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    <p><strong>Heuristics (and/or checklists) to decide if the problem at hand is really a Linear Program.</strong> </p> <p>Here's my attempt at answering, and I have also tried to outline how I'd approach this problem.</p> <p><strong>Questions that indicate that a given problem is suitable to be formulated as an LP/IP:</strong></p> <ol> <li>Are there decisions that need to be taken regularly, at different time intervals? </li> <li>Are there a number of resources (workers, machines, vehicles) that need to be assigned tasks? (hours, jobs, destinations) </li> <li>Is this a routing problem, where different "points" have to be visited? </li> <li>Is this a location or a "layout" problem? (Whole class of Stock-cutting problems fall into this group)</li> </ol> <p>Answering yes to these questions means that an LP formulation might work.</p> <p><strong>Commonly encountered LP's</strong> include: Resource allocation.: (Assignment, Transportation, Trans-shipment, knapsack) ,Portfolio Allocation, Job Scheduling, and network flow problems. <a href="http://homepages.rpi.edu/~mitchj/handouts/lp/lp.pdf">Here's a good list of LP Applications</a> for anyone new to LPs or IPs. That said, there are literally 1000s of different types of problems that can be formulated as LP/IP. The people I've worked with (researchers, colleagues) develop an intuition. They are good at recognizing that a problem is a certain type of an Integer Program, even if they don't remember the details, which they can then look up.</p> <p><strong>Why this question is tricky to answer:</strong> There are many reasons why it is not always straightforward to know if an LP formulation will cut it.</p> <ol> <li>There is a lot of "art" (subjectivity) in the approach to modeling/formulation.</li> <li>Experience helps a lot. People get good at recognizing that this problem can be "likened" to another known formulation</li> <li>Even if a problem is not a straight LP, there are many clever <em>master-slave techniques</em> (sub-problems), or <em>nesting techniques</em> that make the overall formulation work.</li> <li>What looks like multiple objectives can be combined into one objective function, with an appropriate set of weights attached.</li> <li>Experienced modelers employ <em>decomposition</em> and <em>constraint-relaxation</em> techniques and later compensate for it.</li> </ol> <p><strong>How to Proceed to get the basic formulation done?</strong></p> <p>The following has always steered me in the right direction. I typically start by listing the Decision Variables, Constraints, and the Objective Function. I then usually iterate among these three to make sure that everything "fits."</p> <p>So, if you have a problem at hand, ask yourself:</p> <ul> <li><strong>What are the Decision Variables (DV)?</strong> I find that this is always a good place to start the process of formulation. How many <em>types</em> of DV's are there? (Which resource gets which task, and when should it start?) </li> <li><strong>What are the Constraints?</strong><br> Some constraints are very readily visible. Others take a little bit of teasing out. The constraints have to be written in terms of your decision variables, and any constants/limits that are imposed.</li> <li><strong>What is the Objective Function?</strong><br> What are the quantities that need to be maximized or minimized? Note: Sometimes, it is not clear what the objective function is. That is okay, because it could well be a <em>constraint-satisfaction</em> problem.</li> </ul> <p><strong>A couple of quick Sanity Checks</strong> once you think your LP formulation is done:</p> <ol> <li>I always try to see if a trivial solution (all 0s or all big numbers) is not part of the solution set. If yes, then the formulation is most probably not correct. Some constraint is missing. </li> <li>Make sure that each and every constraint is "related"' to the Decision Variables. (I occasionally find constraints that are just "hanging out there." This means that a "<em>bookkeeping constraint</em>" has been missed.)</li> </ol> <p>In my experience, people who keep at it almost always develop the needed intuition. Hope this helps.</p>
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