CSEL LCCC Workshop on Process Control Sept. 28 - 30, 2016 Control - PowerPoint PPT Presentation

Production-Inventory Systems: Modeling, Forecasting and Control Daniel E. Rivera Control Systems Engineering Laboratory School for the Engineering of Matter, Transport and Energy Ira A. Fulton Schools of Engineering Arizona State University http://csel.asu.edu CSEL LCCC Workshop on Process Control Sept. 28 - 30, 2016 Control Systems Engineering Laboratory

Production-Inventory Systems: modeling , CONTROL, and Forecasting Daniel E. Rivera Control Systems Engineering Laboratory School for the Engineering of Matter, Transport and Energy Ira A. Fulton Schools of Engineering Arizona State University with special acknowledgments to: Jay D. Schwartz, Intel Corp. Naresh N. Nandola, ABB CSEL LCCC Workshop on Process Control Sept. 28 - 30, 2016 Control Systems Engineering Laboratory

Outline • Dynamical Model of a Production-Inventory System • Control Strategies: • IMC-PID and 2DoF Feedback-Only IMC • 3DoF Combined Feedback/Feedforward IMC • Model Predictive Control (MPC) • Improved MPC algorithm / Hybrid MPC • Control-relevant Demand Modeling / Demand Forecasting • Summary and Conclusions CSEL 3 Control Systems Engineering Laboratory

Production-Inventory System Starts (Manipulated) u ( t ) θ K d F ( t ) (Throughput (Yield) Forecast Time) LIC LT Demand (Disturbance) Actual Net Stock (Controlled) d ( t ) = d F ( t − θ F ) + d U ( t ) y ( t ) (Delivery θ d Time) y ( s ) = Ke − θ s u ( s ) − e − θ F s d F ( s ) − 1 sd U ( s ) s s Integrating System with Delays CSEL 4 Control Systems Engineering Laboratory

Semiconductor Manufacturing Supply Chain Management LIC C1 M10 C2 Fab Starts Fab/Test1 Assembly Starts Demand Forecast I10 LT M20 Die/Package Actual Assembly/ Inventory Demand Test2 C3 Finish Starts LT I20 I20 Semi-Finished M30 Inventory Finish/Pack LT I30 Components Warehouse C4 Shipments Fabrication/Sort Assembly/Test Finish/Pack • Nonlinear Throughput Time (~Weeks) • Linear Throughput Time (~Days) • Constant Throughput Time (~Shifts) • Stochastic output • Stochastic output • Stochastic Output Package �������� � � X �������� � � - I n c Customer � � � � � � � � � � � � � Faster Faster Demand Factors Good Good Die Product • Stochastic demand Slower Slower • Inaccurate forecasts Not Good Not Good CSEL 5 Control Systems Engineering Laboratory

Whole Hospital Occupancy Multiplicative Indicies for Arrival Peaking by Hour of Day Multiplicative Indicies for Arrival Peaking by Hour of Day (Using data from all BH hospitals) (Using data from all BH hospitals) 1.8 1.8 1.6 1.6 Multiplicative Index Multiplicative Index 1.4 1.4 SA SA 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 Surgery Surgery PACU PACU 0.2 0.2 0.0 0.0 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 Hour of the Day Hour of the Day WIP WIP WIP WIP Surgical Direct Surgical Direct PACU PACU Admits Admits Holding Holding ED Walk-Ins ED Walk-Ins Surgery Surgery Multiplicative Indicies for Arrival Peaking by Hour of Day Multiplicative Indicies for Arrival Peaking by Hour of Day Diverts Diverts (Using data from all BH hospitals) (Using data from all BH hospitals) Multiplicative Indicies for Arrival Peaking by Hour of Day Multiplicative Indicies for Arrival Peaking by Hour of Day 1.8 1.8 (Using data from all BH hospitals) (Using data from all BH hospitals) Multiplicative Index Multiplicative Index 1.6 1.6 1.8 1.8 1.4 1.4 Multiplicative Index Multiplicative Index 1.6 1.6 1.2 1.2 1.4 1.4 1.0 1.0 1.2 1.2 0.8 0.8 1.0 1.0 0.6 0.6 0.8 0.8 0.4 0.4 0.6 0.6 0.2 0.2 0.4 0.4 0.0 0.0 0.2 0.2 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 0.0 0.0 Hour of the Day Hour of the Day 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 Hour of the Day Hour of the Day Medical Direct Medical Direct Multiplicative Indicies for Arrival Peaking by Hour of Day Multiplicative Indicies for Arrival Peaking by Hour of Day Admits Admits (Using data from all BH hospitals) (Using data from all BH hospitals) 1.8 1.8 Multiplicative Index Multiplicative Index 1.6 1.6 1.4 1.4 1.2 1.2 1.0 1.0 0.8 0.8 0.6 0.6 0.4 0.4 0.2 0.2 0.0 0.0 Medical Medical 0 0 1 1 2 2 3 3 4 4 5 5 6 6 7 7 8 8 9 9 10 10 11 11 12 12 13 13 14 14 15 15 16 16 17 17 18 18 19 19 20 20 21 21 22 22 23 23 Hour of the Day Hour of the Day Ambulances Ambulances Diverts Diverts ES ES ED Queue ED Queue EA EA ED ED WIP WIP Amb. Amb. Diverts Diverts ED Holding ED Holding Inpatient Inpatient WIP WIP • Roche, K.T., D.E. Rivera, and J.K. Cochran, “A control engineering framework for managing whole hospital occupancy,” Mathematical and Computer Modelling , Vol. 55, Issues 3-4, pgs. 1401 - 1417, February 2012. CSEL 6 Control Systems Engineering Laboratory

Global Warming/Climate Change • From National Geographic Magazine (http://ngm.nationalgeographic.com/big-idea/05/carbon-bath) CSEL 7 Control Systems Engineering Laboratory

Parental Function-Home Visits Behavioral Intervention as a Production-Inventory Control Problem Parental function PF(t) is built up by providing an intervention I(t) (frequency of home visits), that is potentially subject to delay, and is depleted by potentially multiple disturbances (adding up to D(t)). Controller/ Parental Function Target PF Goal Decision (Setpoint Signal) Rules Intervention I ( t ) Dosage (Manipulated Variable) θ K I ( Delay Time) (Gain) Exogenous Depletion Inflow Effects (Disturbance PF meas ( t ) Variable) Parental Function (Controlled D ( t ) Measured Parental Variable) Function PF ( t ) (Feedback Signal) Outflow PF ( t + 1) = PF ( t ) + K I I ( t − θ ) − D ( t ) • Rivera, D.E., M.D. Pew, and L.M. Collins, “Engineering approaches for the design and analysis of adaptive, time-varying interventions,” Drug and Alcohol Dependence , Special Issue on Adaptive Treatment Strategies, Vol. 88, Supplement 2, pgs. S31-S40, (2007). CSEL 8 Control Systems Engineering Laboratory

Internal Model Control (IMC) Design Procedure r ( s ) u ( s ) y ( s ) r ( s ) u ( s ) y ( s ) q ( s ) p ( s ) c ( s ) p ( s ) + + - - ⇐ ⇒ + p ( s ) ˜ - • Step 1 (Nominal Performance): Obtain an H 2 (ISE)-optimal q(s) - An external input form is specified (e.g., step or ramp) - Closed-form solution for q(s) is obtained - Resulting controller is stable and causal • Step 2 (Robust Stability and Performance) - Augment the IMC controller from Step 1 with a filter, f(s) . - Proper choice and tuning of the filter ensures that: the final controller q(s) is proper. the control system achieves stability and performance under uncertainty. CSEL 9 Control Systems Engineering Laboratory

IMC-PID Tuning Rules p ( s ) = K ( − θ s 2 s + 1) p ( s ) = Ke − θ s q ( s ) = ˜ K ( λ s + 1) s ( θ 2 s + 1) s Representing the delay with a first-order Padé d ( s ) approximation and applying the IMC design procedure leads to the PID with filter controller. � � 1 + 1 1 p d c ( s ) = K c τ I s + τ D s ( τ F s + 1) r ( s ) u ( s ) y ( s ) K ( θ 2 + 4 θλ + 2 λ 2 ) , τ I = 3 3 θ + 4 λ + - p c + - K c = 2 θ + 2 λ Inventory Inventory Factory Target Starts τ D = θ 2 + 2 θλ θλ 2 3 θ + 4 λ , τ F = θ 2 + 4 θλ + 2 λ 2 D.E. Rivera, M. Morari, and S. Skogestad. “ Internal Model Control 4: PID Controller Design” . Ind. Eng. Chem. Process Des. Dev. 25 , 252-265, 1986 . CSEL 10 Control Systems Engineering Laboratory

IMC-PID Controller Response 2000 Forecasted Unforecasted Demand Net Stock 1500 Demand Change Change 1000 Inventory Setpoint 500 Change 0 0 50 100 150 600 Factory Starts 500 400 300 200 100 0 − 100 0 50 100 150 Customer Demand 200 150 100 50 0 0 50 100 150 Time (Days) θ = 5 θ d = 0 λ = 5 K = 1 CSEL 11 Control Systems Engineering Laboratory

Two Degree-of-Freedom (2DoF) Feedback-Only IMC p ( s ) = Ke − θ s p ( s ) = Ke − θ s ˜ s s d ( s ) Demand No approximation is applied to the plant delay. p d r ( s ) u ( s ) y ( s ) + 1 q r ( s ) = s q r p + + - Inventory Inventory Factory Target Starts ( λ r s + 1) n r K q d ( s ) = s ( θ s + 1) ( n d λ d s + 1) - + ˜ p ( λ d s + 1) n d K q d J.D. Schwartz and D.E. Rivera. “ A process control approach to tactical inventory management in production-inventory systems ,” International Journal of Production Economics , Volume 125, Issue 1, Pages 111-124, 2010. CSEL 12 Control Systems Engineering Laboratory

2DoF Feedback-Only IMC 2000 Net Stock 1500 q r q d 1000 500 0 0 50 100 150 600 Factory Starts 500 400 300 200 100 0 − 100 0 50 100 150 Customer Demand 200 150 100 50 0 0 50 100 150 Time (Days) θ = 5 θ d = 0 K = 1 λ r = 1 n r = 2 λ d = 2 n d = 3 CSEL 13 Control Systems Engineering Laboratory