J = the number of selected indicators.

R = the number of provinces.

The above model assumes inter-regional mobility of human resources. Any limitation to this
assumption can be introduced into the model easily. In addition other constraints related to the
scarcity of other resources can be easily added to the model.

Adjusting the computed targets

As we discussed before the main purpose of the suggested procedure is the determination of
T_j^r for the above model or other purposes. However, the targets computed by the above
procedure might not be attainable for different reasons of which the most important one is
usually budget and other resource limitations. If the policy makers for any reason are interested
to consider a proportion of the computed targets in the model it would be possible to modify the
first set of constraints as follow:

n^rj

∑air Xij ≥ δjTj        , for r=1,2,...,R; and J=1,2,...,J.                   (7)

i=1

where coefficient δ_j^r reflects the percentage of the computed targets to be achieved.

The determination of δ_j^r in not necessarily a decision to be made outside the model. Ideed the
model may fail to have a feasible solution due to the limitation of skilled labour, budget or other
reasons. In this case an appropriate choice of δ_j^r could be useful in achieving a solution for the
model.

Before we suggest ways of finding δ_j^r it would be useful to make a small modification to the
above set of constraints. It would also be more appropriate to replace the computed targets, T_j^r ,
with a change in the level of (the concept reflected by) the indicator as follows:

n^rj

∑a_i^r_jX_i^r_j ≥ δ_j^rM_j^r       , for r=1,2,.,R; and J=1,2,.,J.                  (8)

i=1

where M^r_j is the amount of increase in the j^th indicator for the r^th province and is computed as
the difference between the computed targets, T_j^r , and the present actual value of the indicator

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