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.

To reduce the environmental Pollution emissions caused by market activities, cold chain logistics companies also considered the emission of harmful gases for better service in satisfying customers’ demands. In the cold supply chain, goods are supplied and distributed that become corrupt and degraded over time. Therefore, to keep such goods fresh, the temperature must be constantly and continuously controlled, which in turn requires more fuel consumption. Also, in vehicle routing problem, the travel time of a route and fuel consumption does not only depend on the distance traveled, but also on the speed and time of day when that route is traveled. In this study, a new mixed-integer optimization model of the vehicle routing problem in a cold supply chain concerning congestion is presented with the aim is to minimize costs of Pollution emissions. In this model, in addition to the cost of the environmental Pollution emissions, other costs are considered, including the vehicle operating cost, transportation, loss of quality, product freshness, and penalty cost for arriving outside the customer's time window. In continuing, a solution method based on Benders decomposition is applied to solve the proposed model for large size networks. The computational results showed that the presented model provides the optimal route and travel time of the vehicle by considering the reduction of pollution and the appropriate speed. Also, the implementation of the solution algorithm on several test instances with different sizes showed the efficiency of the algorithm in reducing the solution time and obtaining a good solution.

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.

Because of the destructive effects of greenhouse gas emitted by fossil fuels, moving to alternative fuels is an unavoidable. Alternative fuels play a very important role in the transition to a sustainable and clean the transportation sector. The adoption of alternative fuel vehicle fleets is not easy and, particularly at the beginning of the transition period, the lack of infrastructure for producing, distributing and delivering the alternative fuel is one of the most important obstacles. Therefore, the location of alternative fuel stations is an important topic in accelerating the entry of this fuel into the transportation system. Due to the lack of refueling stations, the assumption that all vehicles on intercity trips can travel all paths with only one alternative fuel is unrealistic. One of the practical ways is utilize of bi-fuel vehicles, to use gasoline in an emergency for avoid to stopping the vehicle on the journey by run out of alternative fuel. In this paper, we present a new model to location of alternative fuel station for bi-fuel vehicles. The model's goal is to minimize total emissions from vehicles. Also, we propose an efficient solution algorithm based on Benders decomposition to solve large network. The results show that the use of bi-fuel vehicles can lead to a significant reduce in greenhouse emissions. Moreover, implementation of proposed algorithm on randomly generated examples illustrate that the algorithm is useful in reducing the solving time and obtaining acceptable solution.