HI
Hello, Could you please help me with the modeling in Python the following problem: (e.g., g_t means g with index t) Min∑_(i=1)^n▒∑_(t=1)^l▒[s_i (t)-min[s ̂_i (t)×α_t×exp(g_t ),C_i (t) ] ]^2 subject to s_i (t)=f_i (t)[S_i+f_(i-1) (t)[S_(i-1)+f_(i-2) (t)[S_(i-2)+⋯f_2 (t) [S_2+f_1 (t) S_1 ]…] ] ][1-f_(i+1) (t)] f_i (t)=F_i (t)-F_i (t-1) F_i (t)=(((1-e^(-(X_i (t)-X_i (0) )(p_i+q_i ) )))/(((q_i⁄p_i ) e^(- (X_i (t)-X_i (0) )(p_i+q_i ) )+1)), if t≥τ_i and F_i (t)=0 if t<τ_i X_i (t)=(t-τ_i+1)+ln(〖pr〗_i (t)/〖pr〗_i (0))β α_t≥0, g_t=const 00, ∀i=1,2,…,n Where s ̂_i (t)=p_i S_i +(q_i-p_i ) s_i (t-1)-(q_i/S_i ) [s_i (t-1) ]^2, S_i=μ_i (t)M_i -- http://mail.python.org/mailman/listinfo/python-list
Re: HI
Here we need to estimate p_i, q_i, and β. Thank you, > Min∑_(i=1)^n▒∑_(t=1)^l▒[s_i (t)-min[s ̂_i (t)×α_t×exp(g_t ),C_i > (t) ] ]^2 > subject to > s_i (t)=f_i (t)[S_i+f_(i-1) (t)[S_(i-1)+f_(i-2) (t)[S_(i-2)+⋯f_2 (t) > [S_2+f_1 (t) S_1 ]…] ] ][1-f_(i+1) (t)] > f_i (t)=F_i (t)-F_i (t-1) > F_i (t)=(((1-e^(-(X_i (t)-X_i (0) )(p_i+q_i ) )))/(((q_i⁄p_i ) e^(- > (X_i (t)-X_i (0) )(p_i+q_i ) )+1)), if t≥τ_i and F_i (t)=0 if > t<τ_i > X_i (t)=(t-τ_i+1)+ln(〖pr〗_i (t)/〖pr〗_i (0))β > α_t≥0, g_t=const > 0 S_i>0, > ∀i=1,2,…,n > Where > s ̂_i (t)=p_i S_i +(q_i-p_i ) s_i (t-1)-(q_i/S_i ) [s_i (t-1) ]^2, > S_i=μ_i (t)M_i -- http://mail.python.org/mailman/listinfo/python-list
Re: HI
Dear Ulrich Eckhardt and Jean-Michel Pichavant! First of all thank you for your attention. I'have never expected to receive response. Actually, I am doing my internship in Marketing Division in small company., I got this assignment yesterday morning. My boss wants perfect technology diffusion based forecasting model. I found the required model, modified it..but cannot solve it (university friend suggested Python because it had special tools for optimization). I will appreciate if you help me to find right tools and give some more advises. Thank you for your precious time. As to problem, I should use nonlinear least-square estimation methodology (to estimate p_i, q_i, and β parameters) where the objective of the estimation procedure is minimization of the sum of squared error. Here in problem: F_i (t) the cumulative density function at time t for technology generation i f_i (t) the probability density function at time t for technology generation i p_i the proportion of mass media communication for generation i q_i the proportion of word of mouth for generation i μ_i (t) the market share at time t for generation i (data exists) M_i total market potential for generation i, (data exists) S_i total sales potential for generation i, S_i=μ_i (t)M_i τ_i the introduction time for generation i, τ_i≥1 (data exists) s_i (t) the actual sales of products at time t for generation i (data exists) s ̂_i (t) the estimated sales of products at time t for generation i X_i (t) the cumulative market effects β the effectiveness of the price 〖pr〗_i (t) the price at time t for generation i (data exists) α_t the seasonal factor at time t (data exists) g_t the growth rate at time t (data exists) n the number of generations (data exists) l the number of periods (data exists) C_i (t) the capacity restriction regarding the product at time t for generation i (data exists) -- http://mail.python.org/mailman/listinfo/python-list
