# 3-tran-3 — generated from 3-tran-3.qmd by tools/qmd_to_jl.py # (do not edit by hand; rerun the generator after editing the .qmd) # Cells (## title) follow the Julia VS Code extension convention. # Run a cell: click inside it, then press Alt+Enter. ## Get class-ready — install packages # Run this cell once. It installs every package the course uses, at the # versions pinned in the shared Manifest.toml, by activating the course # project and instantiating it. The project is the nearest folder above # this one holding a Project.toml, or an env/ or materials/env/ beside # one -- this repo keeps it at the root, the materials repo under env/, # so a copy under work/ finds it as ISE754/materials/env. Idempotent: # packages already present at the right version are skipped. import Pkg let dir = @__DIR__ isproj = d -> isfile(joinpath(d, "Project.toml")) env = d -> isproj(joinpath(d, "env")) ? joinpath(d, "env") : joinpath(d, "materials", "env") while !isproj(dir) && !isproj(env(dir)) && dir != dirname(dir) dir = dirname(dir) end isproj(env(dir)) && (dir = env(dir)) isproj(dir) || error("no course project above $(@__DIR__)") Pkg.activate(dir) Pkg.instantiate() end ## Setup # apparatus.jl ships beside the lectures in the materials # repository. Find it from the activated project rather # than from this file, so the script still works from a # copy under work/. let p = dirname(Base.active_project()) include(joinpath(basename(p) == "env" ? dirname(p) : p, "_common", "julia", "apparatus.jl")) end using CairoMakie, DataFrames, Logjam, Optim, Printf # Two device pixels per figure unit, so the raster figures are sharp # at the column's own width. CairoMakie.activate!(px_per_unit = 2) # Thousands separator, so a computed figure can be interpolated into # a result box instead of hand-typed. commafmt(n) = replace(string(n), r"(?<=[0-9])(?=([0-9]{3})+$)" => ",") # 1357 -> "1,357" # Dollars: two decimals, the separator on the whole dollars only. function usd(x) # 4441.7314 -> "4,441.73" whole, cents = split(@sprintf("%.2f", x), ".") return commafmt(whole) * "." * cents end # Sec. 1. Periodic shipments # Example 1: Periodic truck shipment from Raleigh to Gainesville ## Example 1(a): Full truckloads per year # Continuing with the example, and assuming a constant annual demand for # the product of 20 tons, determine the number of full truckloads per # year, and account for why this number should not be rounded to an # integer value. # Code block 1: full truckloads per year # From Example 1 of Lecture 3.2: uwt = 40 # lb ucu = 9 # ft^3 @show s = uwt/ucu # lb/ft^3 Kwt = 25 # ton Kcu = 2750 # ft^3 @show qmax = maxpayld(s; Kwt = Kwt, Kcu = Kcu) # ton # New: f = 20 # ton/yr q = qmax # ton (FTL => q = qmax) @show n = f/q # TL/yr ## Example 1(b): Shipment interval # Determine the shipment interval, and how many days there are between # shipments. # Code block 2: shipment interval @show t = q/f # yr/TL @show 365.25/n # day/TL, days between truckloads # Sec. 2. Full-truckload charge # Example 1: Periodic truck shipment from Raleigh to Gainesville ## Example 1(c): Annual FTL transport cost # Determine the annual full-truckload transport cost. # Code block 3: FTL rate and annual FTL transport cost d = 532 # mi, Google Maps road distance ppiTL = 131.0 # TL PPI for Jan 2018 @show rTL = 2.00ppiTL/102.7 # $/mi @show rFTL = rTL/qmax # $/ton-mi @show TC_FTL = n * rTL * d # $/yr ## Example 1(d): FTL cost with a three-month interval # Determine the cost if the shipments were to be made at least every # three months. # Code block 4: FTL cost with a three-month interval @show tmax = 3/12 # yr/TL @show nmin = 1/tmax # TL/yr @show q = f/max(n, nmin) # ton @show TC′_FTL = max(n, nmin) * rTL * d # $/yr ## Example 1: Periodic truck shipment from Raleigh to Gainesville ppiLTL = 177.4 # LTL PPI for Jan 2018, as in 3.2 cTLh(q) = charge_tl(q, s, d; r = rTL, Kwt = Kwt, Kcu = Kcu, ppi = ppiTL) cLTLh(q) = charge_ltl(q, s, d; ppi = ppiLTL) c0(q) = min(cTLh(q), cLTLh(q)) # independent charge, the upper bound cFTL(q) = rFTL*q*d # allocated full-truckload, the lower # The TL/LTL indifference point, searched only up to the LTL # estimate's cube bound of 650 ft^3. qLTLmax = 650s/2000 qI = optimize(q -> abs(cTLh(q) - cLTLh(q)), 0.075, qLTLmax).minimizer MC_LTL = mincharge_ltl(d; ppi = ppiLTL) # A split horizontal axis: the first 1.5 tons take 45% of the width, # the rest out to two and a half truckloads the other 55%, linear # inside each piece. QSPLIT, QEND = 1.5, 2.5qmax u(q) = q <= QSPLIT ? 0.45q/QSPLIT : 0.45 + 0.55(q - QSPLIT)/(QEND - QSPLIT) blue = RGBf(0.13, 0.35, 0.60) purple = RGBf(0.58, 0.20, 0.72) red = RGBf(0.85, 0.10, 0.10) olive = RGBf(0.40, 0.48, 0.20) fig = Figure(size = (687, 480)) ax = Axis(fig[1, 1]; xlabel = "Shipment size (ton)", ylabel = "Transport charge (\$)", title = "Transport charge for a shipment", titlesize = 17, xlabelsize = 16, ylabelsize = 16, xticklabelsize = 14, yticklabelsize = 14) vlines!(ax, [u(QSPLIT)]; color = (:black, 0.45), linewidth = 1.2, linestyle = :dashdot) qs = range(1/2000, QEND; length = 4000) lines!(ax, u.(qs), cFTL.(qs); color = purple, linewidth = 2.6) # Dotted: LTL past the indifference point, and the one-truckload # charge short of it. qL = range(qI, qLTLmax; length = 200) lines!(ax, u.(qL), cLTLh.(qL); color = blue, linewidth = 1.6, linestyle = :dot) lines!(ax, [0, u(qI)], [rTL*d, rTL*d]; color = blue, linewidth = 1.6, linestyle = :dot) lines!(ax, u.(qs), c0.(qs); color = blue, linewidth = 2.6) # Both axes start at zero, so the origin sits in the corner. The limits # and ticks come before the labels, because a label set along a curve # takes the curve's angle as drawn, and that depends on both. xlims!(ax, 0, 1) ylims!(ax, 0, 1.1*3rTL*d) ax.xticks = (u.([150/2000, qI, qmax, 2qmax]), ["150/2000", @sprintf("%.4f", qI), @sprintf("%.2f", qmax), @sprintf("%.2f", 2qmax)]) # The LTL minimum charge (MC) is named on its own tick: the floor it # labels is too short for a label inside the plot to clear the curve. ax.yticks = ([MC_LTL, rTL*d, 2rTL*d, 3rTL*d], ["MC " * @sprintf("%.2f", MC_LTL); string.(round.(Int, (1:3) .* rTL*d))]) # The angle of a curve on the page, measured in pixels between two of # its points, so that a label rotated to it runs parallel to the curve. function page_angle(c, q1, q2) p1 = Makie.project(ax.scene, :data, :pixel, Point3f(u(q1), c(q1), 0)) p2 = Makie.project(ax.scene, :data, :pixel, Point3f(u(q2), c(q2), 0)) return atan(p2[2] - p1[2], p2[1] - p1[1]) end text!(ax, u(0.4), cLTLh(0.4); text = "Independent", color = red, font = :bold, fontsize = 15, rotation = page_angle(cLTLh, 0.35, 0.45), align = (:center, :bottom), offset = (-8, 6)) text!(ax, u(0.95), 650; text = "Allocated\ntruckload", color = red, font = :bold, fontsize = 15, align = (:center, :center)) text!(ax, u(9.0), cFTL(9.0); text = "Allocated full-truckload", color = red, font = :bold, fontsize = 15, rotation = page_angle(cFTL, 8.0, 10.0), align = (:center, :top), offset = (6, -8)) # The split is a change of scale, not data, so it is named where it is # drawn rather than left for the caption to explain. text!(ax, u(QSPLIT), 1.1*3rTL*d; text = "scale changes at 1.5 ton", color = (:black, 0.6), fontsize = 12, rotation = pi/2, align = (:right, :bottom), offset = (-3, -6)) text!(ax, u(1.25), cLTLh(1.25); text = "LTL", color = olive, font = :bold, fontsize = 14, align = (:right, :bottom), offset = (-6, 0)) for (k, qk) in zip(1:3, [0.5qmax, 1.5qmax, 2.25qmax]) text!(ax, u(qk), k*rTL*d; text = "$k TL", color = olive, font = :bold, fontsize = 14, align = (:center, :bottom), offset = (0, 4)) end fig blue = RGBf(0.13, 0.35, 0.60) red = RGBf(0.85, 0.10, 0.10) ink = RGBf(0.15, 0.15, 0.15) # the time axis and the labels tc, τ = 1.0, 0.5 # cycle and transit time, schematic XEND = 4tc + τ + 0.3 # three shipments, room for the arrow fig = Figure(size = (687, 520)) axs = [Axis(fig[k, 1]) for k in 1:3] for (k, axk) in enumerate(axs) # t0, not s: a name assigned in a top-level loop is the global one, # and s is the product's density. t0 = (k - 1)*tc # one cycle after the last shipment hidedecorations!(axk); hidespines!(axk) # the time axis, with an arrowhead lines!(axk, [0, XEND - 0.08], [0, 0]; color = ink, linewidth = 2.5) scatter!(axk, [XEND - 0.08], [0]; marker = :rtriangle, markersize = 16, color = ink) # origin: builds from 0 to q while it is produced lines!(axk, [t0, t0 + tc], [0, 1]; color = blue, linewidth = 2.6) # destination: drawn down from q to 0 while it is consumed lines!(axk, [t0 + tc + τ, t0 + 2tc + τ], [1, 0]; color = blue, linewidth = 2.6) # the average at each end, q/2 lines!(axk, [t0, t0 + tc], [0.5, 0.5]; color = red, linewidth = 2, linestyle = :dash) lines!(axk, [t0 + tc + τ, t0 + 2tc + τ], [0.5, 0.5]; color = red, linewidth = 2, linestyle = :dash) xlims!(axk, -0.35, XEND) ylims!(axk, k == 1 ? -0.45 : -0.08, k == 1 ? 1.35 : 1.15) end # The first row carries the labels. ax1 = axs[1] for (x, a) in ((0.0, :right), (2tc + τ, :left)) dx = a == :right ? -6 : 6 text!(ax1, x, 0; text = "0", align = (a, :bottom), fontsize = 15, offset = (dx, 2)) text!(ax1, x, 0.5; text = L"\frac{q}{2}", align = (a, :center), fontsize = 17, offset = (dx, 0)) end # The peak labels sit above the peaks, clear of the lines rising and # falling into them. text!(ax1, tc, 1; text = L"q", align = (:center, :bottom), fontsize = 17, offset = (0, 12)) text!(ax1, tc + τ, 1; text = L"q", align = (:center, :bottom), fontsize = 17, offset = (0, 12)) bracket!(ax1, tc, 1.02, tc + τ, 1.02; text = "In-transit", orientation = :down, fontsize = 15, color = ink, textcolor = ink) text!(ax1, tc/2, -0.08; text = "Origin", align = (:center, :top), fontsize = 16) text!(ax1, tc + τ + tc/2, -0.08; text = "Destination", align = (:center, :top), fontsize = 16) # The first row's range is taller, for its labels, so it gets a taller # row in proportion and every row draws q at the same height. rowsize!(fig.layout, 1, Auto((1.35 + 0.45)/(1.15 + 0.08))) rowgap!(fig.layout, 4) fig # One regime: how the origin builds a shipment, how the destination # uses it, and the average (dashed) at each end. function regime!(axr, prod, cons) hidedecorations!(axr); hidespines!(axr) lines!(axr, [0, 1.02], [0, 0]; color = ink, linewidth = 2.5) scatter!(axr, [1.02], [0]; marker = :rtriangle, markersize = 14, color = ink) if prod == :constant # builds steadily over the cycle lines!(axr, [0, 0.4], [0, 1]; color = blue, linewidth = 2.6) lines!(axr, [0, 0.4], [0.5, 0.5]; color = red, linewidth = 2, linestyle = :dash) text!(axr, 0, 0.5; text = L"\frac{q}{2}", align = (:right, :center), fontsize = 16, offset = (-4, 0)) else # made in one short batch before pickup lines!(axr, [0, 0.35], [0.015, 0.015]; color = red, linewidth = 2, linestyle = :dash) lines!(axr, [0.35, 0.4], [0, 1]; color = blue, linewidth = 2.6) text!(axr, 0, 0.015; text = L"\approx 0", align = (:right, :bottom), fontsize = 16, offset = (-2, 2)) end if cons == :constant # drawn down steadily over the cycle lines!(axr, [0.56, 0.96], [1, 0]; color = blue, linewidth = 2.6) lines!(axr, [0.56, 0.96], [0.5, 0.5]; color = red, linewidth = 2, linestyle = :dash) text!(axr, 0.96, 0.5; text = L"\frac{q}{2}", align = (:left, :center), fontsize = 16, offset = (4, 0)) else # used as soon as it arrives lines!(axr, [0.56, 0.61], [1, 0]; color = blue, linewidth = 2.6) lines!(axr, [0.61, 0.96], [0.015, 0.015]; color = red, linewidth = 2, linestyle = :dash) text!(axr, 0.96, 0.015; text = L"\approx 0", align = (:left, :bottom), fontsize = 16, offset = (2, 2)) end text!(axr, 0.2, -0.06; text = "$(titlecase(string(prod))) production", align = (:center, :top), fontsize = 14) text!(axr, 0.78, -0.06; text = cons == :constant ? "Constant consumption" : "Immediate consumption", align = (:center, :top), fontsize = 14) xlims!(axr, -0.14, 1.12); ylims!(axr, -0.3, 1.05) return axr end fig = Figure(size = (687, 470)) cases = [(:constant, :constant, L"\alpha = \frac{1}{2} + \frac{1}{2} = 1"), (:constant, :immediate, L"\alpha = \frac{1}{2} + 0 = \frac{1}{2}"), (:batch, :constant, L"\alpha = 0 + \frac{1}{2} = \frac{1}{2}"), (:batch, :immediate, L"\alpha = 0 + 0 = 0")] for (i, (p, c, lab)) in enumerate(cases) regime!(Axis(fig[fld1(i, 2), mod1(i, 2)]; title = lab, titlesize = 17), p, c) end fig # Sec. 3. Inventory cost # Example 1: Periodic truck shipment from Raleigh to Gainesville ## Example 1(e): Cycle inventory cost at FTL # Give a reasonable estimate for the total annual cycle inventory cost # at the FTL shipment size $q_{\max}$, with $v = \$25{,}000$/ton, $h = # 0.3~\text{yr}^{-1}$, and $\alpha = 1$. # Code block 5: cycle inventory cost at FTL α = 1 v = 25000 # $/ton h = 0.3 # 1/yr @show IC_FTL = α*v*h*qmax # $/yr ## Example 1(f): Total logistics cost at FTL # Combine the transport and inventory costs to obtain the annual total # logistics cost (TLC) for full-truckload TL shipments. # Code block 6: total logistics cost at FTL @show TC_FTL # $/yr @show IC_FTL # $/yr @show TLC_FTL = TC_FTL + IC_FTL # $/yr # Sec. 4. Optimal shipment size # Example 1: Periodic truck shipment from Raleigh to Gainesville ## Example 1(g): Optimal TL shipment size # Allowing shipment sizes less than a full truckload, determine the TL # shipment size $q_{TL}^{}$ that minimizes the annual TLC for TL # service, and the resulting $TLC_{TL}^{}$. # Code block 7: optimal TL shipment size @show qᵒTL = sqrt((f*rTL*d)/(α*v*h)) # ton @show TCᵒ_TL = (f/qᵒTL)*rTL*d # $/yr @show ICᵒ_TL = α*v*h*qᵒTL # $/yr @show TLCᵒ_TL = TCᵒ_TL + ICᵒ_TL # $/yr ## Example 1(h): Allocated FTL # Including the minimum-charge and maximum-payload restrictions, # determine the TLC if a shipment of size $q_{TL}^{*}$ could be made as # an allocated full-truckload (sharing the truck across many shipments). # Code block 8: TLC as an allocated full truckload @show TLC_AllocFTL = f*rTL/qmax*d + α*v*h*qᵒTL # $/yr ## Example 1(i): Optimal LTL shipment size # Determine the LTL shipment size $q_{LTL}^{*}$ that minimizes the # annual TLC for LTL service. # Code block 9: optimal LTL shipment size ppiLTL = 177.4 # LTL PPI for Jan 2018 TLC_LTLh(q) = (f/q) * rate_ltl(q, s, d; ppi=ppiLTL) * q * d + α*v*h*q @show LB = 150/2000 # ton (lower bound on q) @show UB = min(5, 650*s/2000) # ton (upper bound on q) @show qᵒLTL = optimize(TLC_LTLh, LB, UB).minimizer # ton ## Example 1(j): Service choice # Given the optimal TL and LTL shipment sizes, determine which service # minimizes annual TLC. # Code block 10: TL or LTL at $25,000 per ton rLTL = rate_ltl(qᵒLTL, s, d; ppi=ppiLTL) @show rLTL # $/ton-mi @show cLTL = rLTL * qᵒLTL * d # $ @show TCᵒ_LTL = (f/qᵒLTL) * cLTL # $/yr @show ICᵒ_LTL = α*v*h*qᵒLTL # $/yr @show TLCᵒ_LTL = TCᵒ_LTL + ICᵒ_LTL # $/yr @show TLCᵒ_TL TLCᵒ_TL > TLCᵒ_LTL ? println("LTL selected") : println("TL selected"); # The curves the slides draw, for a product worth v $/ton. TC_TL(q) = (f/q)*charge_tl(q, s, d; r = rTL, Kwt = Kwt, Kcu = Kcu, ppi = ppiTL) TC_LTL(q) = (f/q)*charge_ltl(q, s, d; ppi = ppiLTL) IC(q, v) = α*v*h*q qopt_TL(v) = sqrt((f*rTL*d)/(α*v*h)) qopt_LTL(v) = optimize(q -> TC_LTL(q) + IC(q, v), LB, UB).minimizer cred, cblue = RGBf(0.85, 0.10, 0.10), RGBf(0.13, 0.35, 0.60) cgreen = RGBf(0.10, 0.62, 0.20) function costcurves!(ax, v) qT, qL = qopt_TL(v), qopt_LTL(v) rT = range(0.75qL, 1.5qT; length = 400) # TL curves rL = range(0.5qL, 0.99UB; length = 400) rI = range(0.5qL, 1.5qT; length = 2) TLC_TL(q) = TC_TL(q) + IC(q, v) TLC_LTL(q) = TC_LTL(q) + IC(q, v) lines!(ax, rT, TLC_TL; color = cred, linewidth = 2.2) lines!(ax, rL, TLC_LTL; color = cred, linewidth = 2.2) lines!(ax, rT, TC_TL; color = cblue, linewidth = 2.2) lines!(ax, rL, TC_LTL; color = cblue, linewidth = 2.2) lines!(ax, rI, q -> IC(q, v); color = cgreen, linewidth = 2.2) yT, yL = TLC_TL(qT), TLC_LTL(qL) scatter!(ax, [qL, qT], [yL, yT]; color = ink, markersize = 11) ax.xticks = ([qL, qT], [@sprintf("%.2f", qL), @sprintf("%.2f", qT)]) ys = sort([yL, yT]) ax.yticks = (ys, [commafmt(round(Int, y)) for y in ys]) # Labels a fixed fraction of the way across the axis. x0, x1 = 0.5qL, 1.5qT at(p) = x0 + p*(x1 - x0) top = max(1.25max(yL, yT), 1.12TLC_LTL(0.99UB)) lab!(x, y, t, al, o) = text!(ax, x, y; text = t, align = al, fontsize = 15, color = ink, offset = o) # TLC_TL leaves the top of the axis on the left, so its label goes # where the curve comes back into view. xs = range(at(0.12), x1; length = 400) xT = xs[something(findfirst(q -> TLC_TL(q) <= 0.9top, xs), 1)] lab!(xT, TLC_TL(xT), L"TLC_{TL}", (:left, :bottom), (6, 2)) lab!(0.99UB, TLC_LTL(0.99UB), L"TLC_{LTL}", (:right, :bottom), (0, 6)) lab!(at(0.32), TC_TL(at(0.32)), L"TC_{TL}", (:left, :bottom), (6, 2)) # TC_LTL hangs under its curve at the left edge, below the curve's # height a fifth of the way in, so the steep TC_TL stays clear even # in the narrow panels of the next figure. lab!(at(0.0), TC_LTL(at(0.2)), L"TC_{LTL}", (:left, :top), (4, -8)) lab!(at(0.35), IC(at(0.35), v), L"IC", (:left, :top), (6, -4)) xlims!(ax, x0, x1) ylims!(ax, IC(x0, v), top) return ax end fig = Figure(size = (687, 460)) ax = Axis(fig[1, 1]; xlabel = "Shipment size (ton)", ylabel = "\$ per year", xlabelsize = 16, ylabelsize = 16, xticklabelsize = 14, yticklabelsize = 14) costcurves!(ax, 25_000) fig ## Example 1: Periodic truck shipment from Raleigh to Gainesville # c0, the independent charge of Sec. 2.3's figure, takes the cheaper # service at every size, so minimizing TLC with it directly faces both # services' minima at once. lnTLC0(q, v) = log((f/q)*c0(q) + IC(q, v)) function lnpanel(vi, qhi) fig = Figure(size = (340, 380)) axv = Axis(fig[1, 1]; xlabel = "Shipment size (ton)", ylabel = L"\ln TLC_0(q)", xlabelsize = 15, ylabelsize = 15, xticklabelsize = 13, yticklabelsize = 13) qs = range(LB, qhi; length = 1500) lines!(axv, qs, q -> lnTLC0(q, vi); color = cblue, linewidth = 2) qT, qL = qopt_TL(vi), qopt_LTL(vi) scatter!(axv, [qL, qT], [lnTLC0(qL, vi), lnTLC0(qT, vi)]; color = ink, markersize = 10) xlims!(axv, LB, qhi) return fig end lnpanel(25_000, qmax) lnpanel(85_000, 1.8qopt_TL(85_000)) ## Example 1(k): Service choice at higher product value # If the unit value of the product rises to $v = \$85{,}000$/ton, # re-determine the optimal shipment sizes and which service is selected. # Code block 11: TL or LTL at $85,000 per ton v = 85000 # was 25000 @show qᵒTL = sqrt((f*rTL*d)/(α*v*h)) # ton @show TCᵒ_TL = (f/qᵒTL)*rTL*d # $/yr @show ICᵒ_TL = α*v*h*qᵒTL # $/yr @show TLCᵒ_TL = TCᵒ_TL + ICᵒ_TL # $/yr @show qᵒLTL = optimize(TLC_LTLh, LB, UB).minimizer # ton rLTL = rate_ltl(qᵒLTL, s, d; ppi=ppiLTL) @show rLTL # $/ton-mi @show cLTL = rLTL * qᵒLTL * d # $ @show TCᵒ_LTL = (f/qᵒLTL) * cLTL # $/yr @show ICᵒ_LTL = α*v*h*qᵒLTL # $/yr @show TLCᵒ_LTL = TCᵒ_LTL + ICᵒ_LTL # $/yr TLCᵒ_TL > TLCᵒ_LTL ? println("LTL selected") : println("TL selected"); fig = Figure(size = (687, 420)) for (i, vi) in enumerate((25_000, 85_000)) axv = Axis(fig[1, i]; xlabel = "Shipment size (ton)", ylabel = i == 1 ? "\$ per year" : "", title = "($('a' + i - 1)) \$$(commafmt(vi)) per ton", titlesize = 16, xlabelsize = 15, ylabelsize = 15, xticklabelsize = 13, yticklabelsize = 13) costcurves!(axv, vi) end fig ## Model: Minimum-TLC shipment size logjam_rung(:minTLC, "minimum-TLC shipment size") ## Example 1: Periodic truck shipment from Raleigh to Gainesville # Code block 12: Ex. 1(k) again, with the function tr = (r = rTL, Kwt = Kwt, Kcu = Kcu, ppi = ppiTL) sh = DataFrame(f = f, s = s, a = α, v = v, h = h, d = d) res = minTLC(first(sh), tr, ppiLTL) @show res.qᵒ # ton @show res.TLCᵒ # $/yr @show res.isLTL # LTL selected? # Sec. 5. Aggregate periodic shipment # Example 1: Periodic truck shipment from Raleigh to Gainesville ## Example 1(l): A second product # On Jan 10, 2018, determine the optimal independent shipment size and # TLC for a second product, 80 ton/yr of Class 60 material worth # \$5,000/ton, shipped point-to-point from Raleigh to Gainesville, as # before. # Code block 13: a second product push!(sh, first(sh)) # duplicate the row sh[2, [:f, :s, :v]] = [80, 32.16, 5000] # patch the second product sh.qmax = [maxpayld(row, tr) for row in eachrow(sh)] transform!(sh, AsTable(:) => ByRow(row -> minTLC(row, tr, ppiLTL)) => AsTable) prt(sh) ## Example 1(m): Aggregate shipment # Determine the annual TLC if the two products are always shipped # together on the same truck, and compare to the sum of their # independent TLCs. # Code block 14: the aggregate shipment @show fagg = sum(sh.f) # ton/yr @show sagg = fagg/sum(sh.f ./ sh.s) # lb/ft^3 @show vagg = sum(sh.f .* sh.v)/fagg # $/ton ash = aggshmt(sh[:, [:f, :s, :a, :v, :h, :d]]) # the same, by Logjam @show qmax_agg = maxpayld(ash, tr) # ton resa = minTLC(ash, tr) # TL only @show TLC_indep = sum(sh.TLCᵒ) # $/yr, shipped separately @show TLC_agg = resa.TLCᵒ # $/yr, shipped together # Code block 15: the two products and their aggregate, as a table tdays(q, f) = 365.25q/f # interval between shipments, days fmt(x, dg) = x === missing ? "" : @sprintf("%.*f", dg, x) cm(x) = x === missing ? "" : commafmt(round(Int, x)) rows = [("1", sh.f[1], sh.s[1], sh.v[1], sh.qmax[1], sh.TLCᵒ[1], sh.qᵒ[1]), ("2", sh.f[2], sh.s[2], sh.v[2], sh.qmax[2], sh.TLCᵒ[2], sh.qᵒ[2]), ("1 + 2", missing, missing, missing, missing, TLC_indep, missing), ("Aggregate", ash.f, ash.s, ash.v, qmax_agg, TLC_agg, resa.qᵒ)] println("| | \$f\$ | \$s\$ | \$v\$ | \$q_{\\max}\$ | \$TLC\$ | ", "\$q^{*}\$ | \$t\$ |") println("|:--|--:|--:|--:|--:|--:|--:|--:|") for (lab, f_, s_, v_, qm, tlc, q_) in rows t_ = (q_ === missing) ? missing : tdays(q_, f_) println("| ", lab, " | ", cm(f_), " | ", fmt(s_, 2), " | ", cm(v_), " | ", fmt(qm, 2), " | ", tlc === missing ? "" : usd(tlc), " | ", fmt(q_, 2), " | ", fmt(t_, 2), " |") end println("\n: The two products shipped separately and as one aggregate: ", "\$f\$ in ton/yr, \$s\$ in lb/ft^3^, \$v\$ in \\\$/ton, ", "\$q_{\\max}\$ and \$q^{*}\$ in ton, \$TLC\$ in \\\$/yr, and ", "the interval \$t\$ in days. ", "{#tbl-shipment-economics .dense .fit}\n") ## Example 2: Interval-constrained full truckload # On average, 200 tons of components are shipped 750 miles from a # fabrication plant to an assembly plant each year. The components are # produced and consumed at a constant rate throughout the year. # Currently, full truckloads of the material are shipped. Determine the # impact on total annual logistics costs if TL shipments were made every # two weeks. The revenue per loaded truck-mile is \$2.00; a truck's # cubic and weight capacities are 3,000 ft^3^ and 24 tons, respectively; # each ton of the material is valued at \$5,000 and has a density of 10 # lb per ft^3^; the material loses 30% of its value after 18 months; and # in-transit inventory costs can be ignored. # Code block 16: TLC of full truckloads d2 = 750 # mi s2 = 10 # lb/ft^3 Kwt2, Kcu2 = 24, 3000 # ton, ft^3 r2 = 2 # $/mi f2 = 200 # ton/yr v2 = 5000 # $/ton @show hobs2 = 0.3/1.5 # 1/yr: 30% of value lost in 1.5 yr @show h2 = 0.11 + hobs2 # 1/yr: interest + warehousing 0.11 a2 = 1 # constant production and consumption @show qmax2 = maxpayld(s2; Kwt = Kwt2, Kcu = Kcu2) # ton @show cFTL2 = charge_tl(qmax2, s2, d2; r = r2, Kwt = Kwt2, Kcu = Kcu2) # $ @show TLC_FTL2 = totlogcost(qmax2, cFTL2, f2, a2, v2, h2) # $/yr # Code block 17: TLC of two-week shipments @show nFTL2 = f2/qmax2 # TL/yr @show tmax2 = 2*7/365.25 # yr/TL @show nmin2 = 1/tmax2 # TL/yr @show q2wk = f2/max(nFTL2, nmin2) # ton @show c2wk = charge_tl(q2wk, s2, d2; r = r2, Kwt = Kwt2, Kcu = Kcu2) # $ @show TLC_2wk = totlogcost(q2wk, c2wk, f2, a2, v2, h2) # $/yr @show ΔTLC = TLC_2wk - TLC_FTL2 # $/yr