Linear-programming, object function

Question

I have this programming problem with the notation: production units i = 1,.., I there is known from data. But cost, capacity and demand are all assumed to be parameters. We denote the production cost of unit with >0 (in USD/MWh) and the capacity is >0 (in mW). The demand is denoted as d> 0 (in MWh). Decision variables, on the other hand, are unknown (endogenous). The decisions consist of how much it takes produced on each production unit. The production level for unit i is denoted as pi ≥ 0.

I have to formulate the object function as a function of the parameters , i = 1,... , I and the decision variables , i = 1,. . ., I. 2)Formulate the conditions that for each unit ensure that the production level does not exceed the capacity.

Can someone help me with this problem? I maybe think that the object function is ∑=0 where is from data and is unknown? Or what? I'm totally new to lineary programming

I have this programming problem with the notation: production units =1,.., I there is known from data.

But cost, capacity and demand are all assumed to be parameters. We denote the production cost of unit with >0 (in USD/MWh) and the capacity is max >0 ( in mW ). The demand is denoted as >0 (in MWh). Decision variables, on the other hand, are unknown (endogenous).

The decisions consist of how much it takes produced on each production unit. The production level for unit is denoted as ≥ 0.

1. I have to formulate the object function as a function of the parameters :

=1,...,

And the decision variables :

=1,...,

2. Formulate the conditions that for each unit ensure that the production level does not exceed the capacity.

Can someone help me with this problem? I maybe think that the object function is: max∑=0 where is from data and is unknown? Or what? I'm totally new to lineary programming

Answer 1

You´re almost right with the first question. Usually the goal is to minimize the cost. Thus we have

$$\textrm{min} \ \ \sum_{i=1}^I c_i\cdot p_i$$

The upper bound for the index $i$ is $I$ and it starts at $1$. Next you have the capacity constraints:

$$p_i\leq p_i^{\textrm{max}} \ \ \forall \ i\in\{1,2,...,I\}$$

Finally the non-negativity constraints: $p_i\geq 0 \ \ \forall \ i\in\{1,2,...,I\}$