Notation
The symbols used throughout the docs, and where each one appears in the code.
Indices and time
| Symbol |
Meaning |
In code |
| \(i\) |
A SKU |
unique_id |
| \(t\) |
A demand period, counted from 0 |
demand_period in the event table; keys of schedules |
| \(\Delta\) |
The length of one period, a pandas frequency |
freq |
| \(L\) |
Lead time: periods from order to delivery, \(L \ge 0\) |
lead_time |
| \(R\) |
Review period: periods between ordering opportunities, \(R \ge 1\) |
review_period, PeriodicSchedule(every=R) |
| \(u\) |
The next decision period after \(t\) |
schedule.next_decision_period(t) |
| \(H\) |
Protection horizon: periods a decision must cover |
protection_horizon, reorder_horizon |
Stock
| Symbol |
Meaning |
Event table column |
| \(\mathit{OH}_t\) |
On-hand stock |
starting_on_hand, ending_on_hand |
| \(P_t\) |
Pipeline: units on order, not yet received |
starting_on_order, on_order_end |
| \(B_t\) |
Backorders: demand owed to customers |
starting_backorders, backorders_end |
| \(\mathit{IP}_t\) |
Inventory position \(= \mathit{OH}_t + P_t - B_t\) |
decision_inventory_position, inventory_position_end |
| \(D_t\) |
Demand in period \(t\) |
demand |
| \(q_t\) |
Order quantity placed in period \(t\) |
order_quantity |
| \(r_t\) |
Units received in period \(t\) |
received_units |
Policy parameters
| Symbol |
Meaning |
Used by |
| \(S\) |
Order-up-to level |
OrderUpToPolicy, ReorderPointPolicy("sS") |
| \(s\) |
Reorder point: order when \(\mathit{IP} \le s\) |
ReorderPointPolicy |
| \(Q\) |
Fixed order quantity |
ReorderPointPolicy("sQ") |
| \(\alpha\) |
Target probability (the quantile level of a target) |
service_level, target_probability |
| \(z_\alpha\) |
Standard normal quantile, \(\Phi^{-1}(\alpha)\) |
independent-normal targets |
| \(Q_\alpha(X)\) |
The \(\alpha\)-quantile of a random quantity \(X\) |
forecast targets |
| \(p, c, v\) |
Selling price, purchase cost, salvage value |
newsvendor_critical_fractile |