Facility capacity for LSCP #273
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notebooks/lscp_capacity.ipynb
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| "# Location Set Covering Problem (LSCP)\n", | ||
| "\n", | ||
| "*Authors:* [Erin Olson](https://github.com/erinrolson),[Germano Barcelos](https://github.com/gegen07), [James Gaboardi](https://github.com/jGaboardi), [Levi J. Wolf](https://github.com/ljwolf), [Qunshan Zhao](https://github.com/qszhao)\n", | ||
| "\n", | ||
| "Location Set Covering is a problem realized by Toregas, et al. (1971). He figured out that emergency services must have placed according to a response time, since, there is a allowable maximum service time when it's discussed how handle an emergency activity. Therefore he proprosed a model named LSCP that:\n", | ||
| "\n", | ||
| "_Minimize the number of facilities needed and locate them so that every demand area is covered within a predefined maximal service distance or time._ Church L., Murray, A. (2018)\n", | ||
| "\n", | ||
| "**LSCP can be written as:**\n", | ||
| "\n", | ||
| "$\\begin{array} \\displaystyle \\textbf{Minimize} & \\sum_{j=1}^{n}{x_j} && (1) \\\\\n", | ||
| "\\displaystyle \\textbf{Subject to:} & \\sum_{j\\in N_i}{x_j} \\geq 1 & \\forall i & (2) \\\\\n", | ||
| " & x_j \\in {0,1} & \\forall j & (3) \\\\ \\end{array}$\n", | ||
| " \n", | ||
| "$\\begin{array} \\displaystyle \\textbf{Where:}\\\\ & & \\displaystyle i & \\small = & \\textrm{index referencing nodes of the network as demand} \\\\\n", | ||
| "& & j & \\small = & \\textrm{index referencing nodes of the network as potential facility sites} \\\\\n", | ||
| "& & S & \\small = & \\textrm{maximal acceptable service distance or time standard} \\\\\n", | ||
| "& & d_{ij} & \\small = & \\textrm{shortest distance or travel time between nodes} \\quad i \\quad \\textrm{and} \\quad j \\\\\n", | ||
| "& & N_i & \\small = & \\{j | d_{ij} < S\\} \\\\\n", | ||
| "& & x_j & \\small = & \\begin{cases} \n", | ||
| " 1, \\text{if a facility is located at node} \\quad j\\\\\n", | ||
| " 0, \\text{otherwise} \\\\\n", | ||
| " \\end{cases} \\end{array}$\n", | ||
| " \n", | ||
| "_This excerpt above was quoted from Church L., Murray, A. (2018)_\n", | ||
| "\n", | ||
| "This tutorial solves LSCP using `spopt.locate.coverage.LSCP` instance that depends on a array 2D representing the costs between facilities candidate sites and demand points. For that it uses a lattice 10x10 with simulated points to calculate the costs." |
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Update intro with new description and reference/display new capacity formulation
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@ljwolf conflicts were minor and now are resolved. |
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OK, I've updated the notebook wording. I will merge once the tests pass. |
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Just realized there are no tests here. But I suppose we can add later. The functionality is demoed in a basic way in the notebook and that can be translated to a simple test. |
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Hmm, I missed that for sure. I think that the notebook serves as a user test, and the existing option passing is tested already. What's not tested is the more finicky stuff, like argument typing and things... I think it's OK here because the functionality is completely checked by the notebook, but I wouldn't want this to justify future code without tests! |
My thoughts exactly. I will look into adding to @erinrolson's excellent contribution by doing a thorough doc review, adding tests, and probably adding some spice to the notebook. Hopefully I can get to this in the next couple weeks so we can include in the coming meta release. |
Implements facility capacity constraint for solving LSCP for GSoC '22