# Help in solving resource allocation optimization problem

I've been pondering on this question for some work optimization, and I need some help in being directed to the right direction.

I have multiple customers that require an amount of $$X$$, $$Y$$ and $$Z$$ each. From the factories, I have a number of trucks that can carry a few configurations of $$X$$, $$Y$$ and $$Z$$ (either $$1 X$$ and $$3 Y$$ or $$2 Y$$ and $$5 Z$$) to deliver to the customers.

What I would like to do is to select the trucks and configuration that should be sent out in order to reduce the number of trips to the customers.

Example: It's better to have 3 trucks delivering to 3 customers like this: $$[T_1 - C_1,T_2 - C_2,T_3 - C_3]$$ Total trips: $$3$$

Than 2 trucks delivering to 3 customers like this: $$[T_1 - C_1, C_2,T_2 - C_2, C_3]$$ Total trips: $$4$$

The target selection is what has stumped me for now. You can assume that distance does not matter for now.

Here is an example to better explain it.

\begin{align}\text{Configuration}\,1&:3A,2B,1C\qquad&&\text{Customer}\,1:2A,2B,1C\\\text{Configuration}\,2&:1A,3B,3C\qquad&&\text{Customer}\,2:2A\\\text{Configuration}\,3&:4A,1B\qquad&&\text{Customer}\,3:4B,2C\\\text{Configuration}\,4&:2A,3B,1C\end{align}$$\begin{array}{c|cccc|c}&\text{CC}1&\text{CC}2&\text{CC}3&\text{CC}4&\text{Sent To}\\\hline\text{Truck}\,1&1&1&0&0&1,2\\\text{Truck}\,2&1&1&1&0&2,3\\\text{Truck}\,3&0&1&0&1&\text{Not Sent}\\\text{Truck}\,4&1&0&1&0&3\end{array}$$ The objective is to select the number of trucks sent out, what configuration they should hold and minimize the number of trips sent out.

• You say on the one hand that the problem is to "reduce the number of trips to the customers" but on the other hand you want "to minimize the number of trucks sent out". What should the objective be? should both be considered? Maybe you could define cost per truck and costs for number of trucks visiting a customer... – JakobS Oct 11 '19 at 11:33
• The first objective should be considered. The costs are equal for each truck and the number of trucks visiting a customer - basically, we are seeking to minimize the number of trips each truck takes to the customers. – Sylicas Oct 12 '19 at 3:29
• In your first example, what are $T_n$ and $C_n$? In your second example (the table), what are CC1, etc.? Are they the configurations? If so, it seems that Truck 1 contains $4A,5B,4C$, but it only delivers $4A,2B$. Is that right? What happens with the extra? – LarrySnyder610 Oct 17 '19 at 1:24