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 π with ππ>0 (in USD/MWh) and the capacity is ππππ₯π>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 β₯ 0.
I have to formulate the object function as a function of the parameters ππ , i = 1,… , I and the decision variables ππ , 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
πππ₯βπ=0πππππ
where ππ is from data and ππ is unknown? Or what? I'm totally new to lineary programming
I have this programming problem with the notation: production units π=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 π with ππ>0 (in USD/MWh) and the capacity is π max π>0 ( in mW ). The demand is denoted as π>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 π is denoted as ππ β₯ 0.
- I have to formulate the object function as a function of the parameters ππ :
π=1,…,πΌ
And the decision variables ππ :
π=1,…,πΌ
- 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:
maxβπ=0πππππ
where ππ is from data and ππ is unknown? Or what? I'm totally new to lineary programming
Best Answer
YouΒ΄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: $p_i\geq 0 \ \ \forall \ i\in\{1,2,...,I\}$