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South Korea is one of the leading markets for the e-commerce industry. In line with the rapid growth of the e-commerce industry, the parcel delivery volume in Korea has also proliferated. Despite the developments in the Korean e-commerce and courier industries, consumers still experience a high package damage rate. In response, many packaging engineers in Korea have raised the need for new parcel shipping environment tests that reflect the Korean ground shipping environment in order to properly optimize packages. However, only limited information on the Korean parcel shipping environment is currently available. Therefore, this study focused on measuring and analyzing the shock and drop levels that parcels experience during ground shipping in Korea. Shock data were collected from a total of sixty one-way shipments for small, lightweight packages and medium, mid-weight packages. The findings revealed that the two types of boxes do not experience significantly different numbers of shock events or drop heights in the Korean parcel delivery environment. Furthermore, the number of shock events that occur in Korea is substantially less than the international testing standard and less than in previous studies conducted in both Europe and the USA. In contrast, however, the drop heights are higher than those in the international testing standard and previous studies. Shock events were found to occur most frequently on the edges and to be concentrated around the bottoms of the packages. Most shock events happen while packages are loaded and unloaded at hub terminals and sub terminals.

South Korea has one of the largest e-commerce markets in the world. The last-mile delivery segment of e-commerce often causes critical damage to products in protective packages. Despite the rapid growth of the e-commerce market in Korea, the last-mile distribution environment has not yet been thoroughly investigated. The main aim of this study was to provide an understanding of the vibration levels that were measured from various parcel delivery routes within Seoul, Korea, using common types of parcel delivery trucks. Vibration levels of ten delivery trucks were measured and analyzed in terms of power spectral densities (PSDs) and presented as PSD spectra. The last-mile delivery vehicle vibration levels in Korea were found to be consistently lower (in the 1 to 200 Hz frequency range) than those recommended by international standards and lower than the vibration levels of parcel delivery vehicles in the U.S. and Hungary. The results also revealed that the highest intensity peak of the PSD spectrum for Korea was located in the lower frequency range (1.5 to 2 Hz) compared to the ISTA 3A pickup and delivery test profile (3 to 4 Hz) and the test profile recommended for Hungary (13 to 16 Hz). A smoothed composite spectrum was also provided to support Korean packaging engineers in optimizing their packages by simulating proper last-mile truck delivery vibration levels in lab conditions.

In this paper, we present a general framework that provides a comprehensive and uniform treatment of integral majorization inequalities for convex functions and finite signed measures. Along with new results, we present unified and simple proofs of classical statements. To apply our results, we deal with Hermite-Hadamard-Fejér-type inequalities and their refinements. We present a general method to refine both sides of Hermite-Hadamard-Fejér-type inequalities. The results of many papers on the refinement of the Hermite-Hadamard inequality, whose proofs are based on different ideas, can be treated in a uniform way by this method. Finally, we establish a necessary and sufficient condition for when a fundamental inequality of f-divergences can be refined by another f-divergence.

Forklift handling of palletized loads produces shock impacts that cause significant damage, affecting the durability and life cycle of pallets and unit loads. Laboratory testing processes using an incline impact tester have been developed to assess the resistance of pallets and unit loads to shock impact damage. A key element of the pallet durability test using the incline impact tester is the intensity of the impact. However, there is a lack of information on the intensity of the shock impacts during forklift handling. The objective of this research was to investigate the effects of forklift type, pallet design, entry speed, and top load on the horizontal shock responses measured during the interactions between pallets and forklifts. Two data loggers, SAVER 3X90 and 3D15, were used to measure the horizontal shock impacts experienced during the same event on both the pallet and the forklift. The results showed that the average peak acceleration of the forklift was 2.98 G; the same event resulted in a 4.4 times greater peak acceleration in the pallet. The average duration of these impacts was 10–12 ms. Pallet design and entry speed had the greatest effect on the response measured for the forklift, while the pallet was most heavily influenced by entry speed and forklift type. The paper mainly focused on measuring the severity of the impacts and did not attempt to correlate the measured impacts to damage experienced by unit loads.

Current pallet design methodology frequently underestimates the load capacity of the pallet by assuming the payload is uniformly distributed and flexible. By considering the effect of payload characteristics and their interactions during pallet design, the structure of pallets can be optimized and raw material consumption reduced. The objective of this study was to develop a full description of how such payload characteristics affect load bridging on unit loads of stacked corrugated boxes on warehouse racking support. To achieve this goal, the authors expanded on a previously developed finite element model of a simplified unit load segment and conducted a study to screen for the significant factors and interactions. Subsequently, a Gaussian process (GP) regression model was developed to efficiently and accurately replicate the simulation model. Using this GP model, a quantification of the effects and interactions of all the identified significant factors was provided. With this information, packaging designers and researchers can engineer unit loads that consider the effect of the relevant design variables and their impact on pallet performance. Such a model has not been previously developed and can potentially reduce packaging materials’ costs.

Forklifts are one of the most common types of material handling equipment used in warehouses and distribution centers. Vibration generated by forklifts may have an effect on the performance of unit loads and product damage rates. Historical research projects have focused predominantly on the measurement of vibration for over-the-road transportation. Thus, there is still a lack of understanding of the level of vibration caused by forklifts. The goal of this study was to understand how the vibration that is experienced by unit loads while being transported by forklifts is affected by factors such as speed, road condition, unit load weight, type of forklift, and sensor location. For this study, power spectral density (PSD) measurements were collected using a Lansmont Saver 9X30 data logger. Vibration levels were measured for three different industrial forklifts on two different surface types. The forklifts were driven at two different speeds while carrying two different unit load weights. For all of these conditions, the vibration levels were measured at the forklift carriage, at the back of the fork tine heel, and at the fork tine tips. The results obtained show that the highest vibrational intensity occurred at 3–4 Hz, while the highest overall Grms value observed was 0.145 G2/Hz (between 1–200 Hz). An increase in the forklift speed caused an increase in vibration intensity. In contrast, an increase in the unit load weight carried by the forklift caused a decrease in vibration intensity. Among the three forklifts studied, the gas-powered forklift had the highest vibration intensity, and all forklifts, when driven on asphalt, experienced more vibration.

Current pallet design methodology frequently underestimates the load capacity of the pallet by assuming the payload is uniformly distributed and flexible. By considering the effect of payload characteristics and their interactions during pallet design, the structure of the pallets can be optimized, and raw material consumption reduced. The objective of this study was to develop and validate a finite element model capable of simulating the bending of a generic pallet while supporting a payload made of corrugated boxes and stored on a warehouse load beam rack. The model was generalized in order to maximize its applicability in unit load design. Using a two-dimensional, nonlinear, implicit dynamic model, it allowed for the evaluation of the effect of different payload configurations on the pallet bending response. The model accurately predicted the deflection of the pallet segment and the movement of the packages for a unit load segment with three or four columns of boxes supported in a warehouse rack support. Further refinement of the model would be required to predict the behavior of unit loads carrying larger boxes. The model presented provides an efficient solution to the study of the affecting factors to ultimately optimize pallet design. Such a model has not been previously developed. The model successfully acts as a tool to study and predict the load bridging performance of unit loads requiring only widely available input data, therefore providing a general solution.