0

I'm having a hard time to model a scenario where a certain number of labor needs to complete a loading process to trucks within several hour from its start loading time.

In detail:

Say there is a planned loading time for trucks, say at 4PM, and there is 3 trucks coming on 4PM. Say there is to types of truck, large and small, with 2/3 of the shipment comes in small trucks, so at 4PM there is 2 small trucks.

Smaller trucks can be completed within 2 hour, but larger trucks can only be completed in 3.5 hours. Every hour there is always 3 trucks coming, 2 small and 1 large truck. Each truck will be handled by one team, which consists of three people.

How do I calculate the most effective number of team if the cycle continue until 11PM? I really want to formulate this in mathematical equations.

If more information is needed regarding the case, please put in on the comment.

Edit

Please consider that the team can get vacant after working at one truck, and work on another truck if there is any. So, if one team have completed the loading process for one truck, and the other two is still occupied with other trucks, for the fourth truck that will come can be handled by the first team.

el-cheapo
  • 103
  • Are you saying you want to find the optimal people in a team, or the optimal number of teams needed to handle the trucks? Does that mean more than one team can handle a truck at the same time? – spaceman Jul 15 '21 at 08:26
  • @spaceman I want to find the optimum number of team, sorry I shouldn't add the information for the number of people in a team because that would be useless, please just neglect that. One truck can only be handled by one team – el-cheapo Jul 15 '21 at 11:42
  • It is good that you are willing to spend time clarifying what you need. Can you show us your attempts at this problem? – John Douma Jul 15 '21 at 14:27
  • @JohnDouma I've tried to calculate it manually, like simulating how much truck is active in any given hour. If I can find the max. number of truck that is active, I can make sure that I'm having the minimum number of team. But I just cannot put this into equations. – el-cheapo Jul 17 '21 at 02:20
  • The thing is, in this case it can be easy as you can separate the calculation for each truck type, because they keep coming every hour. But, if I make every large truck comes by two truck in five hour, that means from the fourth hour, the team that unloads the large truck can handle the small trucks. Its just very confusing to put this into equation. – el-cheapo Jul 17 '21 at 02:22

1 Answers1

0

If my understanding is correct: two small trucks can be loaded by one team of 3 people in two hours. Also one large truck can be loaded in 3.5 hours by a team of 3 people. Then we have:

Total loading time : t=11-4=7 hrs.In this time you can load:

$7\div 3.5=2$ large truck by one team of 3 people.

$7\div 2=3.5$ , say 4 small truck by one team of 3 people.

Suppose these two teams,which make a group, are working at the same time(simultaneously), so in 7 hours 8 trucks(6 small and 2 large) will be loaded by two teams.

Number of small trucks arriving from 4 to 10 pm= $6\times 2=12$ and number of large trucks arriving is $6\times 1=6$, therefore total number of arriving trucks is $12+6=18$. So the number of groups of teams you need is:

$n=18\div 8\approx 2.3$

So number of teams you need is:

$2.3\times 2=4.6$

So if you have 5 teams you can be sure of loading all 18 arrived trucks. Moreover since each team has 3 people you might handle loading by:

$4.6\times 3=13.8$ say 14 people.

sirous
  • 10,751
  • Please consider that the team can get vacant after working at one truck, and work on another truck if there is any. So, if one team have completed the loading process for one truck, and the other two is still occupied with other trucks, for the fourth truck that will come can be handled by the first team. – el-cheapo Jul 15 '21 at 11:47