A Comparative Study on Meta Heuristic Algorithms for Solving Multilevel Lot-Sizing Problems

Material requirements planning (MRP) is an old field but still now plays an important role in coordinating replenishment decision for materials/components of complex product structure. As the key part of MRP system, the multilevel lot-sizing (MLLS) problem concerns how to determine the lot sizes for producing/procuring multiple items at different levels with quantita‐ tive interdependences, so as to minimize the total costs of production/procurement setup and inventory holding in the planning horizon. The problem is of great practical importance for the efficient operation of modern manufacturing and assembly processes and has been widely studied both in practice and in academic research over past half century. Optimal solution algorithms exist for the problem; however, only small instances can be solved in reasonable computational time because the problem is NP-hard (Steinberg and Napier, 1980). Early dynamic programming formulations used a network representation of the problem with a series structure (Zhangwill, 1968,1969) or an assembly structure (Crowston and Wagner,1973). Other optimal approaches involve the branch and bound algorithms (Afentakis et al., 1984, Afentakis and Gavish, 1986) that used a converting approach to change the classical formulation of the general structure into a simple but expanded assembly structure. As the MLLS problem is so common in practice and plays a fundamental role in MRP system, many heuristic approaches have also been developed, consisting first of the sequential application of the single-level lot-sizing models to each component of the product structure (Yelle,1979, Veral and LaForge,1985), and later, of the application of the multilevel lot-sizing models. The multilevel models quantify item interdependencies and thus perform better than the single-level based models (Blackburn and Millen, 1985, Coleman and McKnew, 1991).