# Tag Info

8

MINTO has not been updated in many years. It was innovative in its day, but most of its ideas like fractional cuts and presolve were incorporated years ago into commercial MILP solvers like CPLEX and Gurobi. For most applications today, the best option is one of the major commercial solvers like CPLEX or Gurobi; these are available at no-cost for academic ...

6

The Mittlemann benchmarks are an excellent benchmark as ever in particular these two: Benchmark of Barrier LP solvers Large Network-LP Benchmark (commercial vs free) Note that Pyomo doesn't have bindings for most of these locally. If you are just looking for high-level modeling language and are not tied to Python you could use the JuMP modeling language ...

5

When defining multiple components in an objective function, you should take care of a couple of items: All elements (i.e.e $a \cdot x_1$, $b\cdot x_2$ etc.) should have the same unit. This sounds obvious, but I have seen adding kg and seconds together. Whenever possible, I would always normalize the sum of the coefficients to 1, so that you can think of ...

5

Introduce a binary variable $\delta \in \{0,1\}$ to indicate whether $q$ is positive or not. You want: $$\sum_{(i,j) \in A}f_{ij} \le |A| - 1 \quad \Longrightarrow \quad \delta=0$$ or the contrapositive: $$\delta=1 \quad \Longrightarrow \quad \sum_{(i,j) \in A}f_{ij} \ge |A|$$ which you can achieve with: $$\sum_{(i,j) \in A}f_{ij} \ge |A| \delta$$ ...

4

If, given inventory level ($q_{i,t}$) and bucket decisions ($z_{i,t,k}$), profit is maximized by maximizing the supplied quantities, you probably can drop the big M constraints and trust the objective to prevent selection of a supplied quantity less than the min of the two upper limits. As an experiment, you could try running without those constraints and ...

4

When you turn CPLEX loose on a model, it runs a presolver that does assorted magic tricks that end up with a modified model. It then solves the modified model and, assuming it finds a solution to the modified model, transforms that solution back to the original model. I believe that the "unscaled infeasibilities" message means that CPLEX found what ...

3

For large LPs you need an interior point solver. On top of what others have mentioned, you can use CLP's interior point method, or, interestingly, just plain old IPOPT can work perfectly fine since it will also apply an interior point algorithm.

2

I have suggestions for your two recently added constraints. Your first one is: $$\text{board}(i_1,i_2,j_1,t,k) + \text{board}(i_1,i_2,j_2,t,k) \leq 1 + m[j_1][j_2]\\\forall i_1,i_2 \in V^2, \forall j_1,j_2 \in J^2, \forall t \in T, \forall k \in K \tag1$$ You do not need to impose $(1)$ when $m[j_1][j_2] = 1$ because it is redundant. You can also ...

2

If I am not mistaken the answer is NO unless $P=NP$. We can reduce Exactly-1 3-satisfiability to your problem. For a proof of 1-IN-3SAT is NP-complete see NP-Completeness of 3SAT, 1-IN-3SAT and MAX 2SAT. Given an instance $I$ of the Exactly-1 3-satisfiability problem. For each variable $x_i$ check whether there is a solution setting it to $1$ and $0$. This ...

2

Dynamic Programming is often a good method of choice for solving this class of problems. Chapter 3 of The Art and Theory of Dynamic Programming refers to this class of problems as Resource Allocation problems. There is one constraint restricting the amount of available resource, the parameter $B$, with a linear or nonlinear objective function. An interesting ...

2

First, let's split this into two separate problems: making the initial assignments; and updating assignments over time. (If you already have assignments in place, you may only need the second problem.) The initial problem can be modeled a generalized assignment problem (GAP). Technically this is an integer linear program, with a zero-one variable for each ...

2

With CPLEX you can use logical constraints. For instance with the OPL API you can write: dvar boolean q; dvar int a; dvar int b; subject to { q==(a+b>=2); } q is 0 iff a+b<=1

1

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This document available on link https://cran.r-project.org/web/packages/Rcplex/Rcplex.pdf for RCplex might be helpful for you. Page 7 & 8 has an example of QCP.

1

Rough-cut capacity planning is an essential tool for rapidly calculating the needed capacity and trade-off between the available and required resources which is frequently used in the planning software. As a reference: RCCP is a long-term plan capacity planning tool that marketing and production use to balance required and available capacity and to ...

1

I managed to understand why the pace of building up the model using Open Solver slows down after a while. The reason is because there were several (in)equations without values, which was why model building was initially fast.

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The question can be understand as determining the truth value of $$(\forall \text{assignments}: \text{relaxation feasible} )\implies \text{problem has integer solution}.$$ However since setting up many LP problems is more expensive then solving a small MILP (or even cheaper 1-in-3 SAT). I instead try to show the opposite: (\forall \text{assignments}: \text{...

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