Economic Models - Convex Optimization

158 Anna-Maria Mouza
3.2.2. Personnel Claims for Salary Increase
According to Eq. (2), I have to introduce the following 10 constraints in
order to define the total salary expenses for each group.
X 10+i − c i X i + d10+i − − d+ 10+i
= 0, (i = 1,...,10). (6)
It is recalled that coefficients c i are presented in Table 3. An additional
variable X 21 is introduced to sum up salary expenses for all personnel at
the final year. The computation of this total is based on Eq. (3).
X 21 −
20∑
i=11
X i + d21 − − d+ 21
= 0. (7)
3.2.3. Complete Utilization of Personnel Capacity in Terms
of Working Hours
The forecasted number of patients for the final year is not exceeding the
clinic capabilities, regarding the existing infrastructure. Furthermore, the
decision maker does not want to alter the existing operation pattern, since
he considers that the present personnel manpower potential will be adequate
to provide satisfactory service to the number of patients forecasted,
provided that the under utilization of the regular working hours will be
avoided. Hence, I introduced the following constraints in accordance to
Eq. (4), which on the other hand may be regarded as a measure to provide
job security to all personnel by avoiding underutilization of their regular
working hours as shown in Table 4.
X 21+i − w i X i + d21+i − − d+ 21+i
= 0, (i = 1,...,10). (8)
Note, the co-efficients w i , are also presented in Table 4.
3.2.4. Patient expenses
The axial-tomography expenses per patient can be expressed as:
X 32 + d32 − − d+ 32 = 9.1.
X-ray expenses per patient:
X 33 + d33 − − d+ 33 = 5.7.
Medical expenses per patient:
X 34 + d34 − − d+ 34 = 59.4.
(9a)
(9b)
(9c)