This paper presents a vendor-managed inventory model for a three-layer supply chain comprised of suppliers, manufacturers, and retailers. This model considers an imperfect production system with a deterministic percentage of defective and deteriorated items, exponential demand for perishable products, and operational costs. The VMI model maximizes the benefits, assuming a Stackelberg approach to find the optimal values of replenishment lot sizes, production rates, selling prices, and product cycle length. A solution algorithm is developed to find the optimal solutions. A case study of the Dairy Industry for highly perishable products is provided to illustrate the applications, evaluate the performance, and obtain managerial insights. The results show that the percentage of defective and deteriorated items and remanufacturing rates are crucial in replenishment, production, and selling policies. The VMI agreement includes remanufacturing defective products to obtain new dairy derivates. The deteriorated products can be sold as near-expired products or inputs for compost, fertilizers, etc. Finally, some conclusions and future research lines are provided.

Diagnosing lithium‐ion battery degradation is a crucial part of managing energy storage systems. Recent research has explored ultrasonic testing for non‐invasive health assessment as an alternative to traditional, time‐consuming, electrical‐only methods. Assessing the state of health is vital for determining quality at end of ‘first’ life, with retired batteries at 70–80 % health still holding value for secondlife applications. Over the coming years, tens of GWh of salvaged batteries will hit the market, requiring rapid noninvasive methods to classify retired batteries according to their state of health. This study uses a 64 – element ultrasonic array to obtain mid‐band quantitative ultrasound spectroscopy parameters – including mid‐band fit, spectral slope, and intercept – from circumferential waves around cylindrical batteries. Thirteen cylindrical cells were used to evaluate the methodology: three pristine and ten retired from the same source. The mid‐band fit showed the ability to track the state of charge and discriminate between the state of health levels in accelerated degradation experiments both with pristine batteries, and also with recovered secondlife batteries with unknown historical use. Linear‐array ultrasonic transducers, coupled with quantitative spectral parameters, show promise for future non‐destructive battery health screening methods, offering valuable insights for the emerging used battery market.

This paper presents an inventory model for a three-echelon supply chain with multiple products and multiple members considering the demand as an increasing function of the marketing effort. In the proposed inventory model, a collaborative approach is studied and an analytical method is applied to obtain the optimal production lot size and the optimal marketing effort in order to achieve the maximum profits. Some numerical examples are illustrated to justify the model. Moreover, a sensitivity analysis is well done in order to analysis the effect of the changes of key parameters of inventory model on the the maximum benefits of all members of the chain.

A numerical study of voids formation in dual-scale fibrous reinforcements is presented. Flow fields in channels (Stokes) and tows (Brinkman) are solved via direct Boundary Element Method and Dual Reciprocity Boundary Element Method, respectively. The present approach uses only boundary discretization and Dual Reciprocity domain interpolation, which is advantageous in this type of moving boundary problems and leads to an accurate representation of the moving interfaces. A problem admitting analytical solution, previously solved by domain-meshing techniques, is used to assess the accuracy of the present approach, obtaining satisfactory results. Fillings of Representative Unitary Cells at constant pressure are considered to analyze the influence of capillary ratio, jump stress coefficient and two formulations (Stokes–Brinkman and Stokes–Darcy) on the filling process, void formation and void characterization. Filling times, fluid front shapes, void size and shape, time and space evolution of the saturation, are influenced by these parameters, but voids location is not.