Operating Research

The United Nations Health Program is devoted to improving health care in the underdeveloped countries of the world. It now has six medical teams available to allocate among four such countries to improve their medical care, health education, and training programs. These four countries are Ivory Coast, Costa Rica, Honduras, and Suriname. The council needs to determine how many teams (if any) to allocate to each of these countries to maximize the total effectiveness of the six teams. The teams must be kept intact, so the number allocated to each country must be integer The measure of performance being used is additional person-years of life. In fact, for a particular country, this measure equals the country's increased life expectancy in years times its population The table below gives the estimated additional person-years of life (in multiples of 1000) for each country for possible allocation of medical teams. No. of Thousands of Additional Person-Years of Life Medical Country Teams Ivory Coast Costa Rica Honduras Suriname 0 0 0 0 0 45 35 50 20 2 80 60 20 45 3 90 65 4 10S 100 90 $ 130 145 140 13 160 163 160 [ 90 95 100 140 6 a) Let - 1. 2. 3. 4 be the countries Ivory Coast, Costa Rica, Honduras, and Suriname respectively. Furthermore, let dit be the measure of performance from allocating #medical teams to country i. Formulate this problem as an integer programming model. b) If this problem is to be solved via dynamic programming, what can be the appropriate stages? c) Define the function to be evaluated during the computations for the stages of dynamic programming (ie define the recursive formula to be evaluated) d) For the initial stage what is (are) the appropriate state()? Why? e) Show the corresponding mathematical calculations for the last stage (assume that last stage is related with the allocation of medical teams to Suriname)