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E[ \ \tau_n, \gamma_n, f_{nm} \ ] = \sum_n {\rm w}_k \sum_nk  \left[ {\rm w}_e \cdot \left( p_{e,n} \ \ (t_k) - \tilde p_{e,n} \ \ (t_k) \right)^2  

+ {\rm w}_{\rm wf} \ \ \cdot \left( p_{{\rm wf},n} \ \ (t_k) - \tilde p_{{\rm wf},n} \ \ (t_k) \right)^2  \right]   \rightarrow \min

where 

LaTeX Math Inline
body--uriencoded--%7B\rm w%7D_e + %7B\rm w%7D_%7B\rm wf%7D = 1
 are the cost weight coefficients for formation pressure and bottom-hole pressure correspondingly

and

LaTeX Math Inline
body--uriencoded--%7B\rm w%7D_k = %7B\rm w%7D(t_k)
 are the the weight coefficients for time (usually the weight of the later times is higher than that for early times). 


The constraints are:

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J_n \geq  0 ,  \quad \gamma_n \geq 0,  \quad f_{nm} \ \geq  0 , \quad \sum_m f^{\uparrow}_{O, nm} \ \leq 1 , \quad \sum_m f^{\uparrow}_{G, nm} \ \leq 1, \quad \sum_m f^{\downarrow}_{W, nm} \ \leq 1, \quad \sum_m f^{\downarrow}_{G, nm} \ \leq 1

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