4. USA Steel Company currently uses a four person crew to unload trucks. This 4
ID: 378024 • Letter: 4
Question
4. USA Steel Company currently uses a four person crew to unload trucks. This 4 person crew can unload 12 trucks per hour. The company is considering changing the size of the unloading crew to either 3 or 5. Each crew member increases the service rate by 3 trucks per hour, by the same token removing a crew member would decrease the service rate by 3 trucks per hour. Each crew member cost the company $175 per hour. The cost of an idle truck and driver costs the company $3,000 per hour. On average a truck arrives for unloading every 7.5 minutes. Which option-3, 4, or 5 person crew will minimum the total costs (25 points)Explanation / Answer
4 person unload - 12 trucks/hour
1 person unloads – 3 trucks/hour (12/4)
Service rate of 1 crew person = 3 trucks /hour
Time to service 1 truck by one person= 60 mins/3 = 20 mins
Truck is idle while it is getting unloaded so this idle time will be calculated for cost.
Cost of 1 crew member = $175/hour
Cost of idle truck and driver= $3000/hr = $50/min
Arrival time for each truck = 7.5 mins
No. of trucks arriving in one hour = 60/7.5 = 8 trucks
Total Cost calculation for 1 hour:
As per above table, The minimum cost is in 3rd option ($2475) when 5 crew members are taken because idle time for trucks is less.
Cost of crew members 3 4 5 no. of trucks/hr 9 12 15 time to unload one truck by all crew members (in Mins) =60mins/no.of trucks 6.7 5 4 time to unload all 8 trucks 53.3 40 32 Cost of crew members 525 700 875 Idle time cost = cost of unloading truck time 2666.667 2000 1600 Total Cost 3191.667 2700 2475Related Questions
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