Course Graph Theory Minimal Path Assignment A product must b

Course: Graph Theory

Minimal Path Assignment

A product must be ground, polished, weighed and inspected. The grinding must precede the polishing and the weighting and the polishing must precede the inspection. Grinding takes 7 units of time, polishing takes 10 units of time, weighting takes 1 unit of time for an unpolished product and 3 units of time for a polished one, and inspection takes 2 units of time for an unweighed product and 3 units of time for a weighed one. What is the fastest production schedule?

Solution

possible combination are

1.grinding->polishing->weighting->inspection

2. grinding->weighting->polishing->inspection

3. grinding->polishing->inspection->weighting

for first case total time is 7+10+3+3=23

for second case 7+1+10+3=21

for third case 7+10+2+3=22

so fastest is the second .