Kalman filter based production control of a failure-prone single-machine single-product manufacturing system with imprecise demand and inventory information |
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| Affiliation: | 1. Department of Mechanical Engineering, Ecole de Technologie Superieure, 1100 Notre Dame West, Montreal, Quebec, Canada;2. Department of System Engineering, Ecole de Technologie Superieure, 1100 Notre Dame West, Montreal, Quebec, Canada;1. Department of Management, College of Business Administration, Marquette University, Milwaukee, WI, 53233, USA;2. Department of Supply Chain Management, W.P. Carey School of Business, Arizona State University, Tempe, AZ, 82801, USA;3. Department of Supply Chain Management, Sam M. Walton College of Business, University of Arkansas, Fayetteville, AR, 72701, USA;1. Mechanical Engineering Department, Ecole de Technologie Superieure, 1100 Notre Dame West, Montreal, Quebec H3C 1K3, Canada;2. Automated Production Engineering Department, Ecole de Technologie Superieure, 1100 Notre Dame West, Montreal, Quebec H3C 1K3, Canada;1. Department of Mechanical Engineering, J.C. Bose University of Science and Technology, YMCA, Faridabad, India;2. Department of Electrical & Electronics Engineering, KIET Group of Institutions, Ghaziabad, India |
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| Abstract: | An adaptive production control structure for failure-prone manufacturing systems under inventory and demand uncertainty is proposed. It contains estimation and forecasting modules incorporated into a control loop. The customer demand is unknown and its rate is composed of ramp-type, seasonal and random components. Information available to decision maker consists of imprecise inventory records, and the Kalman filter technique is used for estimating the inventory level and demand rate online from noisy inventory measurements. Estimates obtained are shown to converge to the actual values in stochastic sense. They are subsequently used for demand component forecasting, once the estimation errors become sufficiently small. A forecasting algorithm allows estimating ramp-type and seasonal demand components, together with their potential errors. Obtained estimates are incorporated into production control procedures, recently developed for manufacturing systems under variable and uncertain demand. Optimality conditions in the form of Hamilton-Jacobi-Bellman equations are obtained. A constructive numerical method for computing sub-optimal production policies is proposed and validated through numerical simulations. |
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| Keywords: | Manufacturing Uncertainty Stochastic processes Forecasting State estimation Kalman filter |
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