Due to the emergence of e-commerce and the proliferation of liberal return policies, product returns have become daily routines for many companies. Considering the significant impact of product returns on the company's bottom line, a growing number of companies have attempted to streamline the reverse logistics process. Products are usually returned to initial collection points (ICPs) in small quantities and thus increase the unit shipping cost due to lack of freight discount opportunities. One way to address this issue is to aggregate the returned products into a larger shipment. However, such aggregation increases the holding time at the ICP, which in turn increases the inventory carrying costs. Considering this logistics dilemma, the main objectives of this research are to minimize the total cost by determining the optimal location and collection period of holding time of ICPs; determining the optimal location of a centralized return centre; transforming the nonlinear objective function of the proposed model formulation by Min et al. (2006a) into a linear form; and conducting a sensitivity analysis to the model solutions according to varying parameters such as shipping volume. Existing models and solution procedures are too complicated to solve real-world problems. Through a series of computational experiments, we discovered that the linearization model obtained the optimal solution at a fraction of the time used by the traditional nonlinear model and solution procedure, as well as the ability to handle up to 150 customers as compared to 30 in the conventional nonlinear model. As such, the proposed linear model is more suitable for actual industry applications than the existing models.
Bone is a heterogeneous material and its mechanical properties vary within the body. Variations in the mechanical response of different bone samples taken from the body cannot be fully explained by only looking at local compositional information at the tissue level. Due to different states of the stress within bones, one might expect that mechanical properties change over the length of a bone; this has not been a matter of systematic research in previous studies. In this study, the distribution of the tissue elastic modulus along the bovine femur is investigated using three-point bending tests. Two bovine femora were split to seven and eight blocks from proximal to distal metaphysis, respectively and twenty beam shaped bone samples were extracted and tested from each block. Based on our findings, the longitudinal elastic modulus follows a gradient pattern along the bovine femur as it increases along the bone from the proximal metaphysis to mid-diaphysis and then decreases toward the distal metaphysis again. Considering long bones to be subjected to bending loads, this mechanism alters the bone structure to support load in the regions where it is needed; similar as outlined by Wolff's law. In another part of this study, microfocus X-ray computed tomography (μCT) was found unable to predict the same trend of changes for the elastic modulus via image-based or density-based elastic moduli calculations. This is insofar important as conventional finite element models of bone are often directly shaped from μCT data. Based on our findings, it seems that current computed tomography based finite element models generated in this manner may not adequately capture the local variation of material behavior of bone tissue, but this may be improved by considering the changes of the elastic modulus along the femur.
Reverse logistics is becoming a very important and necessary part of any business wanting to excel and move forward. One important aspect of reverse logistics is product returns. It is becoming essential to make sound decisions at all levels; strategic, tactical and operational, concerning the return flow of products. Thus, most firms have begun to explore the possibility of managing product returns in a more cost-efficient manner. However, few studies have addressed the problem of determining the number and location of centralized return centers (i.e., reverse consolidation points) where returned products from retailers or end-customers were collected, sorted, and consolidated into a large shipment destined for manufacturers or distributors' repair facilities. To fill the void in such a line of research, this paper proposes a nonlinear-integer programming model that is subsequently transformed into an equivalent mixed integer linear programming model.
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