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Quarantine Facility Location and Assignment: a Case Study based on the Data of Hong Kong

J
Joseph Chow

This document summarizes a study that developed a mathematical model to optimize the assignment of travelers to quarantine hotels in Hong Kong. The model aims to minimize contracting and assignment costs while controlling risk and misplacement. It considers the number and prices of rooms in designated quarantine hotels, passenger traffic data, and travel times between demand nodes and hotels. The model is formulated as a mixed-integer linear program and solved using CPLEX to generate Pareto frontiers under different weights for cost and risk tolerance. The proposed design is then compared to assigning travelers based on the current hotel locations and capacities.

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Quarantine Facility Location and Assignment: a Case Study based on the Data of Hong Kong TR-GY 7013 Term project Yuhao Liu yl8649@nyu.edu 1
Demand nodes Quarantine hotels Introduction 2 Quarantine hotels for the sixth round
System considerations (I) Contracting cost For each contracted hotel, there is a target revenue guaranteed by the government according to the hotel's profitability. If the actual revenue is less than the target revenue, the government needs to subsidize the hotel by the difference between the target revenue and actual revenue. Assignment cost In this project, we assume that the cost is merely related to the travel time from the demand nodes to the hotels. Risk control Ideally, travelers arriving at a same demand node should not be dispersedly assigned to hotels all over the city, so as to contract the range of exposure. 1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 3
System considerations (II) Misplacement Travelers have their preference for rooms. Assume that they can report their room preference in advance of the arrivals. To improve that public acceptance of the quarantine policy, the government should try to assign travelers to the rooms that they prefer. However, given the special public health threat, the government has the right to assign a traveler to a room he/she does not prefer. In this case the demand/traveler is said to be misplaced. 4
5 Model formulation (I) min min kw kw i iw jk ij i ij jk ij i j k w i j k w kk jk jk ij j k i j k R p Q x c Q Q Q ワワ ワワワ ワ ワワ 1, , , , , , (1 ) , , , , , 0 1, , , , , , {0,1} kw ij i w kw jk ij iw i j k kw ij ik j w k kw ik jk ij ik j kw jk ij jk ij k w k ij i kw ij i ik ij j k Q C x i w y i k C Q y M i k Q Q z i j z N j i j k w x y z ワ ワ ワ ワ Subject to
1 2 min min kw i ij jk ij i i j k w kw jk ij i j k T c Q Q Z Z ワワワ ワワ ( 1) , 0, kw i i iw jk ij i j k w i T R p Q x M i T i ワワ Original constraints Subject to Mixed-integer linear program 6 Model formulation (II) 1 1 2 2 min Z Z Weighting method (了1, 了2) Subject to all the constraints Solved through CPLEX Vary (了1, 了2) to identify non-dominated solutions and construct the pareto frontiers
Data Hong Kong government Covid-19 website https://www.coronavirus.gov.hk/eng/ Designated Hotels for Quarantine: number and prices of rooms Statistics on Passenger Traffic 7 Current: 40 hotels Potential: 48 hotels Demand nodes: 3
8 Solution https://www.ibm.com/docs/en/icos/20.1.0
min min kw i ij jk ij i i j k w kk jk ij i j k T c Q Q ワワワ ワワ 9 Benchmark Current locations + optimal assignment 1, , , , , , (1 ) , , , , , kw ij i w kw jk ij iw j k kw ij ik j w k kw ik jk ij ik j kw jk ij jk ij k w k ij i j k Q C i w y i k C Q y M i k Q Q z i j z N j ワ ワ ワ ワ 0 1, , , , 0, , , {0,1} kw ij i kw i i iw jk ij j k w ik ij i j k w T i T R p Q i y z ワワ Subject to
Design v.s. benchmark 10 Pareto frontiers of proposed design with different levels of risk tolerance Pareto frontiers of brenchmark 2 with different levels of risk tolerance
Thank you. Merry Christmas! 11

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Quarantine Facility Location and Assignment: a Case Study based on the Data of Hong Kong

  • 1. Quarantine Facility Location and Assignment: a Case Study based on the Data of Hong Kong TR-GY 7013 Term project Yuhao Liu yl8649@nyu.edu 1
  • 3. System considerations (I) Contracting cost For each contracted hotel, there is a target revenue guaranteed by the government according to the hotel's profitability. If the actual revenue is less than the target revenue, the government needs to subsidize the hotel by the difference between the target revenue and actual revenue. Assignment cost In this project, we assume that the cost is merely related to the travel time from the demand nodes to the hotels. Risk control Ideally, travelers arriving at a same demand node should not be dispersedly assigned to hotels all over the city, so as to contract the range of exposure. 1 0 0 0 1 0 0 0 1 1 1 1 1 1 1 1 1 1 3
  • 4. System considerations (II) Misplacement Travelers have their preference for rooms. Assume that they can report their room preference in advance of the arrivals. To improve that public acceptance of the quarantine policy, the government should try to assign travelers to the rooms that they prefer. However, given the special public health threat, the government has the right to assign a traveler to a room he/she does not prefer. In this case the demand/traveler is said to be misplaced. 4
  • 5. 5 Model formulation (I) min min kw kw i iw jk ij i ij jk ij i j k w i j k w kk jk jk ij j k i j k R p Q x c Q Q Q ワワ ワワワ ワ ワワ 1, , , , , , (1 ) , , , , , 0 1, , , , , , {0,1} kw ij i w kw jk ij iw i j k kw ij ik j w k kw ik jk ij ik j kw jk ij jk ij k w k ij i kw ij i ik ij j k Q C x i w y i k C Q y M i k Q Q z i j z N j i j k w x y z ワ ワ ワ ワ Subject to
  • 6. 1 2 min min kw i ij jk ij i i j k w kw jk ij i j k T c Q Q Z Z ワワワ ワワ ( 1) , 0, kw i i iw jk ij i j k w i T R p Q x M i T i ワワ Original constraints Subject to Mixed-integer linear program 6 Model formulation (II) 1 1 2 2 min Z Z Weighting method (了1, 了2) Subject to all the constraints Solved through CPLEX Vary (了1, 了2) to identify non-dominated solutions and construct the pareto frontiers
  • 7. Data Hong Kong government Covid-19 website https://www.coronavirus.gov.hk/eng/ Designated Hotels for Quarantine: number and prices of rooms Statistics on Passenger Traffic 7 Current: 40 hotels Potential: 48 hotels Demand nodes: 3
  • 9. min min kw i ij jk ij i i j k w kk jk ij i j k T c Q Q ワワワ ワワ 9 Benchmark Current locations + optimal assignment 1, , , , , , (1 ) , , , , , kw ij i w kw jk ij iw j k kw ij ik j w k kw ik jk ij ik j kw jk ij jk ij k w k ij i j k Q C i w y i k C Q y M i k Q Q z i j z N j ワ ワ ワ ワ 0 1, , , , 0, , , {0,1} kw ij i kw i i iw jk ij j k w ik ij i j k w T i T R p Q i y z ワワ Subject to
  • 10. Design v.s. benchmark 10 Pareto frontiers of proposed design with different levels of risk tolerance Pareto frontiers of brenchmark 2 with different levels of risk tolerance
  • 11. Thank you. Merry Christmas! 11