Economic Models - Convex Optimization

Health Service Management 155
Table 3.
Employees’salary at the initial and final year of the planning period.
Groups (i)
Number
of group
members
(X i )
Annual
salary at
year t 0 ,for
all the
members of
group i (in
thousand )
Annual
rate of
increase,
R i (in %)
R i
Salary at
final year t f ,
for all the
members of
group i
(in )
Average
per person
at each
group (c c i )
1 10 260 6.5 356,222 35,622.2
2 1 24.7 6 33,054 33,054
3 3 54.6 4.5 68,040 22,680
4 14 163.8 4 199,290 14,235
5 3 58.5 4.9 74,307 24,769
6 1 27.3 5.8 36,190 36,190
7 3 32.76 3.8 39,476 13,158.666
8 4 41.6 3.6 49,647 12,411.75
9 4 42.64 3.5 50,643 12,660.75
10 10 101.4 3.4 119,851 11,985.10
Another point of interest refers to the average working hours of the
members of each group. The relative figures are analytically presented in
Table 4.
It can be easily verified that in Table 4, column 5 is obtained by multiplying
the elements of column 4 by 52.
Denoting by X 22+i (i = 1,...,10) the total average working hours per
year for all the group members, then I may write
X 22+i = w i × X i (i = 1,...,10). (4)
3. The Nature of the Problem
Given all the information presented in Tables 1–4, the resultant problem
is, how to formulate a feasible operating plan, which should combine
the desired salary increases and the full utilization of working hours,
the expenses incurred, together with the desired gross profit at the final
year set by the decision maker, in the best possible way with the minimum
sacrifice. This problem can be answered by the goal programming
method, originally developed by Charnes and Cooper (1961). It should