Incorporating Vehicle-Routing Problems into a Closed-Loop Supply Chain Network Using a Mixed-Integer Linear-Programming Model

Abstract

In recent years, there has been a tremendous increase in environmental awareness, due to concerns about sustainability. Designing an efficient supply chain network that fulfills the expectation of both business owners and customers and, at the same time, pays attention to environmental protection is becoming a trend in the commercial world. This study proposes a theoretical model incorporating vehicle routing problems (VRPs) into the typical CLSC (closed-loop supply chain) network architecture. This combination assists all operators to act more efficiently in terms of environmental protection and profitability. A mixed-integer-linear-programming model for CLSC network design with fuzzy and random uncertain data is developed to achieve the goals. The parameters of the CLSC network are also programmed using hybrid fuzzy-stochastic mathematical programming. The model is for a single product and a single timeframe. Several numerical examples are provided to demonstrate the validity of the proposed mixed-integer-linear-programming (MILP) model. This study also investigated probabilistic possibilities for recourse variables with a trapezoidal fuzzy number using a problem size of four cases. The result indicates that the model performed well in the numerical test, suggesting it can help the operation to be more profitable if this model is implemented in their daily routines.

Multicast Routing Based on Data Envelopment Analysis and Markovian Decision Processes for Multimodal Transportation

“…Nevertheless, the intricate task of designing such networks is beset with challenges, necessitating a comprehensive approach. Past research has employed various methodologies, such as linear programming, integer programming, and metaheuristic algorithms, to achieve a balance between multiple objectives in optimizing transportation [15][16][17].…”

Modeling the Decision and Coordination Mechanism of Power Battery Closed-Loop Supply Chain Using Markov Decision Processes

“…MDP can consider the stochastic and time-varying nature of the transportation demand and transportation environment and solve the optimal transportation scheduling strategy by methods such as dynamic planning or reinforcement learning. For example, Ali P et al (2023) [10] incorporated the vehicle path problem into the optimization model of a closed-loop supply chain network, considered factors such as product demand, recycling volume, transportation cost, and environmental impacts, and developed a mixed-integer linear programming model to minimize the total cost of the closed-loop supply chain network and proposed an effective solution algorithm; Mehrnaz B et al [11] designed a new closedloop supply chain network with a location-allocation and routing model that considers simultaneous recycling and distribution and optimizes under uncertainty. The model involves problems in transportation scheduling, such as how to determine appropriate location, allocation, and routing schemes according to the recycling and distribution demands in different regions and time periods, so as to optimize the transportation cost, transportation time, transportation distance, and other metrics; Hao G et al [12] proposed a hybrid differential evolutionary algorithm for solving the location-inventory problem in a closed-loop supply chain with product recycling.…”