CASE STUDY $4$: EMERGENCY RESPONSE OPTIMIZATION USING DISCRETE

STRUCTURES

Scenario:

A city's emergency response system needs to be optimized to improve response time and

resource allocation. Emergency services $($firefighters$,$ police, and ambulances$)$ are

dispatched based on realtime data on incidents such as fires, accidents, and medical

emergencies. The city wants to minimize response time, optimize resource allocation, and

assess the probability of delays due to traffic and road closures.

Data Sources:

Kaggle: Emergency incident data and resource allocation data.

OpenStreetMap: Road network and travel time data for emergency services. Government

Data Portals: Traffic data, road closures, and real$-$time incident reports

Task

Counting Principles in Resource Scheduling

The city wants to optimize the number of available emergency vehicles and personnel

based on historical incident data.

Data Source:

Resource allocation and incident frequency data from Kaggle.

Questions:

$1.$Permutations and Combinations:

a$)$ Calculate the different ways emergency personnel can be assigned to shifts to ensure full coverage during peak hours.

$2.$Inclusion$-$Exclusion Principle:

a$)$ Apply the inclusion$-$exclusion principle to avoid assigning too many vehicles to overlapping incidents in high$-$traffic areas