OR-Exchange - latest questionshttp://www.or-exchange.com/feeds/rss?Ask and answer questions.enWed, 04 Mar 2015 15:28:09 -0500[ANN] Discrete Optimization MOOC on Coursera - Session 3http://www.or-exchange.com/questions/11560/ann-discrete-optimization-mooc-on-coursera-session-3<p>The third session of Pascal Van Hentenryck's Discrete Optimization class is now open.</p>
<p><a href="http://www.coursera.org/course/optimization">http://www.coursera.org/course/optimization</a></p>
<p>It can be enjoyable for OR practitioners of all experience levels.</p>carletonWed, 04 Mar 2015 15:28:09 -0500http://www.or-exchange.com/questions/11560/ann-discrete-optimization-mooc-on-coursera-session-3announcementlocal-searchconstraint-programmingmixed-integer-programmingSolving a nonlinear optimization problem with unknown decision variableshttp://www.or-exchange.com/questions/11557/solving-a-nonlinear-optimization-problem-with-unknown-decision-variables<p>Hello,</p>
<p>I need to solve a stochastic nonlinear optimization problem of this form: Find the decision variables Q1,..., Qn and Q_b (order quantities) such that the objective function (G(Q1,.,Qn and Q_b)) is minimized.Here Q1,...,Qn are same type of decision variables whereas Q_b is different.For this, I have considered a two variable case with Q1 and Q_b to find relation between the two.I have taken the relationship as constraint equations. I use fmincon in matlab to solve this problem. However, the last decision variable Q_b is always the same as the given upper bound.I think something is wrong for which the last variable is not optimized. Does matlab have any features to solve this type of problem? Or any other solver is there which can solve this kind of problem.</p>pinkyWed, 04 Mar 2015 08:30:38 -0500http://www.or-exchange.com/questions/11557/solving-a-nonlinear-optimization-problem-with-unknown-decision-variablesnonlinearstochastic-optimizationnonlinear-optimizationsmoothing L1 normhttp://www.or-exchange.com/questions/11538/smoothing-l1-norm<p>Hi all,
How I could apply the L1 smoothing method for the following model: \[ \min \sum_i \alpha*(0.5 - | x_i - 0.5 |) \] where \(x \in [0,1]\) and \( \alpha >= 0 \)?</p>SaberMon, 02 Mar 2015 15:58:02 -0500http://www.or-exchange.com/questions/11538/smoothing-l1-normnonconvexoptimizationnon-smoothScheduling: extend a model with completion date variableshttp://www.or-exchange.com/questions/11551/scheduling-extend-a-model-with-completion-date-variables<p>I have a (classical) scheduling problem using completion date variables, with a constraint like</p>
<p>$$
c_j = s_j + p_j
$$</p>
<p>where \(s_j\) and \(c_j\) are variables representing the start date and the completion date of job \(j\), respectively, and \(p_j\) is a parameter representing the duration of job \(j\) (I skip the other constraints).</p>
<p>Although I understand this may not be the ideal formulation, I am trying to understand - for the sake of experimentation - whether it is possible to detect if a job \(j\) is running during a generic period \(t\) where</p>
<p>$$
\min\left(s_j\right) \leq t \leq \max\left(c_j\right).
$$</p>
<p>I was thinking (so far with no success) about a binary variable \(u_{jt}\) equal to 1 if job \(j\) is being worked in period \(t\) and 0 otherwise.
The rough idea is that I can use the variable \(u\) to represent the status of a resource over time, like a machine or a worker.</p>
<p>Is that possible, keeping the model linear?</p>LibraTue, 03 Mar 2015 12:15:51 -0500http://www.or-exchange.com/questions/11551/scheduling-extend-a-model-with-completion-date-variablesschedulingoptimizationmathematical-modelingReduction from general integer programming to unbounded knapsackhttp://www.or-exchange.com/questions/11455/reduction-from-general-integer-programming-to-unbounded-knapsack<p>$$a^t x =b$$
$$x \ge 0, x ~\text{integer}$$</p>
<p></p><center>(single constraint feasibility problem)</center><p></p>
<p>$$Ax=b$$
$$x \ge 0, x ~\text{integer}$$</p>
<p></p><center>(constraint Matrix feasibility problem)</center><p></p>
<p>Both problems are np-complete, However that means that there is a polynominal-time-reduction from the first one to the second one and vice versa. But how do it look like?</p>
<p>I'm having a hard time finding one, because the second seems much more general.</p>zBirdyMon, 23 Feb 2015 20:19:00 -0500http://www.or-exchange.com/questions/11455/reduction-from-general-integer-programming-to-unbounded-knapsacknp-completePaper on binary nonlinear least squares?http://www.or-exchange.com/questions/11549/paper-on-binary-nonlinear-least-squares<p>Would you please let me know if anyone knows some papers or any references on nonlinear least squares problems with binary variables!</p>SaberTue, 03 Mar 2015 03:54:34 -0500http://www.or-exchange.com/questions/11549/paper-on-binary-nonlinear-least-squaresnonconvexbinary-programmingnonlinear-optimizationGet integer value for a variable without IPhttp://www.or-exchange.com/questions/11505/get-integer-value-for-a-variable-without-ip<p>I have a variable Wmn[m,n,t] and I want the AMPL to solve it as an integer without defining it as integer.</p>ZaidFri, 27 Feb 2015 18:17:01 -0500http://www.or-exchange.com/questions/11505/get-integer-value-for-a-variable-without-ipvariableintegerGrouping weights into bucketshttp://www.or-exchange.com/questions/11471/grouping-weights-into-buckets<p>I have a set of weights which need to be grouped and put into buckets.</p>
<p>Currently the way I am grouping them is: </p>
<ol>
<li>Sort the weights from max weight to
min weight. </li>
<li>Add weights one by one
and check if bucket constraint is
satisfied. </li>
<li>If adding the weight
exceeds the constraint max value
skip this weight and go to next.</li>
<li>When I find a group I fill the
bucket and delete the weights from
the set and start the process from
the beginning again.</li>
</ol>
<p>bucket constraint: a weight range</p>
<p>example:</p>
<ul>
<li>set: {10,12,12,2,1,6}</li>
<li>bucket constraint: 11-13</li>
<li>best output: {10,2},{12,1},{12} leftover: {6}</li>
<li>my output: {12},{12},{10,2} leftover: {6,1}</li>
</ul>
<p>what will be the best approach for doing so? One of my friend suggested me that operations research deals with such problems and I should post my query here. Please suggest. Thank you. </p>
<p>I also dont know the proper tags for this question.</p>kondebWed, 25 Feb 2015 08:09:39 -0500http://www.or-exchange.com/questions/11471/grouping-weights-into-bucketsoperations-researchTime windows constraints in CPLEX via concert C++http://www.or-exchange.com/questions/7885/time-windows-constraints-in-cplex-via-concert-c<p>Here in VRPTW, the depot is labeled with index <code>0</code>, customers are <code>1..n</code>, and vehicles are <code>1..K</code>.<br>
Decision variable <code>y[i][k]</code> denotes the time when customer <code>i</code> is visited by vehicle <code>k</code>.<br>
Binary decision variable <code>x[i][j][k]=1</code>, if vehicle <code>k</code> travles from node <code>i</code> to node <code>j</code>.</p>
<p>To represent the time windows constraint and eliminate subtour, we have the following code:</p>
<pre><code>for(IloInt i=0;i<n;i++)
for(IloInt j=1;j<n;j++)
for(IloInt k=0;k<K;k++) {
model.add(y[i][k]+SerTime[i]+Distance[i][j]<=y[j][k]+M*(1-x[i][j][k]));
}
</code></pre>
<p>where <code>SerTime</code> is the time required to serve customer <code>i</code>, and Distance is the distance between node <code>i</code> and node <code>j</code>.</p>
<p>But why I am always faced up this error:</p>
<blockquote>
<p>This application has requested the Runtime to terminate it in an unusual way.<br>
Please contact the application's support team for more information.</p>
</blockquote>
<p>I am confused, and want to know how to represent the time windows constraint. Thanks very much!</p>a200710920Thu, 25 Apr 2013 07:28:13 -0400http://www.or-exchange.com/questions/7885/time-windows-constraints-in-cplex-via-concert-ctimewindowsubtourcplexvrptwSolving a VRPTW model using CPLEXhttp://www.or-exchange.com/questions/11496/solving-a-vrptw-model-using-cplex<p>Hi, I am a beginner and Iam trying to solve a VRPTW model on cplex but the model that I have contains only a reduced subset of tours (columns) and a set-partitioning formulation is used because requests must be served exactly once. in this case do i need to generate a subproblem and use the column generation methode with cplex?</p>dadadFri, 27 Feb 2015 05:19:03 -0500http://www.or-exchange.com/questions/11496/solving-a-vrptw-model-using-cplexcplexvrptwHow to linearize this optimization problemhttp://www.or-exchange.com/questions/11431/how-to-linearize-this-optimization-problem<p>Maximize \(\prod_{t=1}^{T}{(1+p_th_t)}^{c_tw_t}\)</p>
<p>subject to:</p>
<p>C1: \(\sum_{t=1}^{T}c_tp_t\le P_{\rm{Max}}\)</p>
<p>Here \(w_t>0\) and \(h_t>0\) are given constants and they are positive. \(T\) is an integer multiple of \(N\).</p>dipSat, 21 Feb 2015 00:34:08 -0500http://www.or-exchange.com/questions/11431/how-to-linearize-this-optimization-problemlinearizationModelling time in Mixed Integer Programshttp://www.or-exchange.com/questions/11351/modelling-time-in-mixed-integer-programs<p>If I want to model the aspect of "time" in an optimization problem (usually involving some kind of transport, vehicles, personell in my case) to work with time windows or synchronise the movement of certain objects, I see two possibilities:</p>
<ol>
<li>Assign a list of real-valued time variables to each object, stating e.g. when it reaches its first stop, second stop etc.</li>
<li>Split time into discrete slices and use binary variables to indicate whether an object is at a certain place in a certain time slice.</li>
</ol>
<p>I have the impression that the first kind of modelling usually involves "Big-M-Constraints" with bad consequences for your LP relaxation. The second approach often consists of a large number of variables.</p>
<p>My question is: Can anybody point me to literature that discusses these issues? I would like to understand more thoroughly which formulations are advantageous in which situations, which difficulties arise and what has been achieved so far to overcome them.</p>JF MeierMon, 16 Feb 2015 04:37:36 -0500http://www.or-exchange.com/questions/11351/modelling-time-in-mixed-integer-programsmixed-integer-programmingtimeLP formulation if with 3 caseshttp://www.or-exchange.com/questions/11438/lp-formulation-if-with-3-cases<p>Hi everyone,</p>
<p>In my LP I have three binary decision variables x,y and z (among others) and I need to formulation the following constraint:</p>
<p>\(z=1\) if \(x \neq y\)<br>
\(z=0\) if \(x=y\)</p>
<p>I can express this:<br>
\(z=x+y\) if \(x \neq y\) and<br>
\(z=x-y\) if \(x=y\)</p>
<p>I think I have to use the big M formulation but in my case I have three cases:<br>
if I use \(x+y\) in the constraints: \(x+y=0\) or \(x+y=1\) or \(x+y=2\)<br>
if I use \(x-y\) in the constraints: \(x-y=-1\) or \(x-y=0\) or \(x-y=1\)</p>
<p>I don't know how to do it with 3 cases.</p>
<p>Please let me know if you have any idea. <br>
</p>sushiSat, 21 Feb 2015 14:25:39 -0500http://www.or-exchange.com/questions/11438/lp-formulation-if-with-3-casescaseswitchProblem regarding setting if statement in GAMShttp://www.or-exchange.com/questions/11416/problem-regarding-setting-if-statement-in-gams<p>I have two dimensional variables in my program
and I want to have following if statement :
PVOutR(m,t)$(Battery_load(m,t) gt 0)=0;</p>
<p>But it doesn't work?
Hooman<br>
</p>hoomanThu, 19 Feb 2015 23:20:33 -0500http://www.or-exchange.com/questions/11416/problem-regarding-setting-if-statement-in-gamsgams+constraintOptimize number of integers in LP problem solutionhttp://www.or-exchange.com/questions/11361/optimize-number-of-integers-in-lp-problem-solution<p>What ways are there to both maximize the objective function and maximize the number of integers in a LP problem solution?</p>klonMon, 16 Feb 2015 15:51:38 -0500http://www.or-exchange.com/questions/11361/optimize-number-of-integers-in-lp-problem-solutionlinear-programmingoptimizationCOIN-OR CLP occasionally fails to find a feasible solutionhttp://www.or-exchange.com/questions/11357/coin-or-clp-occasionally-fails-to-find-a-feasible-solution<p>I am new to COIN-OR CLP and am experimenting with the solver.</p>
<p>Often, the CLP fails to find a feasible solution (for cases, I know a feasible solution exists).</p>
<p>I am using the following sample code to solve my problem.</p>
<pre>int maxIterations = 99999999;
int logLevel = 0;
double maxSeconds = 60;
double primalTolerance = 1.0e-8;
double dualTolerance = 1.0e-8;
ClpSimplex model;
model.setLogLevel(logLevel);
model.setMaximumIterations(maxIterations);
model.setMaximumSeconds(maxSeconds);
model.setPrimalTolerance(primalTolerance);
model.setDualTolerance(dualTolerance);
model.loadProblem(matrixA, XL, XU, F, NULL, B);
model.dual();
</pre>
<p>I tried using the ClpInterior but did not have much success.</p>
<p>I have tried reading the documentation, but could not find sufficient information about tweaking the solver performance. I am not familiar with different solver options to experiment with to find what works best for my problem (about 100 variables and 100 constraints).</p>
<p>Do you guys have any recommendation/suggestions?</p>Santosh TiwariMon, 16 Feb 2015 14:53:08 -0500http://www.or-exchange.com/questions/11357/coin-or-clp-occasionally-fails-to-find-a-feasible-solutionlinear-programmingclpdoes effective open-source LP learning material exist?http://www.or-exchange.com/questions/11391/does-effective-open-source-lp-learning-material-exist<p>So, it is mid-February and it is almost time for me to make a final decision about textbooks for next Fall. Isn't it early?!</p>
<p>I teach a junior-level Operations Management course at a business school in the Mountain West. I am considering changing the book. As an OR/MS guy, I feel it is important to spend 2 weeks on LP, involving graphical LP, Excel Solver problems, and brief hand-waving about the simplex method. However, many of the well-known OM textbooks do not include LP. I feel like this limits my choice in books significantly...</p>
<p>I could teach LP on my own, but I would prefer to have a nice supplement.<br>
</p>
<p>My question for this exchange is, do you know about such a supplement? I would prefer to find one that is free or close to free, since the textbooks that the students are already required to buy are typically not cheap. </p>AndreasTue, 17 Feb 2015 13:24:19 -0500http://www.or-exchange.com/questions/11391/does-effective-open-source-lp-learning-material-existteachingbooksLinearizing abshttp://www.or-exchange.com/questions/11390/linearizing-abs<p>Dear All:</p>
<p>I would like to linearize the following objective function (to be maximized):</p>
<p>Maximize z=abs(x-y), x & y are variables</p>
<p>Any help will be highly appreciated.</p>
<p>Best Regards</p>
<p>Noor</p>noorbuetTue, 17 Feb 2015 11:27:28 -0500http://www.or-exchange.com/questions/11390/linearizing-abslinearizeabsConfused about the interpretation of expression "ties may be broken arbitrarily"http://www.or-exchange.com/questions/11347/confused-about-the-interpretation-of-expression-ties-may-be-broken-arbitrarily<p>I have a serious problem in interpreting the expression "ties may be broken arbitrarily" in scheduling algorithms.
For example, in the book "Scheduling Theory, Algorithms and Systems, 4th Edition" by "Michael Pinedo" on page 117 says:</p>
<blockquote>
<p>This particular problem leads to a well-known scheduling rule, the Critical Path (CP) rule, which gives the highest priority to the job at the head of the longest string of jobs in the precedence graph (<strong>ties may be broken arbitrarily</strong>).</p>
</blockquote>
<p>Or on 121:</p>
<blockquote>
<p>The LFJ rule selects, every time a machine is freed, among the available jobs the job that can be processed on the smallest number of machines, i.e., the least flexible job. <strong>Ties may be broken arbitrarily</strong>.</p>
</blockquote>
<p>Or on 155:</p>
<blockquote>
<p>The jobs in Set I go first and they go in increasing order of p 1j (SPT); the jobs in Set II follow in decreasing order of p 2j (LPT). <strong>Ties may be broken arbitrarily</strong>. In what follows such a schedule is referred to as an SPT(1)-LPT(2) schedule. Of course, multiple schedules may be generated this way.</p>
</blockquote>
<p>I would be so thankful anyone help me to get the general interpretation of this expression.</p>monashMon, 16 Feb 2015 01:28:36 -0500http://www.or-exchange.com/questions/11347/confused-about-the-interpretation-of-expression-ties-may-be-broken-arbitrarilyschedulingalgorithmsReference for finding optimal LP extreme point in polynomial timehttp://www.or-exchange.com/questions/11324/reference-for-finding-optimal-lp-extreme-point-in-polynomial-time<p>My problem is as follows: given some LP, we can find an optimal solution for it in (weakly) polynomial time via some interior point method. When there are multiple optima, the found solution might not be an extreme point but on the middle of one of the polyhedrons faces.</p>
<p>Now I want to get from there to an optimal extreme point (for example because I have an integral IP formulation and only the extreme points are interesting for me). This should be possible in polynomial time by traversing the current face until hitting some inequality, reducing the dimension of the face by one and repeating until ending on a desired extreme point.</p>
<p>Does anyone know a good reference or a text book where this issue is dealt with? So far I could not find a proper resource even though this argument seems to be relevant when making conclusions of the type: "This problem has an ideal and compact formulation and can therefore be solved in polynomial time"</p>FDahmsMon, 09 Feb 2015 09:17:17 -0500http://www.or-exchange.com/questions/11324/reference-for-finding-optimal-lp-extreme-point-in-polynomial-timelinear-programmingextreme-pointsideal-formulationinteger-programmingWhat would you teach themhttp://www.or-exchange.com/questions/10817/what-would-you-teach-them<p>In the summer of 2015, I am going to offer a Summer University course over a 2 weeks period. The course bears the rather "rubber" title "Modelling and solving discrete optimization problems within logistics", meaning I can basically do what I want. The course is aimed at master level students at a business school and the level of mathematical knowledge can be assumed not to be sky high. Therefore, we will only consider mixed integer <em>linear</em> programming problems.</p>
<p>My plan so far is to focus on modelling techniques (tricks and stuff) in week 1 and then turn the attention to solution procedures in week 2. Then plan is then to show the students how the different modelling choices affect the solution procedures. My question to you, fellow OR people, is:</p>
<p>"If you could imprison a bunch of students in their summer vacation, and you could teach them some modelling tricks, what would that be?"</p>
<p>So far, I have the following, rather standard, tricks:</p>
<ul>
<li>Big-M formulations, and why we should be precise with the M's.</li>
<li>if x>0 then y=1.</li>
<li>Variable is either 0 or between LB and UB.</li>
<li>Either this constraint or that constraint.</li>
<li>If this constraint, then this constriant too.</li>
<li>SOS1 and SOS2 constraints</li>
<li>Piecewise linear cost funciton</li>
<li>Product of binary and something bounded</li>
</ul>
<p>Much of the above will be hinted in lectures and then the students will have to come up with the actual formulations themselves during "modelling sessions". I have a plan to use some basic models from e.g. location planning and from routing throughout the two weeks, and then add features which illustrate the tricks (interesting models I could use for this purpose is welcome too). </p>SuneMon, 08 Dec 2014 05:05:28 -0500http://www.or-exchange.com/questions/10817/what-would-you-teach-themteachingmodelingPDE as Nonlinear least squares problems with binary variableshttp://www.or-exchange.com/questions/11333/pde-as-nonlinear-least-squares-problems-with-binary-variables<p>Suppose we have an edge-weighted i a heat network, then we want to identify which edges
will be contribute in the heat convection.
I am using heat equation on a network and then solve it via least-squares problem.
I want to solve the heat equation <code>T_t(x,t) = - L_x . T(x,t) + F(x,t)</code> in an edge-weighted graph where <code>L_x = \sum_i x_i e_{ij}</code> is weighted Laplacian matrix of the graph, F() are sources on some nodes and T() is temperature of each node in each time step. Then using Theta method I conclude to the following least squares problem:</p>
<p><code>\min_{x\in \{0,1\}} \|\hat{T}_j(t_i) - T_j(t_i, x)\|_2^2</code></p>
<p>I have done the part which variables(weights) are relaxed to be between [0,1].
I used L1 regularization and active set methods in Matlab's fmincon to approximate the edge weights and then simulate the solution graph using edge-weights.</p>
<p>Next step would be to solve this problem using exact methods, for example:branch and bound, etc.
My question: is there would be right way to go with B&B?(I know it would be expensive to apply exact
methods, but will worth to check and compare the solutions). Any other suggestion would be
really appreciate.</p>
<p>I could not find some references on the discrete methods for nonlinear least squares. Would you lease let me know if you know?</p>SaberTue, 10 Feb 2015 05:17:18 -0500http://www.or-exchange.com/questions/11333/pde-as-nonlinear-least-squares-problems-with-binary-variablesinteger-programmingbinary-programmingnonlinear-optimizationnetworksForcing the value of "consecutive" variableshttp://www.or-exchange.com/questions/9203/forcing-the-value-of-consecutive-variables<p>Sorry I cannot find a clearer title for this question. I have a constraint like the following:</p>
<p>$$
\sum_{t \in T} w_{t} \cdot y_{t} \geq A
$$</p>
<p>where \(w_t\) are given, positive weights, and \(y_t \in \{0,1\} \).</p>
<p>I want to add (if possible) the following constraint:
<strong> all the non-zero \(y_t\) must be consecutive </strong>. That is, this is a valid solution:</p>
<p>$$ y_{t} = \dots 0,0,1,1,1,0,0\dots $$</p>
<p>while this is not:</p>
<p>$$ y_{t} = \dots 0,1,0,1,1,0,0\dots $$</p>
<p>The problem I find is that I don't know <em>a priori</em> how many \(y\) will be non-zero. </p>LibraSat, 01 Feb 2014 18:27:43 -0500http://www.or-exchange.com/questions/9203/forcing-the-value-of-consecutive-variableslinear-programmingconstraintsbinary-programmingmathematical-modelingMac/Xcode/C++ connect with GAMShttp://www.or-exchange.com/questions/11277/macxcodec-connect-with-gams<p>Basically, I failed to trying to implement individual global MINLP solvers (alphaBB, ANTIGONE, BARON, Couenne, LindoAPI, and SCIP) in C++/Xcode/Mac system. On the other hand, I realize that GAMS already integrate a lot of solvers. So I am thinking of using C++/Xcode/Mac system to construct models and let GAMS solve that. What would be the standard practice in this respect? Thank you.</p>ChivalryThu, 05 Feb 2015 19:16:25 -0500http://www.or-exchange.com/questions/11277/macxcodec-connect-with-gamsgamssoftwarestandard format for NLP or MINLPhttp://www.or-exchange.com/questions/11263/standard-format-for-nlp-or-minlp<p>So LP is standard format for linear programming problem MPS is standard format for MILP problem. Is there any standard format for NLP or MINLP format problem? thank you.</p>ChivalryThu, 05 Feb 2015 10:21:21 -0500http://www.or-exchange.com/questions/11263/standard-format-for-nlp-or-minlpnonlinear-optimizationUsng the NLP feature of SCIP using Xcode with c++http://www.or-exchange.com/questions/11267/usng-the-nlp-feature-of-scip-using-xcode-with-c<p>Due to project limitation, I want to use SCIP (especially its NLP or MINLP feature) in Xcode C++ environment. However, I did not find a step by step documentation and I am almost a complete noob in all the compiling details... Could anyone help me? Thank you very much.</p>ChivalryThu, 05 Feb 2015 11:33:43 -0500http://www.or-exchange.com/questions/11267/usng-the-nlp-feature-of-scip-using-xcode-with-cnonlinear-optimizationLearning Optimization Solvers/Modeling Languageshttp://www.or-exchange.com/questions/11219/learning-optimization-solversmodeling-languages<p>Hello everyone,</p>
<p>I'm a graduate student in Operations Research. I have had previous experience in my undergrad years with LINGO as an optimization modeling language and solver, but I'm realizing that it gets no love from academics. I am looking to learn some new optimization software that will help in my research and my future academic career.</p>
<p>I know there a lot of solvers out there, as well as lots of modeling languages. However, the popular ones seem to be Gurobi, CPLEX, and Matlab (esp for nonlinear problems, it seems). Not sure how XPress compares here. On the other side, GAMS and AMPL are probably the two most popular modeling languages.</p>
<p>What would be your advice as to what software I should get started with? Obviously, all of them have pros and cons and at this stage, I can't tell much about those differences. For example, wouldn't it be enough for one to master AMPL and just call his solver of choice no matter the problem type? Why would have to learn or use OPL then for modeling in CPLEX? Are there any advantages for learning a particular solver over just learning one algebraic modeling language? Is it just a matter of preference or experience?</p>
<p>Your help and insights are much appreciated! Thanks!</p>baubaidSat, 31 Jan 2015 21:31:45 -0500http://www.or-exchange.com/questions/11219/learning-optimization-solversmodeling-languagesmodeling-languagessolversIntroduction to OR for children?http://www.or-exchange.com/questions/10457/introduction-to-or-for-children<p>Well, it might be a little Off-topic question here.
However, here is the best place to post the question, I believe. </p>
<p>I have to introduce what I am doing, to children grade 2 & 3. It is a Daddy activity in my daughter's class. </p>
<p>(I know asking homework question is prohibited here. My homework is a little different, so hope you don't mind.)</p>
<p>Other than just saying 'I teach college students', I would like to introduce what is operations research. </p>
<p>I know that if you can explain your research topic to elementary students, you can explain it to anyone. </p>
<p>However, it is a really tough job. They are learning addition, subtraction, multiplication and division, now. </p>
<p>Do you have any experience or any idea on materials (game, story etc.) for 2nd and 3rd graders?</p>Phil KimThu, 16 Oct 2014 02:01:22 -0400http://www.or-exchange.com/questions/10457/introduction-to-or-for-childrenteachingoperations-researchLinearize integer real producthttp://www.or-exchange.com/questions/11186/linearize-integer-real-product<p>Can you linerize x*y where x is integer variable and y real variable.
2 <= x <= N, without writing x as a sum of binary variables?</p>zBirdyWed, 28 Jan 2015 13:16:13 -0500http://www.or-exchange.com/questions/11186/linearize-integer-real-productlinear-programmingLinearizing if then constraintshttp://www.or-exchange.com/questions/11211/linearizing-if-then-constraints<p>Dear All:</p>
<p>I am trying to develop equivalent linear constraints for the following if then condition:</p>
<p>if z=m then x=1, otherwise x=0; where z is an integer variable, x is a binary variables & m is a parameter.</p>
<p>Any suggestion is highly appreciated.</p>
<p>Thanks.</p>
<p>Noor </p>noorbuetFri, 30 Jan 2015 22:46:03 -0500http://www.or-exchange.com/questions/11211/linearizing-if-then-constraintsthenlinearizingif