aggregate second order continuum model for transient production planningAnFactory production is stochastic in nature with time varying input and output processes that are non-stationary stochastic processes. Hence, the principle quantities of interest are random variables. Typical modeling of such behavior involves numerical simulation and statistical analysis. A deterministic closure model leading to a second order model for the product density and product speed has previously been proposed. The resulting partial differential equations (PDE) are compared to discrete event simulations (DES) that simulate factory production as a time dependent M/M/1 queuing system. Three fundamental scenarios for the time dependent influx are studied: An instant step up/down of the mean arrival rate; an exponential step up/down of the mean arrival rate; and periodic variation of the mean arrival rate. It is shown that the second order model, in general, yields significant improvement over current first order models. Specifically, the agreement between the DES and the PDE for the step up and for periodic forcing that is not too rapid is very good. Adding diffusion to the PDE further improves the agreement. The analysis also points to fundamental open issues regarding the deterministic modeling of low signal-to-noise ratio for some stochastic processes and the possibility of resonance in deterministic models that is not present in the original stochastic process.autWienke, MatthewthsArmbruster, DieterdgcJones, DonalddgcPlatte, RodrigodgcGardner, CarldgcRinghofer, ChristianpblArizona State UniversityengPartial requirement for: Ph.D., Arizona State University, 2015Includes bibliographical references (pages 91-94)Field of study: Applied mathematicsby Matthew Wienkehttps://hdl.handle.net/2286/R.I.3602200Doctoral DissertationAcademic thesesvii, 94 pages : illustrations (some color)114489750721630347986154081adminIn CopyrightAll Rights Reserved2015TextApplied MathematicsIndustrial EngineeringProduction management--Mathematics.Production ManagementIndustrial engineering--Statistical methods.