Assignment $1$: Optimize thd allocation of rescue resources

Note: Department of Civil and Environmental Engineering, The Hong Kong Polytechnic University

Disclaimer: These notes have not been subjected to the usual scrutiny reserved for formal

publications. They may be distributed outside this class only with the permission of the Instructor.

Introduction

Hong Kong faces the risk of sudden floods, especially during the typhoon season.

As a government advisor, your task is to optimize the allocation of rescue resources

to minimize potential losses during floods and improve response efficiency. You

need to consider the population density, geographical location, flood risk, and

existing rescue resources of each area.

$2.$Objective Function:

Minimize the total loss, including the cost of rescue operations and potential losses

averted.

A specific formula that may be helpful is:

Total Loss $={\displaystyle \underset{i=1}{\overset{18}{}}}(C_i*x_i-Cr{e}_i*x_i)$

$x_{\text{m}\text{i}\text{n}\text{,}i}=R_{\text{m}\text{i}\text{n}\text{,}i}-E_i$

$x_{i}R{L}_i$ Other conditions you can consider as appropriate.

$3.$Explanation:

$$ Population Density: The population of each district, which affects the

potential demand for rescue.

$$ Flood Risk: The flood risk level of each district, rated from $1$ to $5,$ with $5$

being the highest.

$$ Operational Cost: The cost of deploying rescue resources.

$$ Potential Loss Averted: The estimated loss that could be averted if

rescue operations are conducted.

$$ Resources Limit: The limit on resource allocation.

$,$ Minimum Distribution Rescue: The minimum number of rescue

units that must actually be distributed to each district.

$,$ Minimum Required Resources: The minimum number of rescue

resources required in each district.

$$ Existing Resources: The number of rescue resources already available in

each district.

$4.$Solution

$$ Integer Programming Model: Use integer programming to determine the

allocation of rescue resources for each district to minimize the total loss. $$ Excel Model Construction: Build the model in Excel and use the solver to

find the optimal solution.

$$ Rescue Resource Allocation Strategy: Design a specific rescue resource

allocation strategy based on the model output.

$5.$Tasks

As an advisor, please:

$$ Use the data mentioned to construct an integer programming model.

$$ Solve this problem in Excel.

$$ Prepare a detailed report $($in PDF format$)$ for the government, showcasing

your analysis results and recommendations.

Requirements:

$$ Follow the "Experimental Report Writing Guide.pdf$".$

$$ Submission Deadline: Oct $28,2024,11$:$59$ PM$,$ Hong Kong time.

$$ Submit the report in PDF format.

$$ The report should include screenshots of the Excel model and a detailed

description of the solution.

$$ The report should include your discussion of the results.

Note: Please detail your specific plan for solving this problem, including formulas

and rationale, along with screenshots of key steps