The travelling salesman problem (TSP) is the challenge of finding the shortest yet most efficient route for a person to take given a list of specific destinations. It is an optimization problem in the fields of computer science and operations research. There are obviously a lot of different routes to choose from, but finding the best one the one that will require the least distance or costs, several researchers have spent decades trying to optimize the modeling and the resolution. In some real cases, the classical problem is not able to model the existing problem in a given company. In this paper, we propose models for the TSP, that can be used with linear or quadratic service time functions, and that embeds novel improved lower and upper bounds. With proposed models, the authors consider exponentially many sub-tour eliminations, capacities, and demands constraints, which are separated dynamically. The main purpose is to help the transport manager to select the optimal distribution circuit that optimizes various objectives.
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In contemporary enterprises, leaders strive to enhance their performance and maintain competitiveness in the markets. Notably, logistics plays a crucial role in decision-making processes. One of the pivotal activities in corporate logistics management is establishing an efficient distribution network for goods, which serves as the backbone of operations, aiming to deliver a superior level of service while minimizing costs. Consequently, the modeling of distribution logistics systems equips companies with valuable insights to address network design challenges. In numerous logistics scenarios, accurately estimating the distance that vehicles need to cover to fulfill customer demands is vital. Distribution dilemmas emerge as significant concerns for various companies, posing the challenge of effectively delivering goods or services from the company to its customers.
The optimization of Vehicle Routing Problem (VRP) in the logistics distribution is a well-known research widely concerned problem. Companies more and more attach importance to better design and manage their logistics distribution in order to meet higher level quality services at the lowest possible cost effort. The logistics distribution problem is complex and difficult because the network involves various subsystems, activities, relationships and operations (Chandra and Kumar, 2000). Logistics practices include a set of approaches and activities used by a company to effectively integrate supply and demand to improve its supply chain management (Li et al., 2005). Green et al. (2012) suggested that distribution practices should include internal environmental management and cooperation with customers. Lee et al. (2012) noted that logistics practices are composed of corporate and operational strategies aimed at improving environmental sustainability. Laosirihongthong et al. (2013) studied the impacts of reverse logistics practices on the economic and environmental performance of Thai manufacturing companies.
Nowadays, the integration of environmental practices in every node of supply chain and especially in transportation activities becomes the challenge of many researches. This is due to diverse factors. First of all, environmental considerations are required to guarantee the safety, the health and the survival of living beings which are the most important natural resources to take into account. Then, the future decrease in energy systems which are threatened by a serious loss within 2040 according to the 2019 World Energy Outlook report (World Energy Outlook 2019) as well as the pollution caused by unnatural resources induce to search solutions to this major problem such as the reductions in the renewable energy sources and the continuous advances in the new digital technologies. In addition, hazardous effects of such logistic activities especially those of transportation systems which are responsible for 20% of the total Green House Gas (GHG) emissions (European Environment Agency, 2014b), requests for environmental solutions.
In this respect, environmental issues are considered as a performance key in the supply chain of a company so that they contribute not only to the reduction of waste generation, the resource consumption but also to the pollution control which can influence the safety of humanities and also the hazardous impact in the natural environment (Savino and Batbaatar, 2015).
As a result, environment concerns play now a crucial role in logistical decision making such as transport planning, location, raw material sourcing, supplier selection (Wu and Dunn, 1995)… Therefore, the “Green” concept has been added to “logistics” concept in order to obtain eco-friendly systems based on environmental strategies. In this way, green logistics is considered as a supply chain management activities and practices that include environmental measure in any process of the supply chain (Seroka-Stolka, 2014).