Lagrangian relaxation of the generic materials and operations planning model

Abstract

The supply chain management requires increasingly proposals for the production programming planning that brings together its special singularities. Solving coexisting products and alternative processes or by-products must be allowed by the mathematical programming models. The generic materials and operations planning (GMOP) formulation allows operating with different materials and process lists. The paper presents a procedure to solve the versatile GMOP model by the Lagrange Relaxation. The subgradient update method of the lagrangian multiplier is compared with a linear update method. Obtaining lower bound faster compared to the linear method is allowed by the subgradient method, but the linear method provides better solutions after certain iterations.

Collaborative Distributed Planning with Asymmetric Information. A Technological Driver for Sustainable Development

“…With Lagrangian decomposition, a structured decomposition of the problem is used to achieve coordination. Lagrange multipliers are generally updated with the subgradient method [55][56][57][58], as pointed out by Rius-Sorolla et al [59].…”

Modelo programación lineal para minimizar los costos de producción de una empresa de cintas adhesivas

“…Por otro lado, para la planeación de la producción en general, se conocen de otros modelos heurísticos para resolver problemas de planeación que también apuntan a minimizar costos asociados a niveles de inventario, setup y operaciones [12], así como algortimos para determinar la cantidad a producir en sistemas de coproducción teniendo en cuenta ventajas de costos [13], y para la planificación de requerimientos de materiales [14]. Se conoce también del uso de herramientas y métodos como la aplicación de la relajación lagragiana para resolver problemas de planificación de la producción [15].…”

A Tabu List-Based Algorithm for Capacitated Multilevel Lot-Sizing with Alternate Bills of Materials and Co-Production Environments

“…The algorithm stops with the fulfillment of a maximum number of iterations It. Table 4 shows the parameters used for the definition of the randomly-generated test instances (Based on the methodology in [12,14] and the values defined in [23]). Uniform [5,10] Nine groups of test instances were generated, according to three different sizes: Small (TI1-TI3), medium (TI4-TI6), and large (TI7-TI9).…”

“…This model was proposed in 2011 [17,18] as a robust mixed integer programming (MIP) problem. Since 2013 [19,20], the functioning of GMOP has been improved with the implementation of mathematical relaxation methods and its efficiency in practical applications has been demonstrated (e.g., in the automotive sector) [21][22][23].…”