An augmented Lagrangian approach with general constraints to solve nonlinear models of the large-scale reliable inventory systems

The Augmented Lagrangian method (ALM) is one of the algorithms in a class of methods for constrained optimization of nonlinear problems (NLP) that seeks a solution by replacing the original constrained problem using a sequence of unconstrained subproblems. Also known as the method of multipliers, the ALM approach introduces explicit Lagrangian multiplier estimates at each step. In this paper, an ALM is developed to solve the nonlinear models of the large-scale inventory systems. The proposed ALM is based on successive minimization of the augmented Lagrangian with respect to the possibly occurring between iterations. Our suggested approach is relatively easy to implement because the main computational operation at each iteration of NLP models is minimization of the smooth function to solve the bound-constrained subproblem. Accordingly, a large-scale NLP inventory system is designed and optimized using the ALM. The objectives are to simultaneously minimize the total inventory cost and maximize the total reliability in large-scale NLP inventory systems, while the constraints are satisfied. The results of numerical analyses, and performance comparison show that the proposed approach has satisfactory performance in terms of optimality criteria such as quality of solutions, complementarity, infeasibility, and optimality error.