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paper/paper.bib

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@@ -18,4 +18,16 @@ @article{JuMP
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journal = {Mathematical Programming Computation},
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year = {2023},
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doi = {10.1007/s12532-023-00239-3}
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}
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@article{HiGHS,
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title={Parallelizing the dual revised simplex method},
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author={Huangfu, Qi and Hall, JA Julian},
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journal={Mathematical Programming Computation},
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volume={10},
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number={1},
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pages={119--142},
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year={2018},
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doi={10.1007/s12532-017-0130-5},
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publisher={Springer}
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}

paper/paper.md

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# Summary
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`OperationsResearchModels.jl` is a Julia package [@julia]...
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`OperationsResearchModels.jl` is a Julia package [@julia] that offers comprehensive implementations for numerous topics typically covered in an Operations Research curriculum. Its primary objective during development was to serve academic and pedagogical purposes, providing a clear and accessible platform for learning and applying OR concepts. While not optimized for high-performance computing, the package leverages JuMP for its underlying mathematical modeling, which inherently provides a reasonable level of computational efficiency. This design allows the package to deliver a suite of functions that solve classical operations research problems with remarkable ease and consistency, simplifying the process for students and researchers alike.
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# Statement of Need
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JuMP [@JuMP] provides an excellent interface and macros for uniformly accessing optimizer functionality. Any mathematical optimization problem can be assembled with three core components: the objective function (`@objective`), variable definitions (`@variable`), and constraints (`@constraints`). The researcher's role is to formulate the original problem as a mathematical optimization problem and then translate it using JuMP's macros.
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OperationsResearchModels.jl streamlines the model translation stage by automatically constructing mathematical problems from problem-specific input data. Its extensive functionality encompasses a significant portion of the Operations Research domain. This includes, but is not limited to: the linear transportation problem, the assignment problem, the classical knapsack problem, various network models (Shortest Path, Maximum Flow, Minimum Spanning Tree), project management techniques (CPM and PERT), the uncapacitated p-median problem for location selection, Johnson's Rule for flow-shop scheduling, a genetic algorithm for scheduling problems intractable by Johnson's Rule, a zero-sum game solver, and a Simplex solver for real-valued decision variables.
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Although the majority of computations are performed by the HiGHS optimizer [@HiGHS] through JuMP, OperationsResearchModels.jl incorporates dedicated, hand-coded Simplex routines. These routines serve a valuable pedagogical purpose in Operations Research curricula, enabling users to observe and verify the detailed, step-by-step calculations involved in solving linear programming problems.
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# An Example
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The example below defines a linear transportation problem with a given cost matrix

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