The Vehicle Routing Problem (VRP) and its variants are found in many fields, especially logistics. In this study, we introduced an adaptive method to a complex VRP. It combines multi-objective optimization and several forms of VRPs with practical requirements for an urban shipment system. The optimizer needs to consider terrain and traffic conditions. The proposed model also considers customers' expectations, shipper considerations as goals, and the common goal like transportation cost. We offered compromise programming to approach the multi-objective problem by decomposing the original multi-objective problem into a minimized distance-based problem. We designed a hybrid version of the Genetic algorithm with the Local Search algorithm to solve the proposed problem. We evaluate the effectiveness of the proposed algorithm with the Tabu Search algorithm, the original Genetic algorithm on the tested dataset. The results show that our method is an effective decision-making tool for the multi-objective VRP and an effective solver for the new variation of VRP.

The problem of scheduling is an area that has attracted a lot of attention from researchers for many years. Its goal is to optimize resources in the system. The assigning task to the lecturer is an example of the timetabling problem, a class of scheduling. This study introduces a mathematical model to assign fixed tasks (the time and required skills to be fixed) to university lecturers. Our model is capable of generating a calendar that maximizes faculty expectations. The formulated problem is in the form of a multi-objective problem that optimal makes decisions require the trade-off presence of trade-offs between two or more conflicting objectives. To solve this, we use the Compromise Programming approach to multi-objective programming. We then proposed the new version of the Genetic Algorithm to solve the introduced model. Finally, the model and algorithm tested with real scheduling data collected at the Computing Fundamental Department, FPT University, Hanoi, Vietnam.

The intensifying overexploitation of water resources and the increasing pollution discharge have exacerbated conflicts in water resource utilization, making it urgent to effectively reconcile the contradiction between water resource utilization and environmental protection. This study developed a Cost-Inclusive Multi-Objective Bargaining Methodology (CIMB) coupled with Compromise Programming (CP) method to address conflicts between water use and pollution discharge, considering the economic benefits and the sustainable development of water resources. A deterministic multi-objective bargaining approach was employed, with two players representing the maximization of water use benefits and the minimization of total pollution discharge. This study takes the middle and lower reaches of the Han River region as an example to optimize water resource allocation in ten cities in this area. Using the CIMB-CP model, the water use and pollution discharge for different cities were obtained, and the impact of various factors on the game outcomes was analyzed. The model results indicate that negotiation cost have a significant impact on the Nash equilibrium solution. Compared to the Cost-Exclusive Multi-Objective Bargaining Methodology (CEMB) model, the Nash equilibrium solution of the CIMB-CP model shows an approximately 0.1% decrease in economic benefits and a approximately 0.3% decrease in pollution discharge. The risk attitudes of the participants have a significant impact on the game outcomes, and decision-makers need to formulate corresponding negotiation strategies based on their own risk preferences.

The United Nations' sustainable development goals have underscored the importance of enhancing supply chain sustainability while appropriately distributing orders. This study proposes a novel framework involving Z-number, game theory, indifference threshold-based attribute ratio analysis (ITARA), and combined compromise solution method (CoCoSo) to evaluate the sustainability of suppliers and order allocations. To better reflect the decision makers’ current choices for the sustainability of assessed suppliers and order allocations; enhance the comprehensiveness of decision-making, the importance parameter of the supplier is obtained through game theory objectively for transforming supplier performance into order allocation performance. The Z-numbers are involved in ITARA (so-called ZITARA) and CoCoSo (so-called ZCoCoSo) to overcome the issue of information uncertainty in the process of expert evaluation. ZITARA and ZCoCoSo are applied to assess the objective weight of criteria and the ranking of assessed order allocations, respectively. Afterwards, a case study of China’s company is illustrated the utility of the proposed framework and inform their decision-making process regarding the orders to be assigned to the assessed suppliers.