3
votes
Accepted
Linearize piecewise function without big-M constraints
I don't see or remember a way around the big-M constraints. Thankfully they are not that hard to write. Or you may use indicator constraints which are even simpler.
We add new binary variables, and ...
- 1,842
2
votes
Will adding this constraint help my model?
I tried to test a simple example of what you proposed. I am setting an upper and lower bound $[0,5]$, $[0,4]$ to the variables $x$ and $z$ respectively. By turning off the pre-solving, heuristics, and ...
- 8,390
2
votes
Accepted
Will adding this constraint help my model?
I think the answer is a definitive "maybe". Adding constraint (3) might help the solver to recognize infeasible branches of the search tree sooner (branches with $\delta = 1$ where side ...
- 37.8k
2
votes
Accepted
Workforce scheduling problem
Consider a side-constrained network formulation in which you have a node for each employee-day-shift and a directed arc if the employees are the same, the days are consecutive, and the shifts do not ...
- 30.4k
2
votes
Accepted
MIP formulation for a lower semi-continuous function
You want to maximize $\max(f(x),0)$. Assume $L \le f(x) \le U$ for constants $L$ and $U$. Maximize $g(x)$ subject to
$$
0 \le g(x) \le U y \\
0 \le g(x) - f(x) \le (0-L)(1-y) \\
y \in \{0,1\}
$$
- 30.4k
1
vote
Accepted
How to design a constraint to control flow in a non-network optimization model
Ok, suppose production process $i1$ goes to consumption process $ i2$. You can create a map of $ i1 -> i2$ & define parameters $z_{i1,i2}$such that if $ i1 -> i2$, then $ z_{i1,i2} = 1$, $0$ ...
- 3,343
1
vote
Problems understanding model notation in LPs
The $\wedge$ simply means "and". So for example, constraint III is telling you to sum over all pair of $i$ and $t$ such that $i.NC = 1$ and $i.B=b$.
As for what the authors mean by the "...
- 119
1
vote
Accepted
Compute time between tasks
What you could do is the following: Introduce variable $t_{ij}$ that is the time between tasks $i$ and $j$. This variable is only defined for once per pair $ij$, therefore the $j >i$. Then, you can ...
- 1,461
1
vote
Accepted
Formulation to avoid partial coverage for demand points
Rather than impose your first constraint explicitly, it is better to define a sparse set $(j,t)$, where $t \le d_j$, to be used for both $Y_{ijt}$ and $X_{ijt}$.
Your last constraint goes in the wrong ...
- 30.4k
1
vote
Ways to improve lower bounds while solving MIPs
There are serveral strategies.
I recomend Lagrangian and Surrogate relaxation.
Look for James Davis video "2.6 lagrangian relaxation". I guess it would help.
- 11
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