Operations Research Stack Exchange
Operations Research Stack Exchange

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1500 questions
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2 answers

Identifying problem: Assignment + Job Shop Scheduling

I am new to OR. Hence, I want your advice on the problem I am trying to solve: Given: $O_1 \rightarrow O_2 \rightarrow O_3 \rightarrow ... \rightarrow O_n$: the sequence of operations to produce $1$ product. $M$: the set of machines that can…
torayeff
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How can we write a binary variable as a power to a constant number?

Let $x_{i,j}$ be a two-dimensional binary variable. Is it possible to write $x_{i,j}$ as a power to a number? For example: $$1- 0.3^{x_{i,j}} $$
GTek
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CPLEX Python: Current subproblem model in branch and bound

I have an MILP problem and use CPLEX (Python interface). I am working on user heuristics for branching in the branch-and-bound procedure. With HSCallback I managed to get the information about the current subproblem (all integer variables are…
Elena
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crew scheduling problem with shift priority hard constraints

I am working on a crew scheduling problem formulated as a MIP binary optimization where each employee is represented by a binary variable $X_{ids}$ s.t. $i \in I$ is $i$th employee, $d \in D$ is the day number and $s \in S$ is the shift (ex:…
mathcomp guy
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Trying to accelerate MILP solution

I developed a mathematical model that contains several thousand of binary variables (in addition to several thousand continuous variables). The binary variables model different things, say $X(i)$, $Y(j)$, $Z(k)$, ... I made the observation, that if…
Clement
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Efficiently updating latest finish times via Critical-Path-Method

For a Resource-Constrained-Project-Scheduling problem, I need to calculate Critical-Path-Method (CPM) values for each of the activities. These values are: Earliest Start (ES) Earliest Finish (EF) Latest Start (LS) Latest Finish (LF) The activity…
Rutger
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How to transform a (thermal) range constraint into the objective function

I have an mixed-integer linear optimization problem that includes a energetic difference equation for the temperature of a building for the time $t$: $$T(t) = T(t-1) + \frac{E^{\rm Heating}(t)-E^{\rm Demand}(t)}{V\cdot \rho\cdot c}, t>1$$ I used to…
PeterBe
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How does the VRPTW model ensure the arrival time at next station tightened?

In VRPTW problem, given $[a_i, b_i]$: the time window for node $i$ $x_{ijk}$: a binary variable that represents that the vehicle $k$ travels from node $i$ to $j$ (yes 1 otherwise 0) $s_i$: the service time at node $i$ $t_{ij}$: the traveling time…
BobHU
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bilinear problem proof for NP-completeness of degeneracy check

In the paper "Some NP-complete problems in linear programming" (https://doi.org/10.1016/0167-6377(82)90006-2), there are several proofs given to show that testing for degeneracy in LPs is NP-complete. I don't understand the proof in section 4. Are…
Brannon
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Is this weighted feedback concept a known, solved, problem?

Imagine a fairly standard Thumbs Up/Down feedback system. For each piece of content they consume, every user has the ability to give a binary positive/negative feedback that piece of content. They're not required to give feedback, and they can't…
Brondahl
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Adequate SDP solvers for large problem instances

I have previously used MOSEK for all my SDP needs. Recently, though, I am having a hard time trying to solve some large problems, due to lack of memory. In similar questions around the forum, SCS has been recommended for very large instances due to…
cdg
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How to use max flow to schedule machines? (building a network)

Suppose you manage a machine shop with $k$ machines and have $n$ jobs to process today. Each job $i=1,2,3,4,5,\ldots,n$ requires $p_i>0$ minutes of processing time on any machine and has a processing windows $[a_i,d_i]$ with $a_i+p_i\le d_i$. We…
Fernando Martinez
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How to bundle pairs of trips?

I have a database of real-time optional trip demands. Each with a load that needs to be delivered from a departure point to a…
italo
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Mathematically formulating formal problem of a cloud service scheduler

So, I have been tasked to create a formal mathematical description of problem statement on a cloud service scheduler for my team's university project, which is, honestly, a little weird of a thing to do, which is why I am unsure of how to proceed…
el_bulm
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Difference between solving Assignment Problem using the Hungarian Method vs. LP

When trying to solve for assignments given a cost matrix, what is the difference between using Scipy's linear_sum_assignment function (which I think uses the Hungarian method) describing the LP problem using a objective function with many boolean…
Athena Wisdom
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