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.
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.