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Rik on 8 Jun 2020
Original question posted by Nazli Bilmis retrieved from Google Cache:
1. Two young engineers establish a startup (NewCo) in Izmir with a dream of becoming the second unicorn of Turkey after Peak Games. NewCo develops Internet of Things (IoT) technology solutions. IoT devices sense their environment and deliver their collected data to the gateways (receivers). Gateways communicate the collected data to the Google Cloud where data analytics, machine learning and visualization is performed. Gateways have different coverage ranges according to their technical specifications. IoT devices are placed in a 3D environment where they measure the temperature, pressure, and humidity. The location of 12 IoT devices are given by the A matrix below where each row refers to the x, y, z coordinates of corresponding IoT device. Gateway covers 50 meters and costs $250 (Any additional 20 meter coverage range could be purchased for $50 in different gateway models on top of the base model). One gateway should be placed as in the figure, that should be able to collect data from all of the 12 IOT devices. The distance between the gateway and each IOT device costs the system operator $0.02 electricity per meter per day. The total cost of the IoT infrastructure is evaluated as the sum of gateway cost plus the operation cost (electricity cost) per year (365 days). The customer of the company will use this system for 10 years. Write a code that finds the best location for the gateway to be placed, so that the total lifetime system cost is minimized.
a) Give the optimum coordinates of the gateway (x, y, z) and the coverage range of the gateway that minimizes the total lifetime IoT infrastructure cost.
b) Calculate the minimum IoT infrastructure lifetime cost. Explain how your code works in detail.

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Accepted Answer

Walter Roberson
Walter Roberson on 8 Jun 2020
Given any specific number and position of gateways, how do you calculate the operations cost?
Given any specific number of gateways, how do you optimize the operations cost? Including the possibility of extending the range for some of the gateways?
If you know the minimum operations cost for a particular number of gateways, N, then under what conditions is it possible to lower the cost by adding one more gateway?
If you know the minimum operations cost for N gateways, and the minimum operations cost for N+1 gateways is higher, under what circumstances is it possible for using more than N+1 gateways could lower the operations cost below what you can get with N gateways?
If you try with one gateway and find a cost, and then try with two gateways and find a cost, and so on increasing the number of gateways by one each time, is there ever a point at which you can stop adding gateways knowing that adding more gateways could not possibly reduce the cost?


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