Modelling the Building to Order Supply Chain Management Considering Restriction on Capacities Using Lagrangian Relaxation (LR) Algorithm

Processes of production and supply of products have been changed in pattern in condition of intensifying the competitive atmosphere and are studied in the form of a supply chain network. In the meantime, the importance of the flow of materials in the supply network, and the distribution of products in the distribution network is more important among the three streams of finance, information, and materials. More attention to customer has leaded production process to build to order (BTO). Distribution chain as a part of supply chain is studied in this paper and a new mathematical model is produced for build to order supply chain (BTOSC).  Providing constrains are considered in order to close condition to real world. There is kinds of production units, distribution centers, and retailers. After deterministic an order, it will be sent from distribution centers to a retailer or from a production unit to retailers directly. The objective function is to maximize total profit. First, a new mixed integer linear programing model is developed for the considered problem. Due to the complexity of mathematical model, a new algorithm is introduced to solve it based on Lagrangian Relaxation (LR). Finally, the efficiency of the proposed algorithm is evaluated by solving a numerical example.