benders decomposition algorithm

Designing an efficient construction supply chain involves numerous complexities. Therefore, the imperative of designing an appropriate supply chain, considering the high diversity of resources (nonrenewable), holds significant importance.  Given the variable nature of the project environment, the dynamic progress of the project, and the risks associated with construction projects, the project may deviate from the scheduled timeline. On the other hand, the quality of resources plays a crucial role in the construction quality of construction projects. Therefore, in this study, a multi-objective mixed-integer programming model is proposed for the design of a two-echelon supply chain network in the construction industry. The objectives of the model include minimizing supply chain costs, minimizing deviation from resources time delivery, and maximizing the quality of resources. This framework is capable of dynamically scheduling resources in terms of timing and delivery, as well as selecting appropriate suppliers restricted to authorized facilities within a network. Both classical methods and the Benders Decomposition Algorithm are employed to solve the presented model. The problem was solved for three sizes. The Benders Decomposition Algorithm was able to efficiently solve the problem for all three sizes in a very short amount of time.

Warehouse, as the main link in any large and complex organization, establishes a direct relationship between different parts of the organization and the supply chain. Today, the warehouses are designed to be built in such a way that they can speed up various warehouse operations. Therefore, it is important to attempt to move toward the just-in-time system. Adaptation to this system requires distribution centers. One solution is to use a        cross-dock. In this article, the optimal retail cross-dock layout is investigated by considering distribution operations as JIT. Layout is defined as the allocation of warehouse floor space to retailers. In this regard clusters of the warehouse floor locations are considered to assign to different retailers. Each cluster includes a group of multiple neighboring floor locations that are adjacent to each other and placed one after the other. Products are picked up at the receiving docks and are transported along with the warehouse up to the location where the products for a given retailer are located. The purpose is to determine the allocation of warehouse floor locations to retailers to minimize the distance traveled in the warehouse. Different scenarios for layout of the warehouse have been studied and analyzed. An integer linear programming model is presented and the Benders decomposition method is also used to solve the problem and the results are presented. Finally, ideas and recommendations are presented to develop the model.