Real Options

flexibility in network design, priced

From one site to a network

With two regions the choice is no longer only when and how much, but where. One central hub pools both regions' demand; regional hubs are close to their customers; and opening one hub creates a cheaper option on the next, because systems, people and supplier terms carry over. Here two regions with correlated, uncertain demand are valued together.

PoolingCentral hubOne hub serves both regions; its spare capacity covers whichever region is busy. Best when the regions move independently and shipping is cheap.
ProximityTwo hubs nowA hub in each region, sized together: close to customers, but each must cover its own region's peaks.
Compound optionPilot hubOpen one region's hub now and keep the option on the other, cheaper because the first hub exists.
DeferralWait & see networkServe both regions through 3PLs and open either hub, or both, at the best moment inside the window.

Decision map: what to open, and when

Each cell is one combination of the two regions' demand at the chosen year (further right: more demand in region A; further up: more in region B). Its colour is the optimal move from the network you would have then; faint cells are unlikely to be reached.

Distribution of NPV

The best fixed network against the best flexible strategy, over the same simulated demand paths.

Pooling and correlation

Each strategy's NPV as the correlation between the regions changes (everything else as set). The dashed line is your setting.

Table view

The model

Two regions, money in $M. The equations run in src/network.js, which is checked by its own automated tests, including an exact reduction to the single-site engine when one region is empty.

When the regions move apart, their total is steadier than either: a shared hub can be sized for it.
A pilot hub buys a cheaper option on the second hub: a compound option.
With two regions every decision depends on both demands, so the decision map is two-dimensional.

Joint demand lattice

each region: u = e^(σ√Δt), p = (e^(gΔt) − d)/(u − d) p_uu = p_A·p_B + c p_ud = p_A(1−p_B) − c p_du = (1−p_A)p_B − c p_dd = (1−p_A)(1−p_B) + c c = ρ·√(p_A(1−p_A)p_B(1−p_B))

Four branches per quarter. Each region's growth is reproduced exactly and the moves have correlation ρ; if a growth or a correlation cannot be represented, the page says what is used instead.

Serving the network

own_r = min(D_r, K_r) cross = spare capacity → the other region's shortfall 3PL_r = min(rest_r, outCap·D_r,0) CF = margin·own + (margin − x)·cross + outMargin·3PL − penalty·lost − opcost·(K_A + K_B)

Cross-region service earns the margin less the transport cost x, and is used before the 3PL when it earns more.

Compound option

second hub: (F·(1 − learn) + v·K)·(1+e)^t V_A(t) = max(hold, commit(A → AB) − cost_B) V_0(t) = max(wait, → A, → B, → AB)

With one hub open, the option to open the other; with none, the choice of which to open first, or both. Each project arrives after the build lead time; during it no other project starts.

Fixed designs

fixed(K_A, K_B) = Σ_t e^(−rt) E[CF_t]·Δt − cost central = max over K of fixed(K, 0) two = max over K_A, K_B of fixed(K_A, K_B)

The best fixed network is the better of a central hub and two regional hubs, each optimally sized; the value of flexibility is measured against it.