# Tag Info

Accepted

### Reformulate constraints

It looks like You want to enforce for all $i,t,k$: $$x_{itk}=1 \implies v_{itk} = u_{it} \quad$$ and $$x_{itk}=0 \implies v_{itk} =0$$ You can get rid of the big-M as follows: \begin{align} x_{...
• 13.5k
Accepted

### if else condition with multiple criteria in MIP

Let $\epsilon$ be a small constant positive tolerance, and let $M$ be a constant upper bound on $x_1$. Now impose linear constraints $$\epsilon s_1 \le x_1 \le M s_1.$$
• 32.3k

### Matrix lookup modelling variants

If your modeling API supports indicator constraints, you can impose $$y_j =1 \implies c_i=x_{ij}.$$ @prubinâ€™s answer provides the corresponding big-M formulation of this constraint.
• 32.3k
Accepted

### Matrix lookup modelling variants

You do not really need the $z$ variables. You can just add the constraints $$x_{ij} - M(1-y_j) \le c_i \le x_{ij} + M(1-y_j)\quad \forall j.$$
• 39.3k
Accepted

### Formulation for choosing how many items to manufacture

If you need both $x$ and $y$ in the model, a third option is to enforce \begin{align} y_{m,p,s} &\ge x_{m,p,s} \\ y_{m,p,s} &\le \text{PartsPerShift}_p x_{m,p,s} \end{align} This modification ...
• 32.3k

• 1,572
1 vote
Accepted

### Logical conditions

I'm going to drop the subscript $t$ to save clutter. Let $B = C\cdot x - E.$ Introduce three binary variables $\omega_1,$ $\omega_2,$ $\omega_3$ together with the constraints $y \le \omega_1,$ \$zn \le ...
• 39.3k
1 vote

### Mixed Integer programming, the big M

This is a common modeling techniques in operations research. Another interpretation is if-then relationship or indicator. When you have to count how many days you have to setup to produce then you can ...
• 386

Only top scored, non community-wiki answers of a minimum length are eligible