In this paper we investigate the economic lotsizing problem with the remanufacturing and joint setups case ELSRj where remanufacturing and manufacturing processes share the same production line This problem is modeled as a Mixed Integer Programming MIP formulation and is classified as an NPhard problem In order to strengthen this basic ELSRj model formulation an extended reformulation namely a shortest path SP reformulation and also l S WW inequalities are proposed for this problem Then these formulations are compared with another existing extended reformulation which is a facility location FL reformulation The findings show that all proposed and existing formulations are proven to be theoretically equivalent A computational analysis of average percentage of duality gap is then presented which demonstrates the equivalence and the effectiveness of the proposed and existing formulations These formulations outperform the basic formulation for all data instances tested..

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