This paper proposes a robust model for optimizing collaborative reverse supply chains. The primary idea is to develop a collaborative framework that can achieve the best solutions in the uncertain environment. Firstly, we model the exact problem in the form of a mixed integer nonlinear programming. To regard uncertainty, the robust optimization is employed that searches for an optimum answer with nearly all possible deviations in mind. In order to allow the decision maker to vary the protection level, we used the "budget of uncertainty" approach. To solve the np-hard problem, we suggest a hybrid heuristic algorithm combining dynamic programming, ant colony optimization and tabu search. To confirm the performance of the algorithm, two validity tests are done firstly by comparing with the previously solved problems and next by solving a sample problem with more than 900 combinations of parameters and comparing the results with the nominal case. In conclusion, the results of different combinations and prices of robustness are compared and some directions for future researches are suggested finally.

Abstract This author introduces the concept of Stepwise Strategy Approach (SSA) for dealing with a number of problems arises in the current age of technology. This new idea is combined with the knowledge of Grey Theory for adding flexibility to decision making process. Grey theory is useful for grasping the ambiguity exists in the utilized information and the fuzziness appears in the human judgments and preferences. This article is a very useful source of information for Fuzzy Grey and decision making using more than one decision makers in fuzzy environment. A case study on system selection comprised of 12 attributes and 4 alternatives is constructed and solved by the proposed method and the results are analyzed. For the validation of the results obtained by the Grey theory, the fuzzy VIKOR and Fuzzy TOPSIS were employed for computational purposes. The results of these three approaches on the proposed case study are closely related. Due to the fact that this author proposes the “Stepwise Strategy” approach for implementing a new technology in industries, where already the management of an older compatible type of technology is in existence, along with the grey theory concept and data whitenization approach, its contribution to the literature of operations research is highly recognizable.