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1500 questions
10
votes
2 answers
Advantages/disadvantages of different representations of non-anticipativity constraints
When reading various papers about two-stage (or multi-stage) stochastic programs with recourse, a common representation of the non-anticipativity constraints is:
$$
\sum_{i}H_ix_i=h,
$$
where $i$ indexes the scenarios, and the matrices $H_i$ and…
David M.
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votes
1 answer
Lagrangian Relaxation bound greater than optimal solution
I am working on a Lagrangian relaxation for a minimization MIP.
Everything seemed to be working fine before I started to run a batch of instances.
Checking the log results for one of the instances I found out that the lower bound given by the LR…
seimetz
- 513
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10
votes
2 answers
Use integer/quadratic programming to maximize consecutive zeros in a binary array
A binary array $t = [t_1, t_2, t_3, t_4, t_5]$ with each element a binary integer variable taking values 0 or 1. You can think this vector as slots with 1 representing the slot being taken and 0 otherwise.
Constraints:
Now 2 appointments need to be…
MIMIGA
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10
votes
2 answers
Can we have all reduced costs (strictly) positive?
I had a number of students claim on their homework that "All $z_j-c_j$ values are positive, therefore the solution is optimal." Of course, I noted that they should say "non-negative" instead of "positive" or restrict their statement to just the…
Tim
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10
votes
2 answers
Modelling an if-then-else logic in MIP
I was hoping to get some help in modelling the following logic as an MIP Constraint
If $X_{ij}=1$ and $\text{SDV}_{ikj}=1$ for a particular index $i$, then $\text{SOC}^L_i=100$, else $\text{SOC}^L_i$ can take any value.
$X_{ij}$ and…
gravityman123
- 103
- 5
10
votes
4 answers
Units in the EOQ problem
This is a very basic question about a very basic model, but I can't come up with a satisfactory answer.
In the economic order quantity (EOQ) model, let $\lambda$ be the demand rate (items/year), $h$ be the holding cost (\$/item/year), and let $K$ be…
LarrySnyder610
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- 105
10
votes
1 answer
Floating points in OR-Tools
I'm trying to solve an RCPSPDc model (maximizing the net present value instead of a makespan). The objective function is: $\sum\limits_{j \in \text{Tasks}} e^{-\theta\cdot s_{j}}\cdot p_{j}$, where $s_{j}$ is a decision variable that for each job…
Diego R. Troncoso
- 635
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- 13
10
votes
2 answers
Current Issues of Interest
What are some current issue of interest in Operations Research? I am interested in current topics that experts in the field are interested in researching.
Amanda B.
- 145
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10
votes
1 answer
RCPSP minizinc model
I'm working on a resource‐constrained project scheduling problem (RCPSP) in Minizinc but I have problems with the running times when the dataset is big (like 400 jobs, 2 resources, 1,000 precedences, and maximum time of 30). With Gecode, after two…
Clopen
- 131
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10
votes
1 answer
How to remove or replace sub tour elimination constraints in the VRP variant models?
In many of vehicle routing problems variant (VRP), which can be formulated using MIPs, to avoid creating sub tour, we need to use sub tour elimination constraints (SEC). One of the known SEC is (I also know there are other…
A.Omidi
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10
votes
1 answer
LP sum of variables that are above a threshold
I am trying to code a constraint of the form:
$$\sum_i y_i < K\,\text{where}\,\begin{cases}y_i = x_i\quad\text{if}\,x_i>k_i\\0\quad\text{otherwise}.\end{cases}$$
In other words, I want to constrain the sum of $x_i$ (only) for those $x_i>k_i$, where…
Henry
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10
votes
2 answers
How can I implement a user-written lazy constraint callback in concert CPLEX with C++?
I am trying to implement a user-written lazy constraint callback in concert CPLEX with C++. Although I know there exists a way to implement callbacks in concert CPLEX with C++ via macros, I am looking for a way to implement lazy constraint callback…
Matheus Diógenes Andrade
- 1,238
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- 14
10
votes
1 answer
Relationship between the Assignment Problem and the Stable Marriage Problem
Suppose I'm solving a minimum-weight matching problem in a bipartite graph with sets $\mathcal{I}$ and $\mathcal{J}$, where $w_{ij}$ denotes the weight of matching item $i$ to $j$. I can model the problem as a stable marriage problem and set the…
tuba
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10
votes
1 answer
Partial Relaxation
In the context of a larger optimization problem I realized that I am missing the skill to implement/exploit the following observation:
In the problem I was faced with two related sets of indicator variables which contributed to the objective…
CMichael
- 1,333
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10
votes
1 answer
Scenario Generation and Reduction in Stochastic Optimization
I have to generate scenarios for a stochastic optimization program. I want to reduce this number of scenarios but the assignment of a probability to each scenario is my problem. How can I assign a probability to each scenario?
Background
I have…
shady mamdouh
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