Implementation of scheduling algorithm for optimisation by Lagrangian decomposition model

This paper mainly deals with the design and analysis of Lagrangian model using cyclic scheduling algorithm. An integer programming (IP) model is formulated and then decomposed by using Lagrangian relaxation technique. Two approaches were implemented, the first approach is based on the relaxation of the preference constraints and the second approach is based on the relaxation of the demand constraints. Since proper bounds were not obtained by relaxing the preference constraints, a solution methodology is developed based on the relaxation of demand constraints. Many researchers have discussed the different type of methods, such as bundle method, heuristic and variable fixing. A duality gap exists between the lower bound and the objective function value provided by an IP feasibility heuristic. A variable fixing scheme is introduced for the convergence criteria. Based on the numerical calculations and graphical representations, the minimum cost is obtained to cover the uncovered shifts.