Question

There are N different models of mobiles manufactured at a mobile manufacturing unit. Each
mobile must go through 2 major phases: ‘parts manufacturing’ and ‘assembling’. Obviously,
‘parts manufacturing’ must happen before “assembling’. The time for ‘parts manufacturing’
and ‘assembling’ (pmi and ai for ith mobile) for every mobile may be different. If we have only
1 unit for ‘parts manufacturing’ and 1 unit for ‘assembling’, how should we produce n mobiles
in a suitable order such that the total production time is minimized?

Requirements:
1. Write a Greedy Algorithm to select the mobile ‘parts manufacturing’ and ‘assembling’
in such a way that total production time is minimized.
2. Analyse the time complexity of your algorithm.
3. Implement the above problem statement using Python.
Input:
For example, now there are 6 different Mobiles in total. Time for each mobile ‘parts
manufacturing’ and ‘assembling’ are given as shown:

Mobile i	pmi (minutes)	ai (minutes)
1	5	7
2	1	2
3	8	2
4	5	4
5	pm5	a5
6	pm6	a6

Sample Output: (Vary based on your input)
Mobiles should be produced in the order: 2, 5, 6, 1, 4, 3.
Total production time for all mobiles is: 28
Idle Time of Assembly unit: 2

Question:

Which algorithmnto use?

Whats time complexity?

How to calculate Total production time for all mobiles, Idle Time of Assembly unit?

Note: You can assume any value for pm5, a6 etc. Output value shown above is just example.

Answer 1

Well for Algorithms. All the cases exits i.e; best case, average case and the worst case.
Algorithms mainly depends on the input. The best suitable technique here which I think is Shortest Job First (SJF) depending upon their Parts Manufacturing Time. It will minimize the production cost.
It can be any case depending upon the input.

Greedy Algorithm
TIme Coplexity is O(n)2

Code :

from array import *

def Order():
mobiles = int(input("Enter the total number of Phones you want to Produce: "))
pmi = array('i')
ai = array('i')
pmicopy = array('i')
  
# Taking Input
  
for x in range(mobiles):
x = int(input("Enter the Parts Manufacturing Time for the Mobile{} ".format(x+1)))
pmi.append(x)
pmicopy = pmi.__copy__()
for y in range(mobiles):
y = int(input("Enter the Assembly Time for the Mobile{} ".format(x+1)))
ai.append(y)
  
# Sorting
  
for i in range(len(pmi) - 1):
if pmi[i] > pmi[i + 1]:
pmi[i], pmi[i + 1] = pmi[i + 1], pmi[i]
for i in range(len(ai) - 1):
if ai[i] > ai[i + 1]:
ai[i], ai[i + 1] = ai[i + 1], ai[i]
  
# Calculating IDLE Time
  
aitime = 0
idletime = pmi[0]
fidle = pmi[0]
for j in range(len(pmi)):
k = pmi[i]
dec = aitime - k
if dec > 0:
fidle = idletime + dec
e = sum(ai)
print(e)
production = e + fidle # Production Time
print("Idle Time of Assembly Unit is: ", fidle)

print("Mobiles Phones should be produced in the order: ")
for l in range(len(pmi)):
ind = pmicopy.index(pmi[l])
print(ind+1)
print("Production Cost is: ", production)

Order()

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