more text on paper and bibtex

Author: jbytecode

paper/paper.bib

@@ -11,3 +11,11 @@ @article{julia
   title     = {{J}ulia: A Fresh Approach to Numerical Computing},
   journal   = {{SIAM} Review}
 }
+
+@article{JuMP,
+    author = {Miles Lubin and Oscar Dowson and Joaquim {Dias Garcia} and Joey Huchette and Beno{\^i}t Legat and Juan Pablo Vielma},
+    title = {{JuMP} 1.0: {R}ecent improvements to a modeling language for mathematical optimization},
+    journal = {Mathematical Programming Computation},
+    year = {2023},
+    doi = {10.1007/s12532-023-00239-3}
+}

paper/paper.md

@@ -24,6 +24,37 @@ bibliography: paper.bib
 
 # Statement of Need
 
+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.
+
+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.
+
+# An Example
+
+The example below defines a linear transportation problem with a given cost matrix 
+for transportation cost between sources and targets, demand vector of targets, and 
+supply vector of sources. 
+
+```Julia
+julia> problem = TransportationProblem(
+            [
+                1 5 7 8;
+                2 6 4 9;
+                3 10 11 12
+            ],                    # Cost matrix
+            [100, 100, 100, 100], # Demand vector
+            [100, 100, 200],      # Supply vector
+        )
+```
+
+The multiple-dispacthed `solve` function is responsible to solve many of the models implemented in the package. When the problem is in type of `TransportationProblem`, a special method called and the result is in type `TransportationResult`.
+
+```Julia
+julia> result = solve(problem);
+julia> result.cost
+2400.0
+julia> result.solution
+[0.0 100.0 0.0 0.0; 0.0 0.0 100.0 0.0; 100.0 -0.0 -0.0 100.0]
+```
 
 # Acknowledgements