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The capacitated lot sizing problem (CLSP) is one of the most important production planning problems which has been widely studied in lot sizing literature. The CLSP is the extension of the Wagner-Whitin problem where there is one product and no capacity constraints. The CLSP involves determining lot sizes for multiple products on a single machine with limited capacity that may change for each planning period. Determining the right lot sizes has a critical importance on the productivity and success of organizations. The paper aims to discuss these issues.

This study focuses on the CLSP with setup carryover and backordering. The literature focusing on this problem is rather limited. To fill this gap, a number of problem-specific heuristics have been integrated with fix-and-optimize (FOPT) heuristic in this study. The authors have compared the performances of the proposed approaches to that of the commercial solver and recent results in literature. The obtained results have stated that the proposed approaches are efficient in solving this problem.

The computational experiments have shown that the proposed approaches are efficient in solving this problem.

To address the solution of the CLSP with setup carryover and backordering, a number of heuristic approaches consisting of FOPT heuristic are proposed in this paper.