My question is How to modeling resource constraint with mip model (How should I modify it?)

A factory is a factory that makes blocks. If there is space left at that time, block can be assembled.

I'm asking you this question because I don't know even though I've been thinking about it after reading the reply that someone

(This is what I asked you before. Additional questions are registered as new questions because the sentence is too long to comment.)

Space constraint in scheduling problem

Index

• $i,j$ is the block number

• $f$ is factory number

• $t$ is time

Parameters

• $y_{i,f}=\begin{cases}1\quad\text{if}\,i\,\text{process at factory}\,f\\0\quad\text{otherwise}\end{cases}$

• $sp_i$ is required area for each block

• $c_f$ is available space of factory f

• $P_i$ is procees time of each block

• $M$ is a big number

Variables

• $S_i$, $C_i$ the strat time, completion time of block $i$ respectively

• $y_{i,j,f}=\begin{cases}1\quad\text{if}\,i\,\text{process before}\,j\,\text{at factory}\,f\\0\quad\text{otherwise}\end{cases}$

• $s_{i,f,t}=\begin{cases}1\quad\text{if}\,i\,\text{start at factory }\,f\text{ at time t }\quad\\0\quad\text{otherwise}\end{cases}$

• $s2_{i,f,t}=\begin{cases}1\quad\text{if}\,i\,\text{process at factory }\,f\text{ at time t }\quad\\0\quad\text{otherwise}\end{cases}$

$$ \sum_{t=1} sp_{i,f,t} =1\quad\forall f\quad .$$

$$ \sum_{t}t \cdot s_{i,f,t} = S_i \quad \forall i,f $$

$$ S_i+p_i = C_{i}\quad\quad \forall i $$

$$ \sum_{t=S_i}^{C_i} s2_{i,f,t} = p_{i}\quad\forall f\quad .$$

$$ \sum_{i} sp_i \cdot s2_{i,f,t} \le c_{f}\quad\forall f,t\quad .$$

thanks for your reading