1. 1 Optimal Economic Decision Rules in the Biomass Supply Chain with CO2 Considerations Peter Lohmander Professor Dr., SUAS, Umea, SE-90183, Sweden Peter@Lohmander.com Peter@Lohmander.com ALIO-INFORMS International 2010 Buenos Aires, Monday, June 07, 08:30 - 10:00

2. 2 Optimal Economic Decision Rules in the Biomass Supply Chain with CO2 Considerations Peter Lohmander Abstract: Decisions in the biomass supply chain influence the size of the renewable energy feedstock. Indirectly, the use of fossil fuels, CO2 uptake from the atmosphere, and emissions of CO2 to the atmosphere are affected. CCS, carbon capture and storage, is one method to limit total CO2 emissions. The total decision problem of this system is defined and general economic decision rules are derived. In typical situations, a unique global cost minimum can be obtained.

3. 3 The role of the forest? The best way to reduce the CO2 in the atmosphere may be to increase harvesting of the presently existing forests (!), to produce energy with CCS and to increase forest production in the new forest generations. We capture and store more CO2!

4. 4 Permanent storage of CO2 Coal mine Oil field Natural gas CCS, Carbon Capture and Storage, has already become the main future emission reduction method of the fossile fuel energy industry Energy plant with CO2 capture and separation

5. 5 CO2 Permanent storage of CO2 How to reduce the CO2 level in the atmosphere, not only to decrease the emission of CO2 Energy plant with CO2 capture and separation

6. 6 The role of the forest in the CO2 and energy system The following six pictures show that it is necessary to intensify the use of the forest for energy production in combination with CCS in order to reduce the CO2 in atmosphere! All figures and graphs have been simplified as much as possible, keeping the big picture correct, in order to make the main point obvious. In all cases, we keep the total energy production constant.

7. 7 CO2 Permanent storage of CO2 Coal, oil, gas The present situation. 4 1 5 0 1 CO2 increase in the atmosphere: 5-1 = 4

8. 8 CO2 Permanent storage of CO2 Coal, oil, gas If we do not use the forest for energy production but use it as a carbon sink. Before the forest has reached equilibrium, this happens: 5 5 0 1 CO2 increase in the atmosphere: 5-1 = 4

9. 9 CO2 Permanent storage of CO2 Coal, oil, gas If we do not use the forest for energy production but use it as a carbon sink. When the forest has reached equilibrium, this happens: 5 1 5 0 1 CO2 increase in the atmosphere: 5+1-1 = 5

10. 10 CO2 Permanent storage of CO2 Coal, oil, gas If we use CCS with 80% efficiency and let the forest grow until it reaches equilibrium. 5 1 1 4 1 CO2 increase in the atmosphere: 1+1-1 = 1

11. 11 CO2 Permanent storage of CO2 Coal, oil, gas If we use CCS with 80% efficiency and use the forest with ”traditional” low intensity harvesting and silviculture. 4 1 1 4 1 CO2 increase in the atmosphere: 1-1 = 0

12. 12 CO2 Permanent storage of CO2 Coal, oil, gas If we use CCS with 80% efficiency and use the forest with increased harvesting and high intensity silviculture. 3 2 1 4 2 CO2 ”increase” in the atmosphere: 1-2 = -1

13. 13 General conclusions: The best way to reduce the CO2 in the atmosphere may be to increase harvesting of the presently existing forests (!), to produce energy with CCS and to increase forest production in the new forest generations. We capture and store more CO2!

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19. 19 Observation 1 In optimum, the marginal cost for forest biomass utilization equals the marginal cost of fossil fuel utilization plus the marginal cost of global warming.

20. 20 Observation 2 In optimum, the marginal cost of global warming equals the marginal cost of CCS.

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22. 22 Second order minimum conditions:

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26. 26 Observations of the first and second order conditions:

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31. 31 So, if and or then

32. 32 Then, the solution to represents a (locally) unique minimum.

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34. 34 A numerically specified example:

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36. 36 Comparative statics analysis:

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42. 42 Explicit solution of the example for alternative values of K

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51. 51 Dynamic approach analysis

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58. 58 k is selected in way such that the two equations become identical. This way, the equations only determine the ratio B/A, not the values of A and B. This is necessary since we must have some freedom to determine A and B such that they fit the initial conditions. With two roots (that usually are different), we (usually) get two different ratios B/A. This makes it possible to fit the parameters to the (two dimensional) initial conditions (x(0),y(0)).

59. 59 One way to determine the value(s) of k is to use this equation:

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61. 61 Another way to get to the same equation, is to make sure that the two equations give the same value to the ratio B/A.

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63. 63 Lets us solve the equation!

64. 64 No cyclical solutions! Observe that the expression within the square root sign is positive. As a consequence, only real roots, k, exist. For this reason, cyclical solutions to the differential equation system can be ruled out.

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67. 67 We may observe that As a consequence, both roots to to the equation are strictly negative. Therefore, divegence from the equilibrium solution is ruled out.

68. 68 With only strictly negative roots, we have a guaranteed convergence to the equilibrium. However, this does not have to be monotone. With two different roots (k1 and k2) and with parameters A1 and A2 with different signs (and/or parameters B1 and B2 with different signs), the sign(s) of the deviation(s) from the equilibrium value(s) may change over time.

69. 69 Derivation of the roots in the example:

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72. 72 We may determine the path completely using the initial conditions

73. 73 We also use the earlier derived results:

74. 74 Using the derived roots, we get:

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76. 76 Let us use the initial conditions and determine the parameters!

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80. 80 Using the figures from the example, we get:

81. 81 The solutions to the numerically specified example X(t) = -106.63·EXP(- 0.13612·t) + 6.61·EXP(- 0.02718·t)

82. 82 Y(t) = - 69.95·EXP(- 0.13612·t) - 10.07·EXP(- 0.02718·t)

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84. 84 The cost function from different perspectives: (based on the numerically specified example)

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87. 87 Numerical solution of the example problem using direct minimization:

88. 88 K = 600 model: min = C; k = 600; C = cu + cf + ca + cw; cu = 5*u+1/40*u^2; cf = 10*f + 1/600*f^2; ca = 1/40*(k-u-w)^2; cw = 14*w+1/200*w^2; f = k-u; a = k-w; @free(anet); anet = a - u; @free(eqw); 31*equ+15*eqw=1500 + 16*k; 5*equ+6*eqw = -1400+5*k; end

89. 89 Variable Value Reduced Cost C 8975.806 0.000000 K 600.0000 0.000000 CU 4995.578 0.000000 CF 2516.909 0.000000 CA 1463.319 0.000000 CW 0.000000 0.000000 U 358.0645 0.000000 F 241.9355 0.000000 W 0.000000 1.903226 A 600.0000 0.000000 ANET 241.9355 0.000000 EQW -53.15315 0.000000 EQU 383.7838 0.000000

90. 90 K = 800 model: min = C; k = 800; C = cu + cf + ca + cw; cu = 5*u+1/40*u^2; cf = 10*f + 1/600*f^2; ca = 1/40*(k-u-w)^2; cw = 14*w+1/200*w^2; f = k-u; a = k-w; @free(anet); anet = a - u; @free(eqw); 31*equ+15*eqw=1500 + 16*k; 5*equ+6*eqw = -1400+5*k; end

91. 91 Variable Value Reduced Cost C 13952.25 0.000000 K 800.0000 0.000000 CU 6552.228 0.000000 CF 4022.401 0.000000 CA 2196.271 0.000000 CW 1181.353 0.000000 U 421.6216 0.000000 F 378.3784 0.000000 W 81.98198 0.000000 A 718.0180 0.000000 ANET 296.3964 0.000000 EQW 81.98198 0.000000 EQU 421.6216 0.000000

92. 92 K = 1000 model: min = C; k = 1000; C = cu + cf + ca + cw; cu = 5*u+1/40*u^2; cf = 10*f + 1/600*f^2; ca = 1/40*(k-u-w)^2; cw = 14*w+1/200*w^2; f = k-u; a = k-w; @free(anet); anet = a - u; @free(eqw); 31*equ+15*eqw=1500 + 16*k; 5*equ+6*eqw = -1400+5*k; end

93. 93 Variable Value Reduced Cost C 19357.66 0.000000 K 1000.000 0.000000 CU 7574.872 0.000000 CF 5892.379 0.000000 CA 2615.068 0.000000 CW 3275.339 0.000000 U 459.4595 0.000000 F 540.5405 0.000000 W 217.1171 0.000000 A 782.8829 0.000000 ANET 323.4234 0.000000 EQW 217.1171 0.000000 EQU 459.4595 0.000000

94. 94 Numerical approximation of the dynamics: ! dynsim; ! Peter Lohmander Valencia 20100222; model: sets: time/1..100/:x,y,dx,dy; endsets cxx = 31/300; cxy = 15/300; cyx = 15/300; cyy = 18/300; x(1) = -100; y(1) = -80;

95. 95 @FOR( time(t): dx(t)= -( cxx*x(t) + cxy*(y(t)) )); @FOR( time(t): dy(t)= -( cyx*x(t) + cyy*(y(t)) )); @FOR( time(t)| t#GT#1: x(t)= x(t-1) + dx(t-1) ); @FOR( time(t)| t#GT#1: y(t)= y(t-1) + dy(t-1) ); @for(time(t): @free(x(t))); @for(time(t): @free(y(t))); @for(time(t): @free(dx(t))); @for(time(t): @free(dy(t))); end

96. 96 Conclusions Global warming, forest policy, energy policy and CCS should be studied as one system. This way, the economically most efficient solution can be obtained. General and optimal decision rules have been derived. In typical situations, a unique global cost minimum can be obtained. We should, in the optimally coordinated way: -Increase harvesting of the presently existing forests. -Use more biomass from the forests to produce energy. -Increase forest production in the new forest plantations. -Increase the use of CCS.

97. 97 References Lohmander, P., Adaptive Optimization of Forest Management in a Stochastic World, in Weintraub A. et al (Editors), Handbook of Operations Research in Natural Resources, Springer, Springer Science, International Series in Operations Research and Management Science, New York, USA, pp 525-544, 2007 http://www.amazon.ca/gp/reader/0387718141/ref=sib_dp_pt/701-0734992- 1741115#reader-link http://www.amazon.ca/gp/reader/0387718141/ref=sib_dp_pt/701-0734992- 1741115#reader-link Lohmander, P,. Energy Forum, Stockholm, 6-7 February 2008, Conference program with links to report and software by Peter Lohmander: http://www.energyforum.com/events/conferences/2008/c802/program.php http://www.lohmander.com/EF2008/EF2008Lohmander.htm http://www.energyforum.com/events/conferences/2008/c802/program.php http://www.lohmander.com/EF2008/EF2008Lohmander.htm Lohmander, P., Ekonomiskt rationell utveckling för skogs- och energisektorn i Sverige, Nordisk Papper och Massa, Nr 3, 2008 Lohmander, P., Guidelines for Economically Rational and Coordinated Dynamic Development of the Forest and Bio Energy Sectors with CO2 constraints, Proceedings from the 16th European Biomass Conference and Exhibition, Valencia, Spain, 02-06 June, 2008 (In the version in the link, below, an earlier misprint has been corrected. ) http://www.Lohmander.com/Valencia2008.pdf http://www.Lohmander.com/Valencia2008.pdf

98. 98 Lohmander, P., Economically Optimal Joint Strategy for Sustainable Bioenergy and Forest Sectors with CO2 Constraints, European Biomass Forum, Exploring Future Markets, Financing and Technology for Power Generation, CD, Marcus Evans Ltd, Amsterdam, 16th-17th June, 2008 http://www.Lohmander.com/Amsterdam2008.ppt http://www.Lohmander.com/Amsterdam2008.ppt Lohmander, P., Ekonomiskt rationell utveckling för skogs- och energisektorn, Nordisk Energi, Nr. 4, 2008 Lohmander, P., Optimal resource control model & General continuous time optimal control model of a forest resource, comparative dynamics and CO2 consideration effects, SLU Seminar in Forest Economics, Umea, Sweden, 2008-09-18 http://www.lohmander.com/CM/CMLohmander.ppthttp://www.lohmander.com/CM/CMLohmander.ppt Lohmander, P., Tools for optimal coordination of CCS, power industry capacity expansion and bio energy raw material production and harvesting, 2nd Annual EMISSIONS REDUCTION FORUM: - Establishing Effective CO2, NOx, SOx Mitigation Strategies for the Power Industry, CD, Marcus Evans Ltd, Madrid, Spain, 29th & 30th September 2008 http://www.lohmander.com/Madrid08/Madrid_2008_Lohmander.ppt http://www.lohmander.com/Madrid08/Madrid_2008_Lohmander.ppt Lohmander, P., Optimal CCS, Carbon Capture and Storage, Under Risk, International Seminars in Life Sciences, Universidad Politécnica de Valencia, Thursday 2008-10-16 http://www.lohmander.com/OptCCS/OptCCS.ppt http://www.lohmander.com/OptCCS/OptCCS.ppt

99. 99 Lohmander, P., Economic forest production with consideration of the forest and energy industries, E.ON International Bioenergy Conference, Malmo, Sweden, 2008-10-30 http://www.lohmander.com/eon081030/eon081030.ppthttp://www.lohmander.com/eon081030/eon081030.ppt Lohmander, P., Optimal dynamic control of the forest resource with changing energy demand functions and valuation of CO2 storage, UE2008.fr, The European Forest-based Sector: Bio-Responses to Address New Climate and Energy Challenges? Nancy, France, November 6-8, 2008 http://www.lohmander.com/Nancy08/Nancy08.ppt (See also later versions 2009)http://www.lohmander.com/Nancy08/Nancy08.ppt Lohmander, P., Optimal dynamic control of the forest resource with changing energy demand functions and valuation of CO2 storage, The European Forest-based Sector: Bio-Responses to Address New Climate and Energy Challenges, Nancy, France, November 6-8, 2008, Proceedings: (forthcoming) in French Forest Review (2009) Abstract: Page 65 of: http://www.gip-ecofor.org/docs/34/rsums_confnancy2008__20081105.pdf Presentation as pdf: http://www.gip- ecofor.org/docs/nancy2008/ppt_des_presentations_orales/lohmander_session_3.1.pdf Conference: http://www.gip-ecofor.org/docs/34/nancy2008englishprogramme20081106.pdfhttp://www.gip-ecofor.org/docs/34/rsums_confnancy2008__20081105.pdfhttp://www.gip- ecofor.org/docs/nancy2008/ppt_des_presentations_orales/lohmander_session_3.1.pdfhttp://www.gip-ecofor.org/docs/34/nancy2008englishprogramme20081106.pdf ECOFOR, (in French) Summary of results by Peter Lohmander (on page 8) in “Evaluation du developpement de la bioenergie”, in Bulletin d’information sur les forets europeennes, l’energie et climat, Volume 157, Numero 1, Lundi 10 novembre 2008 http://www.gip-ecofor.org/docs/34/nancy2008synthseiisd.pdfhttp://www.gip-ecofor.org/docs/34/nancy2008synthseiisd.pdf IISD, Summary of results by Peter Lohmander (on page 6) in “Evaluation of Bioenergy Development”, in European Forests, Energy and Climate Bulletin, Published by the International Institute for Sustainable Development (IISD) http://www.iisd.org/, Vol. 157, No. 1, Monday, 10 November, 2008 http://www.iisd.ca/download/pdf/sd/ymbvol157num1e.pdf http://www.iisd.ca/download/pdf/sd/ymbvol157num1e.pdf

100. 100 Lohmander, P., Integrated Regional Study Stage 1., Presentation at the E.ON - Holmen - Sveaskog - SLU Research Meeting, Norrköping, Sweden, 2008-12-10 – 2008-12-11, http://www.lohmander.com/NorrDec08/NorrDec08.ppt, http://www.lohmander.com/NorrDec08/NorrDec08.pdf, http://www.lohmander.com/NorrDec08/NorrDec08RawData.xlshttp://www.lohmander.com/NorrDec08/NorrDec08.ppt http://www.lohmander.com/NorrDec08/NorrDec08.pdf http://www.lohmander.com/NorrDec08/NorrDec08RawData.xls Lohmander, P., Öka avverkningen och hjälp Sverige ur krisen, VI SKOGSÄGARE, Debatt, Nr. 1, 2009 http://www.lohmander.com/PLdebattVIS2009nr1.pdf http://www.lohmander.com/PLdebattVIS2009nr1.pdf Lohmander, P., Economic Forest Production with Consideration of the Forest and Energy Industries (SLU 2009-01-29), http://www.lohmander.com/SLU09/SLU09.pdf http://www.lohmander.com/SLU09/SLU09.ppt http://www.lohmander.com/SLU09/SLU09.pdf http://www.lohmander.com/SLU09/SLU09.ppt Lohmander, P., Rational and sustainable international policy for the forest sector with consideration of energy, global warming, risk, and regional development, SLU, Umea, 2009-02-18, http://www.lohmander.com/IntPres090218.ppthttp://www.lohmander.com/IntPres090218.ppt Lohmander, P., Strategic options for the forest sector in Russia with focus on economic optimization, energy and sustainability (Full paper in English with short translation to Russian), ICFFI News, Vol. 1, Number 10, March 2009 http://www.Lohmander.com/RuMa09/RuMa09.htm http://www.Lohmander.com/RuMa09/RuMa09.htm

101. 101 International seminar, ECONOMICS OF FORESTRY AND FOREST SECTOR: ACTUAL PROBLEMS AND TRENDS, St Petersburg, Russia, March 2009, http://www.lohmander.com/RuMa09/ProgramRuMa09.pdf http://www.lohmander.com/RuMa09/ProgramRuMa09.pdf Lohmander, P., Satsa på biobränsle, Skogsvärden, Nr 1, 2009 http://www.Lohmander.com/PL_SV_1_09.jpg http://www.Lohmander.com/PL_SV_1_09.jpg Lohmander, P., Stor potential för svensk skogsenergi, Nordisk Energi, Nr. 2, 2009 http://www.Lohmander.com/Information/ne1.jpg http://www.Lohmander.com/Information/ne2.jpg http://www.Lohmander.com/Information/ne3.jpg http://www.Lohmander.com/PL_SvSE_090205.pdf http://www.Lohmander.com/PL_SvSE_090205.doc http://www.Lohmander.com/Information/ne1.jpg http://www.Lohmander.com/Information/ne2.jpg http://www.Lohmander.com/Information/ne3.jpg http://www.Lohmander.com/PL_SvSE_090205.pdf http://www.Lohmander.com/PL_SvSE_090205.doc Lohmander, P., Strategiska möjligheter för skogssektorn i Ryssland Nordisk Papper och Massa, Nr 2, 2009 http://www.Lohmander.com/PL_NPM_2_2009.pdf http://www.Lohmander.com/PL_RuSwe_09.pdf http://www.Lohmander.com/PL_RuSwe_09.doc http://www.Lohmander.com/PL_NPM_2_2009.pdf http://www.Lohmander.com/PL_RuSwe_09.pdf http://www.Lohmander.com/PL_RuSwe_09.doc

102. 102 Lohmander, P., Economic forest production with consideration of the forest- and energy industries, Project meeting presentation, Stockholm, Sweden, 2009-05-11, http://www.lohmander.com/EON_090511.ppt http://www.lohmander.com/EON_090511.ppt Lohmander, P., Derivation of the Economically Optimal Joint Strategy for Development of the Bioenergy and Forest Products Industries, European Biomass and Bioenergy Forum, MarcusEvans, London, UK, 8-9 June, 2009, http://www.lohmander.com/London09/London_Lohmander_09.p pt & ttp://www.lohmander.com/London09.pdf http://www.lohmander.com/London09/London_Lohmander_09.p ptttp://www.lohmander.com/London09.pdf Lohmander, P., Rational and sustainable international policy for the forest sector - with consideration of energy, global warming, risk, and regional development, Preliminary plan, 2009-08-05, http://www.lohmander.com/ip090805.pdf http://www.lohmander.com/ip090805.pdf