The City of Port Charles has two hospitals. (Bayview and Lakeshore Hospital) Bay
ID: 3277458 • Letter: T
Question
The City of Port Charles has two hospitals. (Bayview and Lakeshore Hospital) Bayview Hospital has 4 ambulances and Lakeshore Hospital has 2 ambulances. Queueing theory (done outside of this problem)indicates that Bayview can be assigned up to 4.9 calls per hour and that Lakeshore can be assigned up to 1.5 calls per hour. Port Charles has been divided into 12 districts. The travel time per call in each district and the average number of calls per hour emanating from each district are given in table to the left. The objective is to minimize the average travel time needed to respond to a call.Determine the proper assignment of districts (NOT individual ambulances) to hospitals.A given district’s calls do not all have to be assigned to the same hospital. Since these are averages, fractional assignments are expected. Create the written model and formulate in solver(not manually)
.
Ambulance service Travel time per call from each district to each hospital District Bayview Lake shore Calls/hour 1 5 8 0.5 2 6 9 0.6 3 7 10 0.4 4 5 7 0.3 5 6 8 0.4 6 7 9 0.6 7 9 5 0.7 8 10 6 0.9 9 11 7 1 10 7 3 0.2 11 8 4 0.6 12 9 5 0.1Explanation / Answer
District Travel time per call Calls/hour Bayview Lakeshore Total time taken by Bayview total time taken by Lakeshore 1 5 8 0.5 2.5 4 2 6 9 0.6 3.6 5.4 3 7 10 0.4 2.8 4 4 5 7 0.3 1.5 2.1 5 6 8 0.4 2.4 3.2 6 7 9 0.6 4.2 5.4 7 9 5 0.7 6.3 3.5 8 10 6 0.9 9 5.4 9 11 7 1 11 7 10 7 3 0.2 1.4 0.6 11 8 4 0.6 4.8 2.4 12 9 5 0.1 0.9 0.5 50.4 43.5 Average time taken 4.2 3.6 District Travel time per call (lower of 2) Hospital Calls/hour Total calls/hour by hospital Max calls that can be assigned Excess/deficit 1 5 Bayview 0.5 2.8 4.9 2.1 2 6 Bayview 0.6 3 7 Bayview 0.4 4 5 Bayview 0.3 5 6 Bayview 0.4 6 7 Bayview 0.6 7 5 Lakeshore 0.7 3.5 1.9 -1.6 8 6 Lakeshore 0.9 9 7 Lakeshore 1 10 3 Lakeshore 0.2 11 4 Lakeshore 0.6 12 5 Lakeshore 0.1 re- Assigning districts 8 & 9 to Bayview (since calls/hour are maximum) District Travel time per call (post re-assigning Hospital 1 5 Bayview 2 6 Bayview 3 7 Bayview 4 5 Bayview 5 6 Bayview 6 7 Bayview 7 5 Lakeshore 8 10 Bayview 9 11 Bayview 10 3 Lakeshore 11 4 Lakeshore 12 5 Lakeshore Minimized average time and schedule of hospitals by district as per table below District Travel time per call Calls/hour Combined total time taken Bayview Lakeshore 1 5 0.5 2.5 2 6 0.6 3.6 3 7 0.4 2.8 4 5 0.3 1.5 5 6 0.4 2.4 6 7 0.6 4.2 7 5 0.7 3.5 8 10 0.9 9 9 11 1 11 10 3 0.2 0.6 11 4 0.6 2.4 12 5 0.1 0.5 44 Minimized average time 3.67