Waste reduction is a fundamental problem for sustainability. Methods for waste reduction with point-of-sales (POS) data are proposed, utilizing the knowledge of a recent econophysics study on a statistical property of POS data. Concretely, the non-stationary time series analysis method based on the Particle Filter is developed, which considers abnormal fluctuation scaling known as Taylor's law. This method is extended for handling incomplete sales data because of stock-outs by introducing maximum likelihood estimation for censored data. The way for optimal stock determination with pricing the cost of waste reduction is also proposed. This study focuses on the examination of the methods for large sales numbers where Taylor's law is obvious. Numerical analysis using aggregated POS data shows the effectiveness of the methods to reduce food waste maintaining a high profit for large sales numbers. Moreover, the way of pricing the cost of waste reduction reveals that a small profit loss realizes substantial waste reduction, especially in the case that the proportionality constant of Taylor’s law is small. Specifically, around 1% profit loss realizes half disposal at =0.12, which is the actual value of processed food items used in this research. The methods provide practical and effective solutions for waste reduction keeping a high profit, especially with large sales numbers.<\/p>\r\n","references":"[1]\tUnited Nations, \u201cWorld Population Prospects the 2017 Revision,\u201d USA: United Nations, 2017.\r\n[2]\tFood and Agriculture Organization of the United Nations, \u201cFood Wastage Footprint\u2014Impacts on Natural Resources,\u201d Rome: Food and Agriculture Organization of the United Nations, 2013.\r\n[3]\tUnited Nations, \u201cTransforming Our World: The 2030 Agenda for Sustainable Development,\u201d New York: United Nations, 2015.\r\n[4]\tG. Sakoda, H. Takayasu, and M. Takayasu, \u201cTracking Poisson Parameter for Non-Stationary Discontinuous Time Series with Taylors Abnormal Fluctuation Scaling,\u201d Stats, vol. 2, no. 1, pp. 5569, Jan. 2019.\r\n[5]\tG. Sakoda, H. Takayasu, and M. Takayasu, \u201cData Science Solutions for Retail Strategy to Reduce Waste Keeping High Profit,\u201d Sustainability, vol. 11, no. 13, p. 3589, Jun. 2019.\r\n[6]\tG. Fukunaga, H. Takayasu, and M. Takayasu, \u201cProperty of fluctuations of sales quantities by product category in convenience stores,\u201d PLoS One, vol. 11, no. 6, pp. 119, 2016. PLoS ONE 2016, 11, e0157653.\r\n[7]\tL. R. Taylor, \u201cAggregation, variance and the mean,\u201d Nature, vol. 189, pp.732\u2013735, 1961.\r\n[8]\tE. T. Lee, J.W.Wang, \u201cStatistical Methods for Survival Data Analysis,\u201d USA: WILEY, 2013, pp. 133-205.\r\n[9]\tG. Kitagawa, \u201cMonte Carlo Filter and Smoother for Non-Gaussian Nonlinear State Space Models,\u201d J. Comput. Graph. Stat, vol.5, pp.1\u201325, 1996.\r\n[10]\tN. J. Gordon, D.J. Salmond, A.F.M. Smith, \u201cNovel approach to nonlinear\/non-Gaussian Bayesian state estimation,\u201d IEE Proc.F, vol. 140, pp.107\u2013113, 1993.\r\n[11]\tS. R. Cherry, J.A. Sorenson, M.E. Phelps, \u201cPhysics in Nuclear Medicine,\u201d 4th ed. Amsterdam: Elsevier, pp. 126\u2013128, 2012.\r\n[12]\tE. L. Porteus, \u201cStochastic Inventory Theory. Handbooks in Operations Research and Management Science,\u201d Amsterdam: Elsevier, vol. 2, pp. 605\u2013652, 1990.\r\n[13]\tM. Khouja, \u201cThe single-period (news-vendor) problem: Literature review and suggestions for future research,\u201d Omega, vol. 27, pp. 537\u2013553, 1999.\r\n[14]\tY. Qin, R. Wang, A.J. Vakharia, Y. Chen, M.M.H. Seref, \u201cThe newsvendor problem: Review and directions for future research,\u201d Eur. J. Oper. Res., vol. 213, pp. 361\u2013374, 2011.\r\n[15]\tSeven & i Holdings Co., Ltd., \u201cCorporate Outline 2011,\u201d Available online:https:\/\/www.7andi.com\/library\/dbps_data\/_template_\/_res\/en\/ir\/library\/co\/pdf\/2011_07.pdf (accessed on 8 September 2019).","publisher":"World Academy of Science, Engineering and Technology","index":"Open Science Index 156, 2019"}