The recycling of waste products can bring enormous economic and environmental benefits to supply chain participants. Under the government’s reward and punishment system, the manufacturing industry is facing unfolded pressure to minimize carbon emissions. However, various factors related to the design of closed-loop logistics networks are uncertain in nature, including demand, facility capacity, transportation cost per unit of product per kilometer, landfill cost, unit carbon penalty cost, and carbon reward amount. As such, this study proposes a new fuzzy programming model for closed-loop supply chain network design which directly relies on fuzzy methods based on the necessity measure. The objective of the proposed optimization model is to minimize the total cost of the network and the sum of carbon rewards and penalties when selecting facility locations and transportation routes between network nodes. Based on the characteristics of the problem, a genetic algorithm based on variant priority encoding is proposed as a solution. This new solution encoding method can make up for the shortcomings of the four traditional encoding methods (i.e., Prüfer number-based encoding, spanning tree-based encoding, forest data structure-based encoding, and priority-based encoding) to speed up the computational time of the solution algorithm. Several alternative solution approaches were considered to evaluate the proposed algorithm including the precision optimization method (CPLEX) and priority-based encoding genetic algorithm. The results of numerous experiments indicated that even for large-scale numerical examples, the proposed algorithm can create optimal and high-quality solutions within acceptable computational time. The applicability of the model was demonstrated through a sensitivity analysis which was conducted by changing the parameters of the model and providing some important management insights. When external parameters change, the solution of the model maintains a certain level of satisfaction conservatism. At the same time, the changes in the penalty cost and reward amount per unit of carbon emissions have a significant impact on the carbon penalty revenue and total cost. The results of this study are expected to provide scientific support to relevant supply chain enterprises and stakeholders.

Maritime transportation is vital for the movement of cargo between different continents and distant locations but can be disrupted by the frequent occurrence of pirate attacks. Based on the pirate attacks from July 1994 to December 2019, a spatial analysis of pirate attacks using a Geographic Information System (GIS) was conducted in the present study using the data available for tankers, dry bulk carriers, container vessels, general cargo vessels, and tugs. The adoption of the kernel density analysis was intended to identify the spatial pattern of global pirate attacks. The research results demonstrated that the pirate attacks showed a clustering pattern and were mostly associated with areas experiencing economic depression, a high unemployment rate, and social unrest. Accordingly, spatiotemporal hot spot analysis was carried out to recognize the changing directions of cold spots and hot spots over a period of time. The waters off Somalia, the Strait of Malacca, the Philippines, the Bay of Bengal, the Gulf of Guinea, and the northwest of South America were found to be the common locations of pirate attacks. The cold and hot spots of pirate attacks on the three key vessel types, including tankers, dry bulk carriers, and container vessels, were found to be similar. When considering the same area, the trends of cold and hot spots of different vessel types being attacked were substantially different. This study can provide a useful guideline for the International Maritime Organization and other relevant organizations in the world to design and implement targeted strategies to combat and mitigate pirate attacks. Additionally, the introduction of a GIS may help to envision the spatial and temporal distribution of pirate attacks and to explore the characteristics of pirate behaviors at sea and the patterns of piracy.

The two-dimensional strip-packing problem (2D-SPP) emerges as a notable variant of the cutting and packing (C&P) problem, aiming to optimize the arrangement of small rectangular items within unique strips with a fixed width and infinite height to minimize the usage of height. Despite extensive academic exploration, applying 2D-SPP solutions in industrial settings remains challenging. Two significant issues, often overlooked in academia yet frequently encountered in industrial contexts, are the uncertain demand for items, exacerbated by the bullwhip effect, and the need for diverse types of strips to cater to varying customer needs. Our paper addresses this academia–industry gap by proposing a robust optimization model for the uncertain 2D-SPP with variable-sized bins, aiming to manage the demand fluctuations within a box uncertainty set framework. Additionally, we employ the contiguous one-dimensional relaxation technique in conjunction with column generation to tighten the lower bound of the problem, thereby augmenting solution accuracy. Furthermore, we leverage the Karush–Kuhn–Tucker (KKT) condition to transform the model into a more tractable form, subsequently leading to an exact solution. Based on datasets from a real-life plastic-cutting company, comprehensive experiments validate the effectiveness and efficiency of our proposed relaxation method and algorithm, showcasing the potential for an improved industrial application of 2D-SPP solutions.