Economic Models - Convex Optimization

160 Anna-Maria Mouza
where X 43 , as it was mentioned earlier, represents the adequate charge per
patient, in order to satisfy Eq. (12). It is recalled that the coefficient 3625,
which appears in Eq. (11) too, is the stated forecast, regarding the expected
number of patients for the final year t f .
With the above formulation, we see that the number of constraints is
equal to the number of choice variables (43).
3.3. Priority of the goals — The objective function
It is obvious that the decision maker, apart from determining the goals of
the five-year plan, also has to specify the priorities (Gass, 1986), denoted by
P i , in order to accomplish the optimum allocation of resources for achieving
these goals in the best possible manner. One further point, that has to
be considered in the formulation of the model, is the possibility of weighing
the deviational variables at the same priority level (Gass, 1987). The
list of decision maker’s goals is presented below in descending order of
importance.
1. To retain the present operating pattern of the clinic.
This implies that no alterations are desired regarding the number and
composition of the existing personnel (P 1 ). Different weights have been
assigned to the various personnel groups.
2. To achieve the desired level of gross profits. Also, to provide reserves for
the personnel insurance, to cover all expenses for equipment replacements
and installation of a new IVR system (P 2 ).
3. To avoid underutilization of the personnel regular working hours, providing
at the same time job security to all employees (P 3 ).
4. To provide the funds necessary to cover all patient’s expenses (P 4 ).
5. To provide adequate funds for covering laboratory and fixed expenses,
depreciation etc. (P 5 ).
6. To provide the wage increase, claimed by the personnel at the various
groups (P 6 ).
In this case, weights are used to discriminate the salary increase of
each group. Heavier weights have been assigned to groups with lower
salaries.
According to the above ranking of the goals priority and taking into
account the relations for the corresponding totals, the following objective