitative basis to analytically determine the ranking of the factors in SWOT analysis via Evidential Reasoning (ER) approach. This paper applies SWOT and Richard Rumelt & apos; s criteria to evaluate strategies in Evidential Reasoning approach. The ER approach has been developed to support MADA under uncertainty. It is based on Dempster’s rule for evidence combination and uses belief functions for dealing with probabilistic uncertainty and ignorance. This research is the first study in the ranking the factors of SWOT and Richard Rumelt approach. An illustrative example is also presented to show the efficiency of our model.