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nahmias+olsen.jl
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nahmias+olsen.jl
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### A Pluto.jl notebook ###
# v0.19.11
using Markdown
using InteractiveUtils
# ╔═╡ 29d61cca-ad0f-4753-8789-f9da6e557b87
# Load the needed packages
using NewsvendorModel, Distributions, StatsBase, Plots
# ╔═╡ 65eb4c20-8998-11ec-3abf-bb0dda80c6a9
md"""
This notebook illustrates the usage of [NewsvendorModel.jl](https://github.com/frankhuettner/NewsvendorModel.jl) with examples from the **excellent textbook by Nahmias & Olsen 7th** or [8th](https://www.waveland.com/browse.php?t=662) edition.
These notes are not self-contained but should be considered as a companion to the above text book.
You can load this notebook in [Pluto](https://github.com/fonsp/Pluto.jl) from here: [https://github.com/frankhuettner/NewsvendorModel.jl/blob/main/docs/src/textbook/nahmias%2Bolsen.jl](https://github.com/frankhuettner/NewsvendorModel.jl/blob/main/docs/src/textbook/nahmias%2Bolsen.jl)
"""
# ╔═╡ e2cae904-9ac7-4ec7-8ec0-2eda4c286e6f
md"""
## Mac Magazine Store
Unit values:
- cost per unit ordered = 75
- selling price per unit = 25
- salvage value = 10
The following is known about the demand distribution (empirical from previous data)
"""
# ╔═╡ d1735113-39fa-45f7-b5a4-1925d9985e3d
md" ### Demand and distribution fitting"
# ╔═╡ d8d53f72-c901-45ff-99d8-9c0190460442
# store the given data in the variable `observed_demand`
observed_demand = vec([15 19 9 12 9 22 4 7 8 11 14 11 6 11 9 18 10 0 14 12 8 9 5 4 4 17 18 14 15 8 6 7 12 15 15 19 9 10 9 16 8 11 11 18 15 17 19 14 14 17 13 12]);
# ╔═╡ b8f5f21e-edfa-46b4-b574-4723c03db163
D̄ = mean(observed_demand)
# ╔═╡ 6fda8ecb-2b3a-4b89-9bc1-b6aad4efcb1f
s = std(observed_demand)
# ╔═╡ bfbbc931-b36c-4e46-8375-03de53d51cfd
begin
h1 = fit(Histogram,observed_demand, nbins=10)
plot(h1, ylabel="Observed frequency", xlabel = "Number of sales", legend=nothing)
d = Normal(D̄, s)
lo, hi = quantile.(d, [0.01, 0.99])
x = range(lo, hi; length = 100)
plot(twinx(), x, pdf.(d, x), legend=nothing, color = :red, yticks = false)
end
# ╔═╡ 994805b2-c68b-4800-b3ea-def39ec6cd87
md"An alternative is to use MLE:"
# ╔═╡ 1b7eb3b0-0ac9-4bef-9cf9-fc1da1072150
fit(Normal, observed_demand)
# ╔═╡ 44352ed2-e3c2-4ab1-a39e-c695242b5a12
md" ### Newsvendor Model"
# ╔═╡ 11be7ca9-d279-4ff5-8b4d-4d1a5e144e43
# Define the model
mac = NVModel(cost = 25, price = 75, salvage = 10, demand = Normal(D̄, s) )
# ╔═╡ fa3ce275-8a61-4204-af49-01ea8592b288
# Solve the model
solve(mac)
# ╔═╡ e20d3e01-39c4-46f2-8d8a-414bfd3048eb
md"""
### Discrete Demand
"""
# ╔═╡ cce4b651-c1ae-470a-a5b2-3c9e62d0bb4d
h = fit(Histogram, observed_demand, nbins =22)
# ╔═╡ 8a2b3ea9-b376-4d47-9d74-802106db2b98
epd = h.weights / 52
# ╔═╡ 72406e40-a328-4936-91e9-b9ae4c354165
mac_discrete_demand = DiscreteNonParametric(0:22, epd)
# ╔═╡ af1c94ce-4900-4e4d-93b0-096917fd288d
mac_discrete = NVModel(cost = 25, price = 75, salvage = 10,
demand = mac_discrete_demand )
# ╔═╡ 198bb582-9f88-48a7-85ea-d71559f0a34b
md"This yields the following critical fractile for the 1st stage:"
# ╔═╡ 60509577-f814-4770-ab01-41083bac00a5
solve(mac_discrete)
# ╔═╡ 74e1fa73-67f4-473b-84a9-facd895aa666
md"""
## Some exercises
The book offers exercises with solutions. Here is a small selection that illustrates the convinience of Distributions.jl and NewsvendorModel.jl (everything is very brief and a detailed explanation can be found in the book).
### Mac's thesaurus
"""
# ╔═╡ 3f768a78-0051-407d-a6c7-d152ff5cd4c5
c = 1.15
# ╔═╡ b44f2c1e-f62d-4711-85b4-ef88f1595d4b
p = 2.75
# ╔═╡ 76627c7b-5f47-4400-a1bc-2e52a2b81e21
thesaurus_nvm = NVModel(cost = c,
price = p,
demand = truncated(Normal(18, 6), 0, Inf),
backorder = 0.5,
substitute = p - c,
salvage = c,
holding = c * 0.2 / 12,
)
# ╔═╡ 051e3f60-6a38-4a01-a5d1-8ebecc3cdcd9
solve(thesaurus_nvm)
# ╔═╡ eecb6474-3b3c-4862-9356-68dd26e6c075
thesaurus_with_competition_nvm = NVModel(cost = c,
price = p,
demand = truncated(Normal(18, 6), 0, Inf),
backorder = 0.5,
# substitute = p - c,
salvage = c,
holding = c * 0.2 / 12,
)
# ╔═╡ bd5d741f-4550-4883-9618-655ef4de6d15
solve(thesaurus_with_competition_nvm)
# ╔═╡ 8e239e87-682e-4244-8b2e-8c73c7a4737d
md"""
## References
- [NewsvendorModel.jl](https://github.com/frankhuettner/NewsvendorModel.jl)
- Nahmias & Olsen: Production and Operations Analysis, 7th edition
"""
# ╔═╡ 00000000-0000-0000-0000-000000000001
PLUTO_PROJECT_TOML_CONTENTS = """
[deps]
Distributions = "31c24e10-a181-5473-b8eb-7969acd0382f"
NewsvendorModel = "63d3702b-073a-45e6-b43c-f47e8b08b809"
Plots = "91a5bcdd-55d7-5caf-9e0b-520d859cae80"
StatsBase = "2913bbd2-ae8a-5f71-8c99-4fb6c76f3a91"
[compat]
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Plots = "~1.31.7"
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"""
# ╔═╡ 00000000-0000-0000-0000-000000000002
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