“…In order to ful ll the assignment problem we use the result of above model to nd an e cient assignment based on observed data. \begin{gathered} Min\,\,\,\sum\limits_{{i=1}}^{n} {\sum\limits_{{j=1}}^{n} { -{\theta _{ij}}{x_{ij}}} } \h ll \\ s.t., \h ll \\ \sum\limits_{{j=1}}^{n} {{x_{ij}}=1\,\,\,\,\,\,\,\,\,\,\,\,\,1 \leqslant i \leqslant n} \,\,\,\,\,\,\,\,\,\,\, (7) \h ll \\ \sum\limits_{{i=1}}^{n} {{x_{ij}}=1\,\,\,\,\,\,\,\,\,\,\,\,\,1 \leqslant j \leqslant n} \,\,\,\,\,\,\, \h ll \\ {x_{ij}} \in \{ 0,1\} \,\,\,\,\,\,\,\,\,\,\,1 \leqslant i,j \leqslant n \h ll \\ \end{gathered} Note that we use the e ciency of each assignment for the coe cient of objective function, that is, higher is better. That is why a minus is multiplied to the coe cient in contrast with cost coe cient of generic assignment problem of (4).…”