Models and Simulation for Bulk Gas Production and Distribution

Transcription

1 Models and Simulation for Bulk Gas Production and Distribution Jeff Linderoth Dept. of Industrial and Systems Engineering Univ. of Wisconsin-Madison Wasu Glankwamdee ISE Department Lehigh University Jim Hutton Peter Connard Jierui Shen Air Products EWO Annual Meeting Pittsburgh, Pennsylvania November 13, 2007 Linderoth (UW-Madison) Bulk Gas Sim-Opt Pittsburgh, PA 1 / 14

2 Liquid Bulk Gas Production-Distribution LIN Sites S Products P = {, LIN} Customers C LIN LIN LIN LIN LIN Planning Problem How should one set production levels at the sites s S and sourcing decisions (amount delivered from s S to c C) in order to meet customer demand at minimum cost? Linderoth (UW-Madison) Bulk Gas Sim-Opt Pittsburgh, PA 2 / 14

3 What Did We Do Research Objectives 1 What is benefit of considering finer-grain model 2 What is benefit of stochastic/robust planning models. Research Deliverables 1 Optimization Models for Production/Distribution 2 Simulation Engine for Production/Distribution Hooked directly to optimization models (XPRESS-MP) 3 Formats and input for real data from AP Linderoth (UW-Madison) Bulk Gas Sim-Opt Pittsburgh, PA 3 / 14

4 Bulk Gas Wrinkles Production Most sites operate in two modes: Regular and extended Can change fraction of as opposed to LNI Regular Production χ X η N e E Ψe Extended Production Competitor Arrangements Enter contractual take-or-pay arrangements with competitors Allowed to remove (equal) fixed amount of product from each other s sites: Linderoth (UW-Madison) Bulk Gas Sim-Opt Pittsburgh, PA 4 / 14

5 Impact of Finer Grain Random Instances Pictures show simulated total cost and customer outages/month as a function of the number of periods in the planning model Cost Outages $ P 2P 4P 7P 14P Periods Customers P 2P 4P 7P 14P Periods Linderoth (UW-Madison) Bulk Gas Sim-Opt Pittsburgh, PA 5 / 14

6 Impact of Finer Grain Real Instance 615 Cost 250 Outages $ Customers P 2P 4P 7P 14P Periods 0 1P 2P 4P 7P 14P Periods Linderoth (UW-Madison) Bulk Gas Sim-Opt Pittsburgh, PA 6 / 14

7 What s Next? (Actual Slide from 2006) Transfer Technology to Air Products Run on Real Data Need to write code to instantiate objects from data files Keep Considering Uncertainty! Minimax Model Robust Optimization Model Stochastic model Disruption Planning: consider more extreme scenarios. Help build contingency lists for sourcing decisions. Hooray for Us! We did all of these things, save for the last one A focus for 2008! Linderoth (UW-Madison) Bulk Gas Sim-Opt Pittsburgh, PA 7 / 14

8 Opt. Under Uncertainty Primer Optimization Problem min f(x) x X Robust (Minimax) Optimization min max x X ω U F (x, ω) ω U : Some uncertainty set The real cost of doing bizness is F (x, ω) x: Variables you control ω : Variables you don t Stochastic Optimization min E ωf (x, ω) x X ω Ω for some probability space (Ω, F, P). Linderoth (UW-Madison) Bulk Gas Sim-Opt Pittsburgh, PA 8 / 14

9 What s Next? A Stochastic Model The World Is Random! In the planning model, make parameters functions of some random variable ω M st (ω), N st (ω): Production Capacity Uncertain B pct (ω): Demand for product p from customer c in period t is uncertain z prt (ω): Amount of product p contract partner takes out at site r in period t is uncertain. Typically r R t T z prt(ω) = Φ p Linderoth (UW-Madison) Bulk Gas Sim-Opt Pittsburgh, PA 9 / 14

10 We Love Σ, Yes We Do! min X X X η X n(α psnx psn+β psne psn+γ psi psn)+ X X X η X n(f scy pscn)+ X X η n(δ p p P s S n N p P s S c C n N p P c C n N (1a) X s.t x psn M sn, s S, n N (1b) p P X e psn N sn, s S, n N (1c) p P x psn Λ pm sn, p P, s S, n N (1d) e psn Λ pn sn, p P, s S, n N (1e) X y pscn + u pc,ρ(n) v pc,ρ(n) B pcn = u pcn v pcn, p P, c C, n N (1f) s S X y prcn I pr,ρ(n) x prn e prn + I prn = z prn, p P, r R, n N (1g) c C X y pscn I ps,ρ(n) x psn e psn + I psn = 0, p P, s S\R, n N (1h) c C X x pqn + φ pn = φ p,ρ(n), p P, n N (1i) q Q X X d scy pscn D sn, s S, n N (1j) p P c C X d scy pscn K psn, p P, s S, n N (1k) c C I psn U ps, p P, s S, n N (1l) I psn Γ psi ps0, p P, s S, n N (T + 1) (1m) Linderoth (UW-Madison) Bulk Gas Sim-Opt Pittsburgh, PA 10 / 14

11 Random Instances Total Cost Chart shows simulated total cost of different policies: x N, x MM, and x SP, as the true variance of customer demand varies Nominal Minimax SP 4.7 $M Variance Surprising Result: Minimax does better in simulation than SP. Only a small (like 5-10) outcomes considered Linderoth (UW-Madison) Bulk Gas Sim-Opt Pittsburgh, PA 11 / 14

12 A Final Use! Having a realistic, reliable simulator can be very useful. AP wanted to answer the question: How much is the take-or-pay contract worth to us? Total Cost Production Cost Delivery Cost # ($M) ($M) ($M) Outages With Contract No Contract Linderoth (UW-Madison) Bulk Gas Sim-Opt Pittsburgh, PA 12 / 14

13 EWO Outcomes Great Outcomes Simulation code and optimization models turned over to AP Research shows possible benefits to considering finer grain models Research shows possible benefit to more robust PD planning models Research shows the benefit of combining simulation with optimization Even Better Outcomes Jerry hired by AP We wrote a paper! :-) Linderoth (UW-Madison) Bulk Gas Sim-Opt Pittsburgh, PA 13 / 14

14 Lehigh EWO 2008 and Beyond! Will continue the existing research effort for developing computational tools for EWO problems The major contribution of this project will allow for efficient optimization of large-scale process industry problems The models will address the problem of coordinated optimization across different functions (purchasing, manufacturing, distribution, and sales), across different geographical areas, and across different levels (strategic, tactical, and operational) in a company Lehigh Projects Air Products: Design and optimization of supply chain under risk of disruptions. Electricity Contract Pricing. Linderoth (UW-Madison) Bulk Gas Sim-Opt Pittsburgh, PA 14 / 14