Lagrangian based approach to solve a two level capacitated lot sizing problem

• Main Authors: Mayank Verma, R.R.K. Sharma
• Format: Article
• Language: English
• Published: Taylor & Francis Group 2015-12-01
• Series: Cogent Engineering
• Subjects: multi-level; lot sizing; Lagrangian; knapsack; bounded variable linear program
• Online Access: http://dx.doi.org/10.1080/23311916.2015.1008861

Two-level, multi-item, multi-period-capacitated dynamic lot-sizing problem with inclusions of backorders and setup times, TL_CLSP_BS, a well-known NP-hard problem, is solved using a novel procedure. Lagrangian relaxation of the material balance constraint reduces TL_CLSP_BS to a single-constraint continuous knapsack problem. Reduced problem is solved using bounded variable linear programs (BVLPs). We obtain promising bounds, which provides a better start to the branch-and-bound procedure. Limited empirical investigations are carried out on four problem sizes. In terms of computational time, the developed procedure is efficient than the CPLEX solver of GAMS. Further, while GAMS could not solve the largest problem size considered here, our procedure could solve the same in around one second time. This clearly highlights the efficacy of the developed procedure. The solution technique is applicable to any problem structure, which is reducible to the application of BVLPs.