clc clear all %Startzeitpunkt festhalten Start_time = cputime; %################################# %Globalparameter initial festlegen %################################# % Symbolische Laufvariable für die Summen festlegen syms k tau; %Spätester Markteintrittszeitpunkt für die Company und den Competitor %festlegen. Ein späterer Markteintrittszeitpunkt ist nicht möglich. N = 20; %Kalkulationszinssatz festlegen r = 0.03; %Maximale Anzahl an Szenarien festlegen e_max = 2; %Ergebnisvektor vorbelegen Ergebnisse = zeros(e_max,40); %Vektor der Innovations- und Immitationsparameter initial festlegen p = zeros (e_max,2); q = zeros (e_max,2); %############################# %globale Competitor Parameter %############################# %Innovator Profile Competitor v_M = 1; %Spillover Effekte Competitor S_M = 0.25; %########################## %globale Company Parameter %########################## %Increasing/Decreasing Factor of Initial Sales Volume a = 1.15; %Decreasing Factor of FM-Probability (Wettbewerbskennwert für einen Markt) b = 1.8; %Prozentualer Anteil der Ausgaben für Marketing an den Gesamtausgaben %M=0,05 %M=0,1 %M=0,2 M = 0.1; % Marketing-Technologie Matrix definieren A = [1.1 1.05 1.02; 1.15 1.08 1.03; 1.2 1.1 1.04]; %######################################################### %Lokale Parameter für alle Szenarien generieren %######################################################### %Company Innovator profile festlegen und speichern v_C = unifrnd(0,2,e_max,1); Ergebnisse(:,8) = v_C; %Knowledge Potentials der Company pro Innovation festlegen und speichern K_m = unifrnd(0,6,e_max,2); Ergebnisse(:,9) = K_m(:,1); Ergebnisse(:,10) = K_m(:,2); %Initial kumulierte Umsätze pro Markt während der Marktphase festlegen und speichern m_0 = unifrnd(1e6,1e8,e_max,2); Ergebnisse(:,11) = m_0(:,1); Ergebnisse(:,12) = m_0(:,2); %Anfangsauszahlungen der Company pro Innovation festlegen und speichern A_0 = unifrnd(1e6,1e7,e_max,2); Ergebnisse(:,13) = A_0(:,1); Ergebnisse(:,14) = A_0(:,2); % Initial Coefficient of Innovation pro Markt festlegen p_0 = unifrnd(0.001,0.1,e_max,2); Ergebnisse(:,15) = p_0(:,1); Ergebnisse(:,16) = p_0(:,2); % Initial Coefficient of Imitation pro Markt festlegen q_0 = unifrnd(0.2,1.5,e_max,2); Ergebnisse(:,17) = q_0(:,1); Ergebnisse(:,18) = q_0(:,2); %Einen Preis der Innovation initial auf 1 setzen um für den Umsatz die %korrekte Einheit zu haben. Für das weitere Vorgehen nicht relevant. P = 1; %Spillover Effekte der Company für beide Innovationen und alle Szenarien festlegen %Vektor vorbelegen S_C = zeros(e_max,2); for i = 1:e_max %für Innovation 1 if (K_m(i,1) > 5 && K_m(i,1) <= 6) S_C(i,1) = 0.1; elseif (K_m(i,1) > 2 && K_m(i,1) <= 5) S_C(i,1) = 0.25; else S_C(i,1) = 0.6; end %für Innovation 2 if (K_m(i,2) > 5 && K_m(i,2) <= 6) S_C(i,2) = 0.1; elseif (K_m(i,2) > 2 && K_m(i,2) <= 5) S_C(i,2) = 0.25; else S_C(i,2) = 0.6; end end %Spillover Effekte für beide Innovationen im Ergebnisvektor speichern Ergebnisse(:,19) = S_C(:,1); Ergebnisse(:,20) = S_C(:,2); %############################# %Schleife über alle Szenarien %############################# for n = 1 : e_max %Coefficient of Innovation und Imitation pro Innovation und Markt festlegen %Innovation 1 in Markt 1 if (M == 0.05 && K_m(n,1) > 0 && K_m(n,1) <= 2) p(n,1) = p_0(n,1) * A(1,1); q(n,1) = q_0(n,1) * A(1,1); elseif (M == 0.1 && K_m(n,1) > 0 && K_m(n,1) <= 2) p(n,1) = p_0(n,1) * A(2,1); q(n,1) = q_0(n,1) * A(2,1); elseif (M == 0.2 && K_m(n,1) > 0 && K_m(n,1) <= 2) p(n,1) = p_0(n,1) * A(3,1); q(n,1) = q_0(n,1) * A(3,1); elseif (M == 0.05 && K_m(n,1) > 2 && K_m(n,1) < 5) p(n,1) = p_0(n,1) * A(1,2); q(n,1) = q_0(n,1) * A(1,2); elseif (M == 0.1 && K_m(n,1) > 2 && K_m(n,1) < 5) p(n,1) = p_0(n,1) * A(2,2); q(n,1) = q_0(n,1) * A(2,2); elseif (M == 0.2 && K_m(n,1) > 2 && K_m(n,1) < 5) p(n,1) = p_0(n,1) * A(3,2); q(n,1) = q_0(n,1) * A(3,2); elseif (M == 0.05 && K_m(n,1) > 5 && K_m(n,1) <= 6) p(n,1) = p_0(n,1) * A(1,3); q(n,1) = q_0(n,1) * A(1,3); elseif (M == 0.1 && K_m(n,1) > 5 && K_m(n,1) <= 6) p(n,1) = p_0(n,1) * A(2,3); q(n,1) = q_0(n,1) * A(2,3); elseif (M == 0.2 && K_m(n,1) > 5 && K_m(n,1) <= 6) p(n,1) = p_0(n,1) * A(3,3); q(n,1) = q_0(n,1) * A(3,3); end %Innovation 2 in Markt 1 if (M == 0.05 && K_m(n,2) > 0 && K_m(n,2) <= 2) p(n,1) = p_0(n,1) * A(1,1); q(n,1) = q_0(n,1) * A(1,1); elseif (M == 0.1 && K_m(n,2) > 0 && K_m(n,2) <= 2) p(n,1) = p_0(n,1) * A(2,1); q(n,1) = q_0(n,1) * A(2,1); elseif (M == 0.2 && K_m(n,2) > 0 && K_m(n,2) <= 2) p(n,1) = p_0(n,1) * A(3,1); q(n,1) = q_0(n,1) * A(3,1); elseif (M == 0.05 && K_m(n,2) > 2 && K_m(n,2) < 5) p(n,1) = p_0(n,1) * A(1,2); q(n,1) = q_0(n,1) * A(1,2); elseif (M == 0.1 && K_m(n,2) > 2 && K_m(n,2) < 5) p(n,1) = p_0(n,1) * A(2,2); q(n,1) = q_0(n,1) * A(2,2); elseif (M == 0.2 && K_m(n,2) > 2 && K_m(n,2) < 5) p(n,1) = p_0(n,1) * A(3,2); q(n,1) = q_0(n,1) * A(3,2); elseif (M == 0.05 && K_m(n,2) > 5 && K_m(n,2) <= 6) p(n,1) = p_0(n,1) * A(1,3); q(n,1) = q_0(n,1) * A(1,3); elseif (M == 0.1 && K_m(n,2) > 5 && K_m(n,2) <= 6) p(n,1) = p_0(n,1) * A(2,3); q(n,1) = q_0(n,1) * A(2,3); elseif (M == 0.2 && K_m(n,2) > 5 && K_m(n,2) <= 6) p(n,1) = p_0(n,1) * A(3,3); q(n,1) = q_0(n,1) * A(3,3); end %Innovation 1 in Markt 2 if (M == 0.05 && K_m(n,1) > 0 && K_m(n,1) <= 2) p(n,2) = p_0(n,2) * A(1,1); q(n,2) = q_0(n,2) * A(1,1); elseif (M == 0.1 && K_m(n,1) > 0 && K_m(n,1) <= 2) p(n,2) = p_0(n,2) * A(2,1); q(n,2) = q_0(n,2) * A(2,1); elseif (M == 0.2 && K_m(n,1) > 0 && K_m(n,1) <= 2) p(n,2) = p_0(n,2) * A(3,1); q(n,2) = q_0(n,2) * A(3,1); elseif (M == 0.05 && K_m(n,1) > 2 && K_m(n,1) < 5) p(n,2) = p_0(n,2) * A(1,2); q(n,2) = q_0(n,2) * A(1,2); elseif (M == 0.1 && K_m(n,1) > 2 && K_m(n,1) < 5) p(n,2) = p_0(n,2) * A(2,2); q(n,2) = q_0(n,2) * A(2,2); elseif (M == 0.2 && K_m(n,1) > 2 && K_m(n,1) < 5) p(n,2) = p_0(n,2) * A(3,2); q(n,2) = q_0(n,2) * A(3,2); elseif (M == 0.05 && K_m(n,1) > 5 && K_m(n,1) <= 6) p(n,2) = p_0(n,2) * A(1,3); q(n,2) = q_0(n,2) * A(1,3); elseif (M == 0.1 && K_m(n,1) > 5 && K_m(n,1) <= 6) p(n,2) = p_0(n,2) * A(2,3); q(n,2) = q_0(n,2) * A(2,3); elseif (M == 0.2 && K_m(n,1) > 5 && K_m(n,1) <= 6) p(n,2) = p_0(n,2) * A(3,3); q(n,2) = q_0(n,2) * A(3,3); end %Innovation 2 in Markt 2 if (M == 0.05 && K_m(n,2) > 0 && K_m(n,2) <= 2) p(n,2) = p_0(n,2) * A(1,1); q(n,2) = q_0(n,2) * A(1,1); elseif (M == 0.1 && K_m(n,2) > 0 && K_m(n,2) <= 2) p(n,2) = p_0(n,2) * A(2,1); q(n,2) = q_0(n,2) * A(2,1); elseif (M == 0.2 && K_m(n,2) > 0 && K_m(n,2) <= 2) p(n,2) = p_0(n,2) * A(3,1); q(n,2) = q_0(n,2) * A(3,1); elseif (M == 0.05 && K_m(n,2) > 2 && K_m(n,2) < 5) p(n,2) = p_0(n,2) * A(1,2); q(n,2) = q_0(n,2) * A(1,2); elseif (M == 0.1 && K_m(n,2) > 2 && K_m(n,2) < 5) p(n,2) = p_0(n,2) * A(2,2); q(n,2) = q_0(n,2) * A(2,2); elseif (M == 0.2 && K_m(n,2) > 2 && K_m(n,2) < 5) p(n,2) = p_0(n,2) * A(3,2); q(n,2) = q_0(n,2) * A(3,2); elseif (M == 0.05 && K_m(n,2) > 5 && K_m(n,2) <= 6) p(n,2) = p_0(n,2) * A(1,3); q(n,2) = q_0(n,2) * A(1,3); elseif (M == 0.1 && K_m(n,2) > 5 && K_m(n,2) <= 6) p(n,2) = p_0(n,2) * A(2,3); q(n,2) = q_0(n,2) * A(2,3); elseif (M == 0.2 && K_m(n,2) > 5 && K_m(n,2) <= 6) p(n,2) = p_0(n,2) * A(3,3); q(n,2) = q_0(n,2) * A(3,3); end %###################### %Funktionen definieren %###################### % Company Auszahlungen für R&D CF_R_11 = A_0(n,1) / 10 * K_m(n,1); CF_R_12 = A_0(n,1) / 10 * K_m(n,1); CF_R_21 = A_0(n,2) / 10 * K_m(n,2); CF_R_22 = A_0(n,2) / 10 * K_m(n,2); % Company Auszahlungen für Marketing zum Eintrittszeitpunkt CF_M_11 = @(t) M * CF_R_11 * t(1,1); CF_M_12 = @(t) M * CF_R_12 * t(1,2); CF_M_21 = @(t) M * CF_R_21 * t(2,1); CF_M_22 = @(t) M * CF_R_22 * t(2,2); % Verschiebungsparameter festlegen if (v_C(n,1) > 0 && v_C(n,1) < 1) z_C_11 = @(t) (1 - 0.5 * v_C(n,1)) * t(1,1); z_C_12 = @(t) (1 - 0.5 * v_C(n,1)) * t(1,2); z_C_21 = @(t) (1 - 0.5 * v_C(n,1)) * t(2,1); z_C_22 = @(t) (1 - 0.5 * v_C(n,1)) * t(2,2); else z_C_11 = @(t) 1 / (2 * v_C(n,1)) * t(1,1); z_C_12 = @(t) 1 / (2 * v_C(n,1)) * t(1,2); z_C_21 = @(t) 1 / (2 * v_C(n,1)) * t(2,1); z_C_22 = @(t) 1 / (2 * v_C(n,1)) * t(2,2); end % Company Wissen definieren K_C_11 = @(t) S_C(n,1) * K_m(n,1) - K_m(n,1) * (1 - S_C(n,1)) / (1 + exp(v_C(n,1) * z_C_11(t)))... + K_m(n,1) * (1 - S_C(n,1)) / (1 + exp(-v_C(n,1) * (t(1,1) - z_C_11(t)))); K_C_12 = @(t) S_C(n,1) * K_m(n,1) - K_m(n,1) * (1 - S_C(n,1)) / (1 + exp(v_C(n,1) * z_C_12(t)))... + K_m(n,1) * (1 - S_C(n,1)) / (1 + exp(-v_C(n,1) * (t(1,2) - z_C_12(t)))); K_C_21 = @(t) S_C(n,2) * K_m(n,2) - K_m(n,2) * (1 - S_C(n,2)) / (1 + exp(v_C(n,1) * z_C_21(t)))... + K_m(n,2) * (1 - S_C(n,2)) / (1 + exp(-v_C(n,1) * (t(2,1) - z_C_21(t)))); K_C_22 = @(t) S_C(n,2) * K_m(n,2) - K_m(n,2) * (1 - S_C(n,2)) / (1 + exp(v_C(n,1) * z_C_22(t)))... + K_m(n,2) * (1 - S_C(n,2)) / (1 + exp(-v_C(n,1) * (t(2,2) - z_C_22(t)))); % Competitor Wissen definieren K_M_11 = @(tau) 0.25 * K_m(n,1) - 0.75 * K_m(n,1) / (1 + exp(0.5 * tau))... + 0.75 * K_m(n,1) / (1 + exp(-0.5 * tau)); K_M_12 = @(tau) 0.25 * K_m(n,1) - 0.75 * K_m(n,1) / (1 + exp(0.5 * tau))... + 0.75 * K_m(n,1) / (1 + exp(-0.5 * tau)); K_M_21 = @(tau) 0.25 * K_m(n,2) - 0.75 * K_m(n,2) / (1 + exp(0.5 * tau))... + 0.75 * K_m(n,2) / (1 + exp(-0.5 * tau)); K_M_22 = @(tau) 0.25 * K_m(n,2) - 0.75 * K_m(n,2) / (1 + exp(0.5 * tau))... + 0.75 * K_m(n,2) / (1 + exp(-0.5 * tau)); % Company Sales Potential als First Mover definieren m_FM_C_11 = @(t) m_0(n,1) * a^K_C_11(t); m_FM_C_12 = @(t) m_0(n,2) * a^K_C_12(t); m_FM_C_21 = @(t) m_0(n,1) * a^K_C_21(t); m_FM_C_22 = @(t) m_0(n,2) * a^K_C_22(t); % Competitor Sales Potential als First Mover definieren m_FM_M_11 = @(tau) m_0(n,1) * a^K_M_11(tau); m_FM_M_12 = @(tau) m_0(n,2) * a^K_M_12(tau); m_FM_M_21 = @(tau) m_0(n,1) * a^K_M_21(tau); m_FM_M_22 = @(tau) m_0(n,2) * a^K_M_22(tau); % Company Sales Potential als Late Mover definieren m_LM_C_11 = @(t,tau) m_0(n,1) * a^(K_C_11(t) - t(1,1) + tau); m_LM_C_12 = @(t,tau) m_0(n,2) * a^(K_C_12(t) - t(1,2) + tau); m_LM_C_21 = @(t,tau) m_0(n,1) * a^(K_C_21(t) - t(2,1) + tau); m_LM_C_22 = @(t,tau) m_0(n,2) * a^(K_C_22(t) - t(2,2) + tau); % Erfolgswahrscheinlichkeiten für die Innovationen in den Märkten definieren Pr_S_11 = @(t) 1.1^(p(n,1) + q(n,1) + K_C_11(t)) * t(1,1) / ... (1.1^(p(n,1) + q(n,1) + K_m(n,1)) * t(1,1) + 1.4^(-t(1,1))); Pr_S_12 = @(t) 1.1^(p(n,2) + q(n,2) + K_C_12(t)) * t(1,2) / ... (1.1^(p(n,2) + q(n,2) + K_m(n,1)) * t(1,2) + 1.4^(-t(1,2))); Pr_S_21 = @(t) 1.1^(p(n,1) + q(n,1) + K_C_21(t)) * t(2,1) / ... (1.1^(p(n,1) + q(n,1) + K_m(n,2)) * t(2,1) + 1.4^(-t(2,1))); Pr_S_22 = @(t) 1.1^(p(n,2) + q(n,2) + K_C_22(t)) * t(2,2) / ... (1.1^(p(n,2) + q(n,2) + K_m(n,2)) * t(2,2) + 1.4^(-t(2,2))); % Scheiterwahrscheinlichkeit für die Innovationen in den Märkten % definieren Pr_F_11 = @(t) 1 - Pr_S_11(t); Pr_F_12 = @(t) 1 - Pr_S_12(t); Pr_F_21 = @(t) 1 - Pr_S_21(t); Pr_F_22 = @(t) 1 - Pr_S_22(t); % S-Kurve für Cashflows der Company und des Competitor pro Markt und Innovation definieren % S-Kurven der Company definieren S_C_11 = @(t,k) (p(n,1) + q(n,1))^2 / p(n,1) * ... exp(-(p(n,1) + q(n,1)) * (k - t(1,1))) / (1 + (q(n,1) / p(n,1)) * ... exp(-(p(n,1) + q(n,1)) * (k - t(1,1)))); S_C_12 = @(t,k) (p(n,2) + q(n,2))^2 / p(n,2) * ... exp(-(p(n,2) + q(n,2)) * (k - t(1,2))) / (1 + (q(n,2) / p(n,2)) * ... exp(-(p(n,2) + q(n,2)) * (k - t(1,2)))); S_C_21 = @(t,k) (p(n,1) + q(n,1))^2 / p(n,1) * ... exp(-(p(n,1) + q(n,1)) * (k - t(2,1))) / (1 + (q(n,1) / p(n,1)) * ... exp(-(p(n,1) + q(n,1)) * (k - t(2,1)))); S_C_22 = @(t,k) (p(n,2) + q(n,2))^2 / p(n,2) * ... exp(-(p(n,2) + q(n,2)) * (k - t(2,2))) / (1 + (q(n,2) / p(n,2)) * ... exp(-(p(n,2) + q(n,2)) * (k - t(2,2)))); % S-Kurven des Competitor definieren S_M_11 = @(tau,k) (p(n,1) + q(n,1))^2 / p(n,1) * ... exp(-(p(n,1) + q(n,1)) * (k - tau)) / (1 + (q(n,1) / p(n,1)) * ... exp(-(p(n,1) + q(n,1)) * (k - tau))); S_M_12 = @(tau,k) (p(n,2) + q(n,2))^2 / p(n,2) * ... exp(-(p(n,2) + q(n,2)) * (k - tau)) / (1 + (q(n,2) / p(n,2)) * ... exp(-(p(n,2) + q(n,2)) * (k - tau))); S_M_21 = @(tau,k) (p(n,1) + q(n,1))^2 / p(n,1) * ... exp(-(p(n,1) + q(n,1)) * (k - tau)) / (1 + (q(n,1) / p(n,1)) * ... exp(-(p(n,1) + q(n,1)) * (k - tau))); S_M_22 = @(tau,k) (p(n,2) + q(n,2))^2 / p(n,2) * ... exp(-(p(n,2) + q(n,2)) * (k - tau)) / (1 + (q(n,2) / p(n,2)) * ... exp(-(p(n,2) + q(n,2)) * (k - tau))); % Cashflow Funktionen der Company pro Markt und Innovation definieren % First Mover Cashflows definieren CF_FM_C_11_1 = @(t,k) m_FM_C_11(t) * S_C_11(t,k); CF_FM_C_11_2 = @(t,k,tau) m_FM_C_11(t) * S_C_11(t,k) * (1 - S_M_11(tau,k)); CF_FM_C_21_1 = @(t,k) m_FM_C_21(t) * S_C_21(t,k); CF_FM_C_21_2 = @(t,k,tau) m_FM_C_21(t) * S_C_21(t,k) * (1 - S_M_21(tau,k)); CF_FM_C_12_1 = @(t,k) m_FM_C_12(t) * S_C_12(t,k); CF_FM_C_12_2 = @(t,k,tau) m_FM_C_12(t) * S_C_12(t,k) * (1 - S_M_12(tau,k)); CF_FM_C_22_1 = @(t,k) m_FM_C_22(t) * S_C_22(t,k); CF_FM_C_22_2 = @(t,k,tau) m_FM_C_22(t) * S_C_22(t,k) * (1 - S_M_22(tau,k)); % Late Mover Cashflows definieren CF_LM_C_11 = @(t,k,tau) S_C_11(t,k) * (m_LM_C_11(t,tau) + m_FM_M_11(tau) * S_M_11(tau,k)); CF_LM_C_21 = @(t,k,tau) S_C_21(t,k) * (m_LM_C_21(t,tau) + m_FM_M_21(tau) * S_M_21(tau,k)); CF_LM_C_12 = @(t,k,tau) S_C_12(t,k) * (m_LM_C_12(t,tau) + m_FM_M_12(tau) * S_M_12(tau,k)); CF_LM_C_22 = @(t,k,tau) S_C_22(t,k) * (m_LM_C_22(t,tau) + m_FM_M_22(tau) * S_M_22(tau,k)); % Durchschnittliche Erwartungswerte der Company-NPV´s definieren % First-Mover NPV´s NPV_FM_C_11 = @(t) symsum(Pr_S_11(t) * (-A_0(n,1) + symsum(-CF_R_11 / (1 + r)^k,k,1,t(1,1)-1) + ... (CF_FM_C_11_1(t,k) - CF_M_11(t)) / (1 + r)^t(1,1) + symsum(CF_FM_C_11_1(t,k) / (1 + r)^k,k,t(1,1)+1,tau-1) + ... symsum(CF_FM_C_11_2(t,k,tau) / (1 + r)^k, k,tau,N)) + ... Pr_F_11(t) * (-A_0(n,1) + symsum(-CF_R_11 / (1 + r)^k, k,1,t(1,1)-1) + ... (CF_FM_C_11_1(t,k) - CF_M_11(t)) / (1 + r)^t(1,1)),tau,t(1,1)+1,N) / (N - t(1,1)); NPV_FM_C_12 = @(t) symsum(Pr_S_12(t) * (-A_0(n,1) + symsum(-CF_R_12 / (1 + r)^k, k,1,t(1,2)-1) + ... (CF_FM_C_12_1(t) - CF_M_12(t)) / (1 + r)^t(1,2) + symsum(CF_FM_C_12_1(t) / (1 + r)^k, k,t(1,2)+1,tau-1) + ... symsum(CF_FM_C_12_2(t) / (1 + r)^k, k,tau,N)) + ... Pr_F_12(t) * (-A_0(n,1) + symsum(-CF_R_12(t) / (1 + r)^k, k,1,t(1,2)-1) + ... (CF_FM_C_12_1(t) - CF_M_12(t)) / (1 + r)^t(1,2)),tau,t(1,2)+1,N) / (N - t(1,2)); NPV_FM_C_21 = @(t) symsum(Pr_S_21(t) * (-A_0(n,2) + symsum(-CF_R_21 / (1 + r)^k, k,1,t(2,1)-1) + ... (CF_FM_C_21_1(t) - CF_M_21(t)) / (1 + r)^t(2,1) + symsum(CF_FM_C_21_1(t) / (1 + r)^k, k,t(2,1)+1,tau-1) + ... symsum(CF_FM_C_21_2(t) / (1 + r)^k, k,tau,N)) + ... Pr_F_21(t) * (-A_0(n,2) + symsum(-CF_R_21(t) / (1 + r)^k, k,1,t(2,1)-1) + ... (CF_FM_C_21_1(t) - CF_M_21(t)) / (1 + r)^t(2,1)),tau,t(2,1)+1,N) / (N - t(2,1)); NPV_FM_C_22 = @(t) symsum(Pr_S_22(t) * (-A_0(n,2) + symsum(-CF_R_22 / (1 + r)^k, k,1,t(2,2)-1) + ... (CF_FM_C_22_1(t) - CF_M_22(t)) / (1 + r)^t(2,2) + symsum(CF_FM_C_22_1(t) / (1 + r)^k, k,t(2,2)+1,tau-1) + ... symsum(CF_FM_C_22_2(t) / (1 + r)^k, k,tau,N)) + ... Pr_F_22(t) * (-A_0(n,2) + symsum(-CF_R_22(t) / (1 + r)^k, k,1,t(2,2)-1) + ... (CF_FM_C_22_1(t) - CF_M_22(t)) / (1 + r)^t(2,2)),tau,t(2,2)+1,N) / (N - t(2,2)); % Late-Mover NPV´s NPV_LM_C_11 = @(t) symsum(Pr_S_11(t) * (-A_0(n,1) + symsum(-CF_R_11 / (1 + r)^k,k,1,t(1,1)-1) + ... (CF_LM_C_11(t,k,tau) - CF_M_11(t)) / (1 + r)^t(1,1) + symsum(CF_LM_C_11(t,k,tau) / (1 + r)^k,k,t(1,1)+1,N) + ... Pr_F_11(t) * (-A_0(n,1) + symsum(-CF_R_11 / (1 + r)^k, k,1,t(1,1)-1) + ... (CF_LM_C_11(t,k,tau) - CF_M_11(t)) / (1 + r)^t(1,1))),tau,t(1,1)+1,N) / (N - t(1,1)); NPV_LM_C_12 = @(t) symsum(Pr_S_12(t) * (-A_0(n,1) + symsum(-CF_R_12 / (1 + r)^k,k,1,t(1,2)-1) + ... (CF_LM_C_12(t,k,tau) - CF_M_12(t)) / (1 + r)^t(1,2) + symsum(CF_LM_C_12(t,k,tau) / (1 + r)^k,k,t(1,2)+1,N) + ... Pr_F_12(t) * (-A_0(n,1) + symsum(-CF_R_12 / (1 + r)^k, k,1,t(1,2)-1) + ... (CF_LM_C_12(t,k,tau) - CF_M_12(t)) / (1 + r)^t(1,2))),tau,t(1,2)+1,N) / (N - t(1,2)); NPV_LM_C_21 = @(t) symsum(Pr_S_21(t) * (-A_0(n,2) + symsum(-CF_R_21 / (1 + r)^k,k,1,t(2,1)-1) + ... (CF_LM_C_21(t,k,tau) - CF_M_21(t)) / (1 + r)^t(2,1) + symsum(CF_LM_C_21(t,k,tau) / (1 + r)^k,k,t(2,1)+1,N) + ... Pr_F_21(t) * (-A_0(n,2) + symsum(-CF_R_21 / (1 + r)^k, k,1,t(2,1)-1) + ... (CF_LM_C_21(t,k,tau) - CF_M_21(t)) / (1 + r)^t(2,1))),tau,t(2,1)+1,N) / (N - t(2,1)); NPV_LM_C_22 = @(t) symsum(Pr_S_22(t) * (-A_0(n,2) + symsum(-CF_R_22 / (1 + r)^k,k,1,t(2,2)-1) + ... (CF_LM_C_22(t,k,tau) - CF_M_22(t)) / (1 + r)^t(2,2) + symsum(CF_LM_C_22(t,k,tau) / (1 + r)^k,k,t(2,2)+1,N) + ... Pr_F_22(t) * (-A_0(n,2) + symsum(-CF_R_22 / (1 + r)^k, k,1,t(2,2)-1) + ... (CF_LM_C_22(t,k,tau) - CF_M_22(t)) / (1 + r)^t(2,2))),tau,t(2,2)+1,N) / (N - t(2,2)); % ###### First-Mover-Wahrscheinlichkeiten ###### p_FM_11 = @(t) b^(1 - t(1,1)) .* (t(1,1) >= 1) + 0 .* (t(1,1) == 0); p_FM_12 = @(t) b^(1 - t(1,2)) .* (t(1,2) >= 1) + 0 .* (t(1,2) == 0); p_FM_21 = @(t) b^(1 - t(2,1)) .* (t(2,1) >= 1) + 0 .* (t(2,1) == 0); p_FM_22 = @(t) b^(1 - t(2,2)) .* (t(2,2) >= 1) + 0 .* (t(2,2) == 0); % ###### Late-Mover-Wahrscheinlichkeiten ###### p_LM_11 = @(t) 1 - p_FM_11(t) .* (t(1,1) >= 1) + 0 .* (t(1,1) == 0); p_LM_12 = @(t) 1 - p_FM_12(t) .* (t(1,2) >= 1) + 0 .* (t(1,1) == 0); p_LM_21 = @(t) 1 - p_FM_21(t) .* (t(2,1) >= 1) + 0 .* (t(1,1) == 0); p_LM_22 = @(t) 1 - p_FM_22(t) .* (t(2,2) >= 1) + 0 .* (t(1,1) == 0); % ###### Zielfunktion für die Optimierung ###### objective = @(t) -(p_FM_11(t) * NPV_FM_C_11(t) + p_LM_11(t) * NPV_LM_C_11(t) + ... p_FM_12(t) * NPV_FM_C_12(t) + p_LM_12(t) * NPV_LM_C_12(t) + ... p_FM_21(t) * NPV_FM_C_21(t) + p_LM_21(t) * NPV_LM_C_21(t) + ... p_FM_22(t) * NPV_FM_C_22(t) + p_LM_22(t) * NPV_LM_C_22(t)); % Startwert für die Optimierung festlegen t0 = [1 2;3 4]; % ########################### % Nebenbedingungen % ########################### % ###### Obere und untere Grenzen ###### % untere Grenzen lb = zeros(2,2); % obere Grenzen ub = N * ones(2,2); % ###### Lineare Nebenbedingungen ###### % lineare Ungleichungen Ao = []; bo = []; % lineare Gleichungen Aeq = []; beq = []; % ###### Nichtlineare Nebenbedingungen ###### c = []; ceq = []; % ###### optimize with fmincon ###### % ###### [X,FVAL,EXITFLAG,OUTPUT,LAMBDA,GRAD,HESSIAN] ###### % = fmincon(FUN,X0,A,B,Aeq,Beq,LB,UB,NONLCON,OPTIONS) x = fmincon(objective,t0,Ao,bo,Aeq,beq,lb,ub,c,ceq) end % ###### Ergebnisse ###### % show final objective disp(['Final Objective: ' num2str(objective(x))]) % print solution disp('Solution') disp(['x1 = ' num2str(x(1))]) disp(['x2 = ' num2str(x(2))]) disp(['x3 = ' num2str(x(3))]) disp(['x4 = ' num2str(x(4))])