Production Variability in Sales & Operations Planning: A Data-Driven Approach Bruno A. Calfa, Ignacio E. Grossmann Department of Chemical Engineering Carnegie Mellon University Pittsburgh, PA 15213

Anshul Agarwal, Scott J. Bury, John M. Wassick The Dow Chemical Company Midland, MI 48674

March 11th, 2015 1 EWO Meeting – March 2015

Motivation • Sales & Operations Planning (S&OP) – Business and decision-making process. – Tactical plans in every business area. – Goal: balance demand and supply for products.

• Stages in the S&OP process Monthly Process This work 1.

Sales Planning

Gather data on past sales, demand forecasting EWO Meeting – March 2015

2.

Operations Planning

Assess ability to meet demand, account for production variability

3.

Reconciliation of Plans

Match supply and demand with financial considerations

Adapted from Ling & Goddard (1988)

4.

S&OP Implementation and Evaluation

Distribute and execute plan (scheduling level), evaluate performance 2

Problem Statement • Production planning of a network of chemical plants • Given – – – –

Deterministic monthly product demand, Maximum installed capacity of each plant, Transportation, production, and inventory costs. Optional: current production plan (production targets)

• Goals ① Propose a new production plan by incorporating historical production variability, ② Evaluate the performance of the proposed plan using tradeoff average return vs. risk.

• Schematic of proposed approach Statistical Analysis S&OP Data

Quantile Regression

Optimization/Si mulation Return vs. Risk Tradeoff 3

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Deviation from Plan • Given historical operational data (planned and actual production rates). • Define deviation: Δ = Plan – Actual  Production Variability • Use quantile regression to model distribution of Δ conditional on a particular Plan value. w.u.: weight units • Example: 3.00 ∆ (w.u.)

2.00 1.00 0.00 -1.00 -2.00 0.00

Less variability

5.00

10.00

15.00

20.00

Plan (w.u.)

Plan = 10 w.u. ∆ (w.u.)

[-1.5, 2.0]

∆ (w.u.)

[-0.6, 0.4]

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30.00

More variability

Plan = 1.5 w.u.

Probability

25.00

Probability

4

Motivating Example • Process network structure B C D A

E F G

• Main objective

*↑

↑ Reliability* ↑ Margin

Spread of Δ around 0  ↑ Variability  ↓ Reliability

– Demonstrate the different allocation schemes as a function of financial risk tolerated. 5 EWO Meeting – March 2015

94.25%

321.00

P3

Region I 316.00

94.15% 94.10%

P2

311.00

7.00

94.05%

Region II

P1

306.00

11.00 15.00 19.00 23.00 Standard Deviation of Profit (m.u.) Profit Margin

• •

94.20%

94.00% 27.00

Average Overall Service Level

Average Profit (m.u.)

Efficient Frontier

Service Level

Average overall service level does not increase after point P2. Increase in overall expected margin is accompanied by increase in financial risk – More A is allocated to less reliable, high-margin plants (next slide).

m.u.: money units 6 EWO Meeting – March 2015

Allocation 206.00

120.00

204.00

118.00 116.00

202.00

114.00

200.00

112.00

198.00

110.00

196.00

108.00

Allocation of A to G (w.u.)

Allocation of A to B (w.u.)

• Total average allocation of A to highest-margin and lowest-margin plants.

Point 120 180 240 Point 360 420 480 540 600 Point P1 P2 P3 ε Value (m.u.)2

•

Overall allocation of A from Region I (less risk) to Region II (more risk) – ↓ low-margin plants – ↑ high-margin plants

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B G

Contributions and Conclusions • General framework to model production variability conditional on production Plan. o Historical deviation from plan: Δ = Plan − Actual. o Quantile regression to generate scenarios.

• Trade-off analysis for different material allocation schemes. • Optimization-based approach + Simultaneously minimizes risk and accounts for production variability, + Directly accounts for constraint violations, − Difficult or impossible to use explicit model for Δ given Plan.

• Implementation considerations o Data analysis framework can be used to profile Plan-Actual mismatches. o Possible memory limitation for larger instances (more scenarios).

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References • •

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Birge, J. R., and Louveaux, F. 2011. Introduction to Stochastic Programming. Springer Science+Business Media, LLC., second edition. New York, NY. USA. Conn, A. R.; Scheinberg, K.; and Vicente, L. N. 2009. Introduction to Derivative-Free Optimization. Society for Industrial and Applied Mathematics (SIAM) and the Mathematical Programming Society (MPS). Philadelphia, PA. USA. Koenker, R. 2005. Quantile Regression. Cambridge University Press. New York, NY. USA. Li, Q., and Racine, J. S. 2007. Nonparametric Econometrics: Theory and Practice. Themes in Modern Econometrics. Princeton University Press. New Jersey, NJ. USA. Ling, R. C., and Goddard, W. E. 1988. Orchestrating Success: Improve Control of the Business with Sales & Operations Planning. John Willey & Sons, Inc. New York, NY. USA. Miettinen, K. 1999. Nonlinear Multiobjective Optimization, volume 12 of International Series in Operations Research & Management Science. Kluwer Academic Publishers. Boston, MA. USA. Montgomery, D. C., and Runger, G. C. 2003. Applied Statistics and Probability for Engineers. John Wiley & Sons, Inc., third edition. New York, NY. USA. Roelofs, M., and Bisschop, J. 2013. Advanced Interactive Multidimensional Modeling System (AIMMS). http://www.aimms.com/.

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