144 The UMaP Journal 28. 2 (2007) Analysis of Model Our two variables to indicate strength of model strategy are the number of people in the waitlist(or the number of people who get transplants)and optimizing the matches so as to maximize lifetime after receiving a transplant. Efficient Allocation of Kidney Transplants We build a new model to take into account the effects of both distance and optimal match. A kidney arriving at a center can be given to the best matching candidate at that center, the best in the region, or the best in the countr Of 10,000 candidate recipients, on average 37 are from the center, 873 are from the region outside the center, and 9,090 are from the nation outside the region. Using a uniform distribution on (0, 1), we randomly assign scores to each of the 10,000, rank them by score, and take the highest rank at each level. We iterate this process 10,000 times and find the average rank of the toy candidate in each area(Table 4). Table 4 Average quality of top candidate in each area. Probability that top candidate Average rank(from botton is in this group Center 037% 97397 Region outside center I-270 8.72% Nation outside region 1 90.90 Transportation of the kidney can lead to damage, because of time delay in transplanting. Thus, we posit a damage function f that depends on the location of the recipient: lower in the center, slightly higher in the region but outside the center, and even higher in the country but outside the f(local)< f(regional)< f(national) Let us assume that when a kidney arrives in a center, it goes to the center, the region, or outside the region with probabilities a1, a2, and a3. Let G be the weighted score for the kidney, with G= a1 (1-f(local ) scorelocal+a2(1-f(regional)scorereglonal +a3(1-f(national).scorenat and expected value E(G)=a1(1-f(oca)9739.7+a2:(1- f(regional)97 (1-f(national) Optimizing G as a function of the ai is a linear programming problem, but we cannot solve it without assessing the damage function for different regions.144 The UMAP Journal 28.2 (2007) Analysis of Model Our two variables to indicate strength of model strategy are the number of people in the waitlist (or the number of people who get transplants) and optimizing the matches so as to maximize lifetime after receiving a transplant. Efficient Allocation of Kidney Transplants We build a new model to take into account the effects of both distance and optimal match. A kidney arriving at a center can be given to the best matching candidate at that center, the best in the region, or the best in the country. Of 10,000 candidate recipients, on average 37 are from the center, 873 are from the region outside the center, and 9,090 are from the nation outside the region. Using a uniform distribution on (0,1), we randomly assign scores to each of the 10,000, rank them by score, and take the highest rank at each level. We iterate this process 10,000 times and find the average rank of the top candidate in each area (Table 4). Table 4. Average quality of top candidate in each area. Probability that top candidate Average rank (from bottom) is in this group of top candidate among 10,000 Center = 0.37% 9739.7 Region outside center 11 o 8.72% 9989.7 Nation outside region 1 90.90% 9999.9 Transportation of the kidney can lead to damage, because of time delay in transplanting. Thus, we posit a damage function f that depends on the location of the recipient: lower in the center, slightly higher in the region but outside the center, and even higher in the country but outside the region, i.e., f(local) < f(regional) < f(national). Let us assume that when a kidney arrives in a center, it goes to the center, the region, or outside the region with probabilities al, a2, and a3. Let G be the weighted score for the kidney, with G = a1 • (1 - f(local)) , scorelo,.l + a2 . (I - f(regional)) • scoreregional + a3" (1 - f (national)) , scorena,tonal. (1) and expected value E(G) = al' (1 - f(local)). 9739.7 + a2. (1 - f(regional)). 9989.7 + a3 . (1 - f(national)). 9999.9. (2) Optimizing G as a function of the ai is a linear programming problem, but we cannot solve it without assessing the damage function for different regions