consider we are interested in the required average interarrival-time (the time between two arrivals) of container-ships in order to deliver a total quantitiy of containers (1 million) to a container port. Available work days are 365 days.
For the delivery we will use two types of ships, large ships and small ships. Large ships can carry 3000 Containers/ship, small ships can carry 750 containers/ship. There should be 3 times more small ships used for delivery than large ships.
To solve the problem for the interarrival-times of the two ship categories large and small ship, I defined two variables:
- x = [days/large_ship] and
- y = [days/small_ship]
The restriction is that x = 3*y so that the quantity will be ~3 times lower for x.
I then proceeded to make two equations that which I thought would represent the problem:
- 3000 * 1/x [moves/large_Ship][large_ship/days] + 750 * 1/y [moves/small_Ship][small_ship/days] = 1000000/365 [moves/work_days]
- 1/3000 * x [large_Ship/moves][days/large_ship] + 1/750 * y [small_Ship/Moves][days/small_ship] = 365/1000000 [work_days/moves]
I have attached two pictures of the equations
Equation nr. 1 gives the correct results (I hope). Equation Nr. 2 seems absolutely reasonable to me as well, when judging by the variables, however it gives the wrong results.
Where in the equation-definition-phase did I gone wrong?
The problem is that I tried to add days/moves + days/moves and of course, e.g., 2 days/moves + 5 days/moves is not 7 days/moves.