# Bloomington has two hospitals. Hospital 1 has four ambulances, and hospital 2 has two ambulances. Ambulance service is deemed adequate if there is only a 10% chance that no ambulance will be available when an ambulance call is received by a hospital. The average length of an ambulance service call is 20 minutes. Given this information, queueing theory indicates that hospital 1 can be assigned up to 4.9 calls per hour and that hospital 2 can be assigned up to 5.5 calls per hour. Bloomington has been divided into 12 districts. The average number of calls per hour emanating from each district is given in the file P05_71.xlsx. This file also shows the travel time (in minutes) needed to get from each district to each hospital. The objective is to minimize the average travel time needed to respond to a call. Determine the proper assignment of districts to hospitals. ( Note : A given districtâ€™s calls do not all have to be assigned to the same hospital.)

### Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659

Chapter
Section

### Practical Management Science

6th Edition
WINSTON + 1 other
Publisher: Cengage,
ISBN: 9781337406659
Chapter 5, Problem 71P
Textbook Problem
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## Bloomington has two hospitals. Hospital 1 has four ambulances, and hospital 2 has two ambulances. Ambulance service is deemed adequate if there is only a 10% chance that no ambulance will be available when an ambulance call is received by a hospital. The average length of an ambulance service call is 20 minutes. Given this information, queueing theory indicates that hospital 1 can be assigned up to 4.9 calls per hour and that hospital 2 can be assigned up to 5.5 calls per hour. Bloomington has been divided into 12 districts. The average number of calls per hour emanating from each district is given in the file P05_71.xlsx. This file also shows the travel time (in minutes) needed to get from each district to each hospital. The objective is to minimize the average travel time needed to respond to a call. Determine the proper assignment of districts to hospitals. (Note: A given district’s calls do not all have to be assigned to the same hospital.)

Summary Introduction

To assign: Districts to the hospitals.

Introduction: In linear programming, the unbounded solution would occur when the objective function is infinite. If no solution satisfied the constraints, then it is said to be unfeasible solution.

### Explanation of Solution

Determine the total travel time:

Formulae to determine the total travel time:

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