# How to model best combination of resources

I don't have an economics background, I come from CS. I am sorry if this question seems weird.

We want to model the combination of a set of resources to either answer the cost of the model, minimize the cost of the model, or find the cheapest combination of resources.

Precisely, we have a network of computers, with some producing data, and some consuming data, organised in stages of Producers and Consumers: P -> C -> P -> C ... but the network is more like a graph with cycles on the data. We already have the model of this communication paradigm from a CS point of view, we are interested on the Economics side since we have to scale, redesign, and build the system in the future.

What are the existing approaches to model such questions?

• Without further details your question is very unclear. – Giskard Mar 31 '16 at 11:46
• Is this a network or a strictly serial procedure? – Alecos Papadopoulos Apr 30 '16 at 17:07

It sounds like you could simply use the Cost Minimization Problem: $$\underset{z_1,...z_N}{min}\sum_{i=1}^N q_iz_i$$ $$s.t.\quad f(z_1,...,z_N)\geq \bar{y}$$ $$z_1,...z_n\geq0$$ Where $z_i$ and $q_i$ are the quantity and price of input $i$, respectively, $\bar{y}$ is some predetermined level of output, and $f(\frac{}{})$ is the production function.

A production function relates physical output of a production process to factors of production. Of course, it seems to me that it may be a challenge to characterize a production function for your case. However, the production function can be any function which satisfies the following:

1) Strict Monotonicity: If $z'>z$ then $f(z')>f(z)$

2) Quasi-concavity: $V(y)=\{ z:f(x)\geq y\}$ is a convex set

3) $V(y)$ is closed and non-empty

4) $f(z)$ is finite, nonnegative, real valued, and single valued $\forall z\geq 0$

5) $f(z)$ is a $C^2$ function

To be more specific to your case (data is the input and output) the problem reduces to: $$\underset{d_i}{min}\; d_iq+wl+rk$$ $$s.t.\quad f(d_i)\geq \bar{d_o}$$ $$d_i,l,k\geq 0$$

Where $d_i$ is the data used as input, $d_o$ is the data output, $q$ is the price of input data, $w$ is wage, $l$ is labor hours, $r$ is the rental price of capital and $k$ is quantity of capital.

Again, this type of production process is foreign to me, so I cannot make an informed suggestion regarding specification of the production function, but maybe someone who is more apt on this site may offer a suggestion. I hope this helps!