Adding the LP sensitivity report print function for solution_summary

[AtsushiSakai]

I added the LP sensitivity report print function for solution_summary to fix #2662.

Currently, just a printing function is added, not using Table.jl interfaces.
This is a print example:

* Solver : Mock
* Status
  Termination status : OPTIMAL
  Primal status      : FEASIBLE_POINT
  Dual status        : FEASIBLE_POINT
  Message from the solver:
  "solver specific string"
* Candidate solution
  Objective value      : 2.1
  Dual objective value : 2.1
* Work counters
  Solve time (sec)   : 5.00000
* LP sensitivity summary
- Variables sensitivity
  Variable name : x
    Objective value coefficient : 1.1
    Reduced cost : 0.1
    Lower bound : -1.0
    Upper bound : 1.0
    Optimal value : 1.0
    Allowable increase in objective coefficient : Inf
    Allowable decrease in objective coefficient : 0.1
  Variable name : y
    Objective value coefficient : 1.0
    Reduced cost : -0.0
    Lower bound : 0.0
    Upper bound : Inf
    Optimal value : 1.0
    Allowable increase in objective coefficient : 0.1
    Allowable decrease in objective coefficient : 1.0
- Constraints sensitivity
  Constraint name : c1
    Right hand side (RHS) coefficient : 1.0
    Shadow price : -0.0
    RHS optimal value : 1.0
    Allowable increase in RHS coefficient  : Inf
    Allowable decrease in RHS coefficient  : Inf
  Constraint name : c2
    Right hand side (RHS) coefficient : 2.0
    Shadow price : 1.0
    RHS optimal value : 2.0
    Allowable increase in RHS coefficient  : Inf
    Allowable decrease in RHS coefficient  : 1.0

I'm not sure how to get slack or surplus value for each constraint.
If someone can advise me how to do it, I'd like to add it.

[codecov]

Codecov Report

Merging #2794 (dc251a7) into master (37eac58) will increase coverage by 0.10%.
The diff coverage is 100.00%.

@@            Coverage Diff             @@
##           master    #2794      +/-   ##
==========================================
+ Coverage   94.26%   94.36%   +0.10%     
==========================================
  Files          43       43              
  Lines        5524     5576      +52     
==========================================
+ Hits         5207     5262      +55     
+ Misses        317      314       -3     

Impacted Files	Coverage Δ
src/print.jl	94.50% <100.00%> (+1.24%)	⬆️
src/variables.jl	98.63% <0.00%> (+<0.01%)	⬆️
src/constraints.jl	95.58% <0.00%> (+0.02%)	⬆️

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[odow]

Have you ever used Excel?

The reason for a table is that Excel has a sensitivity report function that is often used to teach students in a LP-101 class.

I expect this functionality to be used very rarely in JuMP outside the classroom, so we should put it in a separate function and reproduce exactly what teachers expect: https://www.solver.com/how-correctly-interpret-sensitivity-reports-premium-solver

It's also going to be slow, so we don't want to run this for large LPs, and it won't work for any other type of problem, which are other reasons for putting this in a separate function.

[AtsushiSakai]

Have you ever used Excel?

Unfortunately, I have not used Excel sensitivity report.

so we should put it in a separate function and reproduce exactly what teachers expect:

OK. Do you mean a separate function means a separate print function?

[odow]

We already have

JuMP.jl/src/lp_sensitivity2.jl

Lines 9 to 63 in 744888c

	"""
	SensitivityReport
	See [`lp_sensitivity_report`](@ref).
	"""
	struct SensitivityReport
	rhs::Dict{ConstraintRef,Tuple{Float64,Float64}}
	objective::Dict{VariableRef,Tuple{Float64,Float64}}
	end
	Base.getindex(s::SensitivityReport, c::ConstraintRef) = s.rhs[c]
	Base.getindex(s::SensitivityReport, x::VariableRef) = s.objective[x]
	"""
	lp_sensitivity_report(model::Model; atol::Float64 = 1e-8)::SensitivityReport
	Given a linear program `model` with a current optimal basis, return a
	[`SensitivityReport`](@ref) object, which maps:
	- Every variable reference to a tuple `(d_lo, d_hi)::Tuple{Float64,Float64}`,
	explaining how much the objective coefficient of the corresponding variable
	can change by, such that the original basis remains optimal.
	- Every constraint reference to a tuple `(d_lo, d_hi)::Tuple{Float64,Float64}`,
	explaining how much the right-hand side of the corresponding constraint can
	change by, such that the basis remains optimal.
	Both tuples are relative, rather than absolute. So given a objective coefficient
	of `1.0` and a tuple `(-0.5, 0.5)`, the objective coefficient can range
	between `1.0 - 0.5` an `1.0 + 0.5`.
	`atol` is the primal/dual optimality tolerance, and should match the tolerance
	of the solver used to compute the basis.
	Note: interval constraints are NOT supported.
	# Example
	model = Model(GLPK.Optimizer)
	@variable(model, -1 <= x <= 2)
	@objective(model, Min, x)
	optimize!(model)
	report = lp_sensitivity_report(model; atol = 1e-7)
	dx_lo, dx_hi = report[x]
	println(
	"The objective coefficient of `x` can decrease by \$dx_lo or " *
	"increase by \$dx_hi."
	)
	c = LowerBoundRef(x)
	dRHS_lo, dRHS_hi = report[c]
	println(
	"The lower bound of `x` can decrease by \$dRHS_lo or increase " *
	"by \$dRHS_hi."
	)
	"""
	function lp_sensitivity_report(model::Model; atol::Float64 = 1e-8)

So perhaps we should implement

Base.show(io::IO, report::SensitivityReport)

or

Base.print(io::IO, report::SenstivityReport)

I'm not sure whether we should print it to the screen, or print it as a CSV for people to open in Excel.

I've used this before: https://github.com/ronisbr/PrettyTables.jl. Not sure if we want it as a JuMP dependency though.

[joaquimg]

Suggested change

	solution_summary(model::Model; verbose::Bool = false, sensitivity = false)
	solution_summary(model::Model; verbose::Bool = false, lp_sensitivity = false)

since its only for LP

[odow]

I'm going to close this as stale.

@AtsushiSakai thanks for taking a stab. It's always useful to see different design ideas, even if they don't end up being integrated. We're still interested in something like this, but it should be a separate print-out using the SensitivityReport, and be in the form of a table, not part of solution_summary.

[odow]

Ah, @AtsushiSakai I see you were following my suggestion in #2662. I guess that was bad advice. Apologies. 😄

[AtsushiSakai]

I'm sorry I left this PR. It is OK to close this PR. I will try this again when I have time.