A NOVEL MIXED INTEGER PROGRAMMING FORMULATION AND PROGRESSIVELY STOCHASTIC SEARCH FOR CAPACITATED LOT SIZING

The capacitated multi-level lot sizing problem is to schedule a number of different items with a bill-of-materials structure over a horizon of finite periods.To advance techniques of solving this class of problems,this paper proposes a new mixed integer programming formulation.Theoretical proofs and computational tests are provided to show that this formulation is able to provide better linear programming relaxation lower bounds than a previously-proposed strong mixed integer programming formulation.Based on the new strong formulation,a progressively stochastic search approach is proposed for solving the problem.Computational results showed that the approach generates high quality solutions,especially for problems of large sizes.