maximize U_p=(1-p)(c_(p_N)^T-c_RN d_N )+p(c_(p_M)^T-c_RM d_M )-Z

Subject to, B_N d_N-c_(p_N)^T≥0

v/(1+αZ)^β ×Κ×d_M-c_(p_M)^T-c_a-(1-e^(-kZ) )/(1+e^(-kZ) )×L×d_M≤0

B_N d_N-c_(p_N)^T-B_N d_M+c_(p_M)^T≥0

v/(1+αZ)^β Κd_M-c_(p_M)^T-c_a-(1-e^(-kZ) )/(1+e^(-kZ) )×L×d_M-v/(1+αZ)^β Κd_N+c_(p_N)^T+c_a+(1-e^(-kZ) )/(1+e^(-kZ) )×L×d_N≥0

d_N,d_M,c_(p_N)^T,c_(p_M)^T,Z≥0