A potential answer to retailer's shelf out‐of‐stocks (OOS), where the item is in the store but customers cannot find it, is to employ third‐party service providers to execute audits and corrections. However, given the nontrivial cost of executing external audits, it is still necessary to assess whether external audits are capable of reducing shelf‐OOS, whether they can be performed in an economical way, and whether the benefits from the audits translate into higher sales. In an effort to address these questions, we partnered with a product manufacturer and a retail service provider and conducted a field experiment in a national retailer's store set. We used transactional data to detect abnormal operations and respond to possible shelf‐OOS by sending auditors to correct empty shelves and incorrect inventory records. At the conclusion of the experiment, we found that Stock Keeping Units in the treatment group were less likely to have shelf‐OOS and inventory record inaccuracies, and that our intervention had a positive effect on sales. Furthermore, we found that the external audit initiative is economically viable since these improvements required low auditing efforts after a transitional period, and in steady state the cost of running the program is a small fraction of the benefits it generates. We discuss the limitations of our study and the implications of our findings for researchers and practitioners.

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In this study, we studied the phosphor sedimentation effect in white phosphor-converted light-emitting diode packages by modeling the multi-layer phosphors with gradient concentrations. The essence of phosphor sedimentation can attribute to the variation of phosphor concentrations. By modifying the Kubelka-Munk theory, we built a multi-layer phosphor model with considering the light scattering, light absorption, and light conversion process simultaneously. With a brief review of Kubelka-Munk theory, multi-layer phosphors were modeled on the basis of single-layer phosphor model. The phosphor sedimentation effect was characterized by modeling multi-layer phosphors with gradient concentrations, whereas keeping the total amount of phosphors at the same level. It is found from the five calculation cases that phosphor sedimentation will cause the drop of light extraction efficiency (LEE) by 13.04%. Furthermore, the phosphor layer with inverse-gradient concentrations will enhance the LEE 16.56%. To figure out the reasons, the light losses were calculated, and it is proved that the light loss is enhanced when phosphor sedimentation happens. V

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