diff --git a/Project.toml b/Project.toml
index 3805d8c..df26ff3 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,12 +1,14 @@
 name = "BlockDiagonals"
 uuid = "0a1fb500-61f7-11e9-3c65-f5ef3456f9f0"
 authors = ["Invenia Technical Computing Corporation"]
-version = "0.1.26"
+version = "0.1.27"
 
 [deps]
 ChainRulesCore = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
+Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
 FillArrays = "1a297f60-69ca-5386-bcde-b61e274b549b"
 FiniteDifferences = "26cc04aa-876d-5657-8c51-4c34ba976000"
+JuMP = "4076af6c-e467-56ae-b986-b466b2749572"
 LinearAlgebra = "37e2e46d-f89d-539d-b4ee-838fcccc9c8e"
 
 [compat]
@@ -14,13 +16,16 @@ ChainRulesCore = "1"
 ChainRulesTestUtils = "1"
 FillArrays = "0.6, 0.7, 0.8, 0.9, 0.10, 0.11, 0.12, 0.13"
 FiniteDifferences = "0.12.3"
+JuMP = "0.23"
 julia = "1"
 
 [extras]
 ChainRulesTestUtils = "cdddcdb0-9152-4a09-a978-84456f9df70a"
+Dates = "ade2ca70-3891-5945-98fb-dc099432e06a"
+Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
 Documenter = "e30172f5-a6a5-5a46-863b-614d45cd2de4"
 Random = "9a3f8284-a2c9-5f02-9a11-845980a1fd5c"
 Test = "8dfed614-e22c-5e08-85e1-65c5234f0b40"
 
 [targets]
-test = ["ChainRulesTestUtils", "Documenter", "Random", "Test"]
+test = ["ChainRulesTestUtils", "Dates", "Distributions", "Documenter", "Random", "Test"]
diff --git a/src/BlockDiagonals.jl b/src/BlockDiagonals.jl
index 1d69dfe..d8b375b 100644
--- a/src/BlockDiagonals.jl
+++ b/src/BlockDiagonals.jl
@@ -4,6 +4,7 @@ using Base: @propagate_inbounds
 using ChainRulesCore
 using FillArrays: Zeros
 using FiniteDifferences
+using JuMP: AffExpr
 using LinearAlgebra
 
 import ChainRulesCore.ProjectTo
@@ -15,5 +16,6 @@ include("blockdiagonal.jl")
 include("base_maths.jl")
 include("chainrules.jl")
 include("linalg.jl")
+include("jump.jl")
 
 end  # end module
diff --git a/src/jump.jl b/src/jump.jl
new file mode 100644
index 0000000..0217f2e
--- /dev/null
+++ b/src/jump.jl
@@ -0,0 +1,9 @@
+"""
+    function Base.:*(A::BlockDiagonal, x::Vector{T}) where {T<:AffExpr}
+
+Multiply a `BlockDiagonal` with a `Vector{AffExpr}` from JuMP so we don't need to convert
+the `BlockDiagonal` to a `Matrix` first.
+"""
+function Base.:*(A::BlockDiagonal, x::Vector{T}) where {T<:AffExpr}
+    return mul!(similar(x, T, axes(A, 1)), A, x)
+end
diff --git a/test/jump.jl b/test/jump.jl
new file mode 100644
index 0000000..08671d5
--- /dev/null
+++ b/test/jump.jl
@@ -0,0 +1,34 @@
+@testset "JuMP" begin
+    num_nodes = 2
+    num_targets = 2
+    nodes = [randstring(3) for _ in 1:num_nodes]
+    targets = [DateTime(2020, 1, 1, h) for h in 1:num_targets]
+
+    dists = Vector{MvNormal}()
+    for k in targets
+        mu = randn(num_nodes * num_targets)
+        X = rand(num_nodes * num_targets, num_nodes * num_targets)
+        sigma = X * X' + I
+        push!(dists, MvNormal(mu, sigma))
+    end
+
+    covs = [Matrix(cov(d)) for d in dists]
+    means = [mean(d) for d in dists]
+
+    preds = (mean=vcat(means...), cov=BlockDiagonal(covs), target=targets, nodes=nodes)
+
+    @testset "Multiplication" begin
+        model = JuMP.Model()
+
+        n = length(preds.mean)
+        v = (
+            supply_mwh=@variable(model, supply_mwh[1:n] >= 0),
+            demand_mwh=@variable(model, demand_mwh[1:n] <= 0),
+        )
+
+        volume = v.supply_mwh + v.demand_mwh
+        normalized_sqrt_cov = cholesky(preds.cov).U / 24
+
+        @test normalized_sqrt_cov * volume == Matrix(normalized_sqrt_cov) * volume
+    end
+end
diff --git a/test/runtests.jl b/test/runtests.jl
index 552e1af..dafa79a 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -1,11 +1,17 @@
 using BlockDiagonals
 using ChainRulesCore
 using ChainRulesTestUtils
+using Dates
+using Distributions
 using Documenter
 using FiniteDifferences # For overloading to_vec
+using JuMP
+using Random
 using Test
 using LinearAlgebra
 
+Random.seed!(42069)
+
 push!(ChainRulesTestUtils.TRANSFORMS_TO_ALT_TANGENTS, x -> @thunk(x))
 
 @testset "BlockDiagonals" begin
@@ -15,4 +21,5 @@ push!(ChainRulesTestUtils.TRANSFORMS_TO_ALT_TANGENTS, x -> @thunk(x))
     include("base_maths.jl")
     include("chainrules.jl")
     include("linalg.jl")
+    include("jump.jl")
 end  # tests