Table 1 Symbols and definitions.

Set

\({\mathscr {J}}\)

Set of physicians, \({\mathscr {J}} = \{1,2,\ldots ,I\}\)

\({\mathscr {W}}\)

Set of weeks in the decision period, \({\mathscr {W}} = \{1,2,\ldots ,W\}\)

\({\mathscr {D}}\)

Set of days in each week, \({\mathscr {D}} = \{1,2,\ldots ,7\}\)

\({\mathscr {D}}^w\)

Set of holidays in week \(w.\)

\({\mathscr {K}}\)

Set of patient categories, \({\mathscr {K}} = \{1,2,\ldots ,K\}.\)

Parameters

\({\tilde{y}}_{k,d}\)

Random demand for the \(k\)-th patient category on day d.

\(a_{i,k}\)

Service capacity ratio of the \(k\)-th patient category for physician \(i.\)

\(c_i\)

Maximum service capacity for physician i per outpatient shift.

\(T^{\text {min}}\)

Average minimum number of outpatient shifts during holidays per week.

\(T^{\text {max}}\)

Average maximum number of outpatient shifts during holidays per week.

\(H^{\text {min}}\)

Average minimum total number of outpatient shifts per week.

\(H^{\text {max}}\)

Average maximum total number of outpatient shifts per week.

Decision variables

\(\chi _{i,w,d}\)

Number of outpatient shifts assigned to physician \(i\) on day \(d\) of week \(w.\)