Optimizing Scheduling for Academic Meetings: Minimizing Makespan and Managing Breaks

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Optimizing Scheduling for Academic Meetings: Minimizing Makespan andManaging Breaks1.My colleagueDrWuwishes to visit all the attractionsin the Park of AssessmentThree.(For ease of reference,directdistances withinthepark are given below.)roadELEPEGLWLTLPGPGWTWTPPWlength(m)170350240530290330240600250220240Use the nearest-neighbour method to find such routes.Which is the shortest? Are anyof themHamiltonian cycles?Given Data:Road lengths (in meters) between various locations in the Park of Assessment Three:Nearest-Neighbor Method:The nearest-neighbor method involves starting at a particular point (e.g., Entrance (EL)) andselecting the closest unvisited point at each step until all points are visited.Steps for Nearest-Neighbour Method:1.Start at EL(Entrance)2.Find the nearest point:The distances from EL to other locations are:oEL to EP = 170oEL to EG = 350oEL to LW = 240oEL to LT = 530oEL to LP = 290oEL to GP = 330oEL to GW = 240oEL to TW = 600oEL to TP = 220oEL to PW = 240The closest point isEP(170 meters).3.From EP, find the nearest point to EP that has not been visited:The remaining points are:oEP to EG = 240oEP to LW = 530oEP to LT = 290oEP to LP = 330oEP to GP = 240oEP to GW = 600oEP to TW = 250oEP to TP = 220oEP to PW = 240The closest point isEG(240 meters).4.From EG, find the nearest point:The remaining points are:oEG to LW = 530

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oEG to LT = 290oEG to LP = 330oEG to GP = 240oEG to GW = 600oEG to TW = 250oEG to TP = 220oEG to PW = 240The closest point isLP(240 meters).5.From LP, find the nearest point:The remaining points are:oLP to LW = 530oLP to LT = 290oLP to GP = 330oLP to GW = 600oLP to TW = 250oLP to TP = 220oLP to PW = 240The closest point isPW(240 meters).6.From PW, find the nearest point:The remaining points are:oPW to LW = 530oPW to LT = 290oPW to GP = 330oPW to GW = 600oPW to TW = 250oPW to TP = 220The closest point isTP(220 meters).7.From TP, find the nearest point:The remaining points are:oTP to LW = 530oTP to LT = 290oTP to GP = 330oTP to GW = 600The closest point isGW(250 meters).8.From GW, find the nearest point:The remaining points are:oGW to LW = 530oGW to LT = 290oGW to GP = 330The closest point isLT(290 meters).9.From LT, find the nearest point:The remaining point isLW(530 meters).10.Route Summary:The nearest-neighbour path is:EL → EP → EG → LP → PW → TP → GW → LT → LW11.Hamiltonian Cycle:A Hamiltonian cycle requires visiting all vertices and returning to the starting point. In this case, theroute does not return to the starting point (EL), so this isnota Hamiltonian cycle.

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