Operations Research Stack Exchange
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Multiple Pick-Up Delivery Problem with Time Windows

I am learning pick-up drop-off problems (variant of vehicle routing problems) with time windows. My problem is as follows: There are orders that need to to shipped from pickup locations to delivery addresses. The shipper want to minimize the number…
mars
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Why do we use the square root as a proportional measure?

I originally posted this on the Mathematics Stack Exchange site, but I think it fits more on the OR-site. I'm reading a paper where the goal is to determine the weights of a weighted arithmetic mean to create a sales forecast for a future event…
Steven01123581321
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How to transfer an optimization problem written with GUROBI (in python) in a grammar that can be readily solved with another solver?

Trying to use an opensource optimization tool in python (having used only gurobi for years) I see that the whole code (representing the optimization problem in pythonic language) must be written differently in order to use such tools (pyomo etc.).…
Makis Karasavvidis
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The importance of evaluating the number of constraints

If I introduce a problem, say as an ILP formulation, should I also discuss the number of introduced constraints? If yes, why?
Daniele Cuomo
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Optimality in L Shaped or Bender Decomposition

I was working on solving a two-stage stochastic problem using L Shaped method (Benders Decomposition). I have discussed the model here: Stochastic Facility Location Model. Do the single-cut/ multi-cut methods guarantee optimality? Is there any way…
mars
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Chance constrained optimization - interpretation

Suppose that we have a stochastic vector $\psi$ and $S$ realisations of $\psi$ given by $\psi_1,\dots,\psi_S$ with equal probability of occurrence. In addition, we have constraints of the form \begin{equation} h_i(x,\psi)\leq b_i,\quad \forall…
Djames
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Inverse of weighted sum of positive definite matrices

Let us suppose $I_1, \ldots, I_n$ are symmetric and positive definite matrices. Let $\mathbf{u}$ be the vector with $n$ 1s. I'm interested in the following optimization problem: $$\min \; u^T (x_1I_1+x_2I_2+\ldots + x_nI_n)^{-1}u$$ such that $0 \leq…
Jagadish
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Is it possible to identify all possible Irreducible Infeasible Sets (IIS) for an infeasible Integer Linear Programming problem? (ILP)?

For an Integer Linear Programming problem (ILP), an irreducible infeasible set (IIS) is an infeasible subset of constraints, variable bounds, and integer restrictions that becomes feasible if any single constraint, variable bound, or integer…
Ramy Fouad
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What fraction of the search space has been searched for ILP?

Is there a way to make Gurobi output (an estimate of) how much of the search space has already been cut off as infeasible? If not with Gurobi are you aware of any binary only (912 of them) ILP solver that does provide that information? I suspect the…
worldsmithhelper
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How to optimize on a fixed-cost based on number of results?

I am trying to create an LP problem which is like the knapsack problem but where there is a fixed bonus/penalty based on the number of items chosen. There are 20 items to choose from with some weight between 1 to 20. Knapsack can hold a total…
Eddie
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How to linearize the product of two integer variables?

Given two integer variables $L_x \leq x \leq U_x$ and $L_y \leq y \leq U_y$, how can we linearize the product $x \cdot y$?
joni
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Is there any open source solver for MILP that can output the top N best results instead of the global best?

I am working on an MILP problem, and the project needs to output the top N best results rather than the global best. I am looking for an open source solver which has a callback function. Can anyone provide help on this?
Chemmyyu
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Maximum eigenvalue across subsamples

I have an $N$-dimensional vector of data, say $X_{t}$, with $1 \leq t \leq T$. Of this vector $X_{t}$, I want to consider sub-vectors, say $X_{t}^{b}$, which are $m$-dimensional combinations of elements of the original vector $X_{t}$. In total, I…
Lorenzo Trapani
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What is the relation between dual variables and reduced costs?

My background: Pure math current Undergrad, learned the theory of Operations Research, but pretty basic. All we covered have been dealing with problems that have only 1 constraint matrix. I have dealt with 2-dimensional variables, but not worked…
AyamGorengPedes
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Combinatorial Feasibility Cuts for Benders Decomposition

Are there any advantages of adding constraints in the Benders master problem that ensure the feasibility of the subproblems? This would not add any feasibility cuts. Or is it beneficial to have a master problem find an assignment and then determine…
Amogh Bhosekar
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