MULTI-STAGE STOCHASTIC PROGRAMING MODEL FOR SUSTAINABLE NANOMANUFACTURING CAPACITY EXPANSION PLANNING

Transcription

1 MULTI-STAGE STOCHASTIC PROGRAMING MODEL FOR SUSTAINABLE NANOMANUFACTURING CAPACITY EXPANSION PLANNING Serkan Erbis, Jacqueline A. Isaacs, Sagar Kamarthi, Thomas P. Cullinane 2 nd Sustainable Nanotechnology Organization Conference Santa Barbara, California November 4 th, 2013 SNM EEC

2 Outline 2 Introduction Nanomanufacturing expansion planning Operation Research (OR) for capacity expansion planning Simulation model Effect of uncertainty on total cost Multi-stage stochastic programming model Decision making under uncertainty Summary

3 Number of products Growing Market size in Nanotechnology 3 Nanotechnology Consumer Products Inventory (2013) $3.3 trillion - The estimated market size for nanotechnology goods in Source: PEN Consumer Products Inventory at Source: Market Research Report - Nanotechnology, Global Industry Analysts, Inc. at

4 MWCNT (MT/ year) Total MWCNT Sales (M$) Growing Demand for Carbon Nanotubes 4 10 year MWCNT demand forecast - Lux Research (2011) 1200 $ Total MWCNT sales (M$) $ $ $ $ $ Sporting goods Aerospace Wind O&G Auto Source: Lux Research Ross Kozarsky s presentation in NanoBusiness 2011, Boston, 26 September 2011 at

5 Issues for Commercialization in Nanotechnology 5 Commercialization Social Impact Uncertainties Regulation Uncertainties Environmental Health & Safety Uncertainties Demand Uncertainties Economic Uncertainties Technology Uncertainties

6 Operation Research (OR) Techniques for Capacity Expansion Planning 6 Capacity expansion size and timing of the expansion need to be optimized in order to maximize the profit (or minimize the cost) Capacity Discrete capacity step change Capacity Demand Capacity expansion planning under uncertainty in nanotechnology demand, technology improvement rate, regulations for occupational safety Time between two consecutive expansion Time Optimization Problems Under Uncertainty Multi-Stage Stochastic Programming Model

7 Assumptions for Simulation and Optimization Models 7 One Facility SWCNT, MWCNT Increase in demand for CNTs New generation of existing CNTs synthesis methods released every year with higher yields assumed Expected stricter limits expected for occupational exposures CNTs 8-h TWA Recommended Exposure Limit for CNTs = 7 µg/m 3 in h TWA Recommended Exposure Limit for CNTs = 1 µg/m 3 in 2013 Likely increase in occupational exposure as production increases Source: Current Intelligence Bulletin 65: Occupational Exposure to Carbon Nanotubes and Nanofibers, April 2013 at Source: NIOSH. Approaches to Safe Nanotechnology: Managing the Health and Safety Concerns Associated with Engineered Nanomaterials. at

8 Monte Carlo (MC) Simulation Model for Analyzing the Uncertainty in Nanotechnology 8 Process flow of MC simulation model Generate Exposure Limit (Regulation) Excess Exposure Safety Cost Exposure Check Availability of Technology? Capacity Production Cost Total Cost Generate Demand (MWCNT and SWCNT) Inventory Shortage Cost Inventory Cost Run 20 periods for 100 replications Fixed capacity expansion (one process line) in each time period

9 Significant Long Term Effect of Uncertainty 9 on Inventory Level Technological improvement - Random number No Technological Improvement - Random number > INVENTORY 0 SHORTAGE

10 High Variability in Total Cost 10 Technological improvement --Random number No No Technological Improvement --Random number >

11 11 Minimize Subject to i S S i11 C i11 MSSP Model for Nanomanufacturing N + π k π m N kmigt C igt k m i Capacity Expansion Planning g t=2 I U + π k π m I kmjt C jt + U kmjt C jt k m j t=2 + π k π m π n X km nt k m n t=2 H + π k π m H kmigjt C igjt k m i g j t=2 Z π k π m Z kmigt C igt G kmi12 = P i11 + S i11 k, s, i (1) G kmigt = G kmig (t 1) + N kmig (t 1) T mg (t 1) Z kmig (t 1) k, m, i, g, t = 3,, T (2) S i11 a i (3) N kmigt a k, m, i, g, t = 2,3,, T (4) G kmigt Q k, m, i, g, t = 2,3,, T (5) S kmigt Z kmigt = V kmigt k, m, i, g, t = 2,3,, T (6) S kmigt + Z kmigt = V kmigt k, m, i, g, t = 2,3,, T (7) j F kmigjt k G kmigt k, m, i, g, t = 2,3,, T (8) F km 3g2t = 0 k, m, g, t = 2,3,, T (9) H kmigjt F kmigjt R igj k, m, i, g, j, t = 2,3,, T (10) i g j H kmigjt ε 10 6 A V nt + E km nt k, m, n, t = 2,3,, T (11) E km nt d p+1 + M 1 Y kmnpt k, m, n, p, t = 2,3,, T (12) E km nt d p M 1 Y kmnpt k, m, n, p, t = 2,3,, T (13) X X km nt C pt p Y kmnpt i g j H kmigjt m i M 1 Y kmnpt k, m, n, p, t = 2,3,, T (14) = 1 k, m, n, p, t = 2,3,, T (15) I kmjt U kmjt = H kmigjt i g D kjt k, m, j, t = 2,3,, T (16) G kmigt, S i11, F kmigjt, I kmjt, U kmjt, E km nt, H kmigjt 0 k, m, n, i, g, j, t = 2,3,, T (17) G kmigt, S kmigt, F kmigjt, I kmjt, U kmjt, E km nt, H kmigjt Z k, m, n, i, g, j, t = 2,3,, T (18) Y kmnpt {0,1} k, m, n, p, t = 2,3,, T (19) non anticipativity constraints (20) g t=2 Uncertain variables Exposure limits Demand for CNTs Technology improvement rate Decision variables Expansion size (number of process lines) Production volume Occupational safety level Equipment replacement if necessary

12 12 Example of Decision Made with MSSP Model No New New Technology Technology Period 1 Period 2 Period 3 Period 4 ARC - 2 HiPco Occupational Safety Level: 12 3 SWCNT ARC HiPco CVD - 2 HiPco MWCNT ARC CVD

13 Summary 13 MC simulation model used to analyze the uncertainty in nanomanufacturing facility expansion Uncertainties regarding demand, technological improvement and occupational safety regulations MC used to determine how decisions affect mfg cost Results indicate significant influence on total mfg cost Multi-stage stochastic programming then used to optimize expansion decisions to minimize variability in long term Offers ability to consider alternative scenarios Generates insights for decision makers Models to be verified to with real case data

14 QUESTIONS / SUGGESTIONS THANK YOU! SERKAN ERBIS erbis.s@husky.neu.edu