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Maximum distance problem The Set Covering Problem

16. 10. 10. 10. 26. 7. 8. 6. 10. 9. 4. 3. 2. 1. 5. 12. 10. 12. 12. 10. 20. 14. 22. 10. 12. 26. Maximum distance problem The Set Covering Problem.

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Maximum distance problem The Set Covering Problem

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  1. 16 10 10 10 26 7 8 6 10 9 4 3 2 1 5 12 10 12 12 10 20 14 22 10 12 26 Maximum distance problem The Set Covering Problem Let us consider that local authorities want to locate fire brigades at some places from the set 1, 2, 3 and4 so that a distance from the worst located dwelling place from set {1, 2, …, 10}to fire brigade location be at most 25 km. The numberof fire brigades should be minimised. All dwellingplaces must be covered. Transportationnetworkwithdistances is onthepicturebelow. Usetheshortestdistancesmatrix and calculateincidentalmatrix from shortestdistancesmatrix in Mosel. i’ i aij=1 ai’j=0 j customers D

  2. Maximum distance problem The Set Covering Problem Mathematic model of the Maximum distance problem

  3. Maximum distance problem The Set Covering Problem Solve the previous problem but now a distance from the worst located dwelling place from set {1, 2, …, 10}to fire brigade location be at most 20km. Canweobtainfeasiblesolutionnow? Use getprobstatfunction. procedureprint_status! To findoutthe status ofthesolution declarations status:array({XPRS_OPT, XPRS_UNF, XPRS_INF, XPRS_UNB}) ofstring end-declarations status:=['Optimum found', 'Unfinished', 'Infeasible', 'Unbounded'] writeln(status(getprobstat)) end-procedure OR if (getprobstat != XPRS_OPT) then writeln(“Optimal solution not found”)

  4. 16 10 10 10 26 7 10 8 6 1 2 5 4 9 3 12 10 12 12 10 20 14 22 10 12 26 The Medical Emergency Design ProblemThe Allocation Model Let us consider that local authorities want to locate 1ambulance vehicle at one place from the set 1, 2, 3 and4 so that the size of the part of population from set {1, 2, …, 10}, which is out of the time limitTmax =30, should be minimized. Solveusingtheallocationapproach. Populationbjin nodes {1, 2, …, 10}: 100, 150, 100, 200, 150, 100, 100, 200, 150, 100 Transportationnetworkwith travel times is onthepicturebelow. Usetheshortestdistancesmatrix. We definecij =bj, if dij >Tmaxand cij =0 otherwise.

  5. The Medical Emergency Design ProblemThe Allocation Model Distance Matrix (travel time)

  6. The Medical Emergency Design ProblemThe Allocation Model

  7. 16 10 10 10 26 7 8 6 10 9 4 3 2 1 5 12 10 12 12 10 20 14 22 10 12 26 The Medical Emergency Design ProblemThe Covering Model Let us consider that local authorities want to locate 1ambulance vehicle at one place from the set 1, 2, 3 and4 so that the size of the part of population from set {1, 2, …, 10}, which is out of the time limitTmax =30, should be minimized. Solveusingthecoveringapproach. Populationbjin nodes{1, 2, …, 10}: 100, 150, 100, 200, 150, 100, 100, 200, 150, 100 Transportationnetworkwith travel times is onthepicturebelow. Usetheshortestdistancesmatrix. xj=0 i i’ ai’j=0 aij=1 j customers Tmax The xj is allowed to be zero only if no ambulance is located in the radius Tmax from j.

  8. The Medical Emergency Design ProblemThe Covering Model

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