6. Inventory Policy Simulation Lab

The earlier chapters derived policy settings under clear assumptions. In this lab, turn those settings into executable Python and inspect a small, reproducible demand trace. The data is deliberately supplied rather than randomly sampled: that makes timing and expected outputs easy to verify before you experiment with random demand.

The exercises use Python's standard library only. They focus on three practical tasks:

1. Calculate continuous and periodic safety-stock targets.
2. Simulate an $(R,S)$ policy with a fixed lead time and lost sales.
3. Classify current on-hand against policy inventory reference levels.

Check the model before coding

Quiz

Simulation assumptions and timing

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With fixed lead time L = 4 periods, which protection period is used by an (R, S) policy reviewed every R = 3 periods?

Pick an answer to see if you are right.

Start with the protection-period targets

Given per-period mean demand $\mu$, standard deviation $\sigma$, lead time $L$, review interval $R$, and service factor $z$, calculate:

$$SS_{s,Q}=z\sigma\sqrt{L},\qquad s=\mu L+SS_{s,Q}$$ $$SS_{R,S}=z\sigma\sqrt{L+R},\qquad S=\mu(L+R)+SS_{R,S}$$

Use the demand and time units consistently. The test data supplies $z$ directly, so the exercise can focus on translating the policy equations into code.

Case	Mean demand / period	Demand SD / period	$L$	$R$	$z$
A	40	13.6	4	1	1.645
B	100	10	4	5	1.0

Simulate a periodic-review policy

Use this six-period demand trace to test the order/receipt timing. The policy reviews every $R=2$ periods, targets $S=8$ units of inventory position, and has lead time $L=1$ period. Start with 8 units on hand and no pipeline stock. Unfilled demand is lost, not backordered.

Period	Demand, trace A	Demand, trace B
1	3	2
2	7	2
3	2	2
4	6	2
5	1	2
6	4	2

Use these timing rules:

• Receive any shipment due at the start of a period, then satisfy as much demand as on-hand stock allows.
• At the end of every second period, order $\max(0,S-\text{inventory position})$.
• Inventory position is on-hand plus outstanding pipeline orders; lost sales are not subtracted as backorders.
• An order placed at the end of period $t$ with $L=1$ becomes available at the start of period $t+2$, after one full intervening period in transit.
• A cycle is a block of $R$ periods. A cycle is successful only if every period in it has no stockout; period service counts individual no-stockout periods.

Rank the simulation loop

Put the steps in order for one run of the periodic policy.

Quiz

Run one simulated period

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Order the recurring simulation steps, starting from a prepared demand series and initialized inventory state.

OrderDrag the handle to rearrange — top should be first.

1. ⋮⋮1Record whether the period had a stockout.
2. ⋮⋮2Apply current demand to on-hand stock and record fulfilled and unfilled units.
3. ⋮⋮3Schedule any new order to arrive after the stated lead-time convention.
4. ⋮⋮4Receive any shipment due at the start of the current period.
5. ⋮⋮5At a review boundary, calculate inventory position and the order quantity.

Drag items into the correct order (or use ↑↓), then check.

Implement simulate_rs(demands, lead_time, review_period, target). Begin with target units on hand and no pipeline stock. Unfilled demand is lost, not backordered.

Classify an inventory snapshot

The values below are policy-analysis inputs. They are not all observations from the six-period traces above. For this exercise, the routine on-hand band runs from safety stock through safety stock plus maximum cycle stock. For continuous review, maximum cycle stock is $Q$; for periodic review it is $\mu R$.

Policy	Safety stock	$Q$	$\mu$	$R$	Current on-hand
Continuous $(s,Q)$	44.7	40	40	1	30
Periodic $(R,S)$	50	N/A	40	1	65

Implement stock_zone(on_hand, safety_stock, maximum_cycle_stock). Return shortage at or below zero, below safety for a positive balance below safety stock, within cycle band through the upper reference, and above cycle range beyond it. This is a diagnostic label, not an order trigger; ordering decisions still use the policy's inventory-position rule.

Key takeaways

• Check inventory position and expected stock components separately; pipeline is not on-hand stock.
• Keep each policy's protection period and order rule explicit.
• Simulation results depend on receipt timing, review timing, and lost-sales versus backorder treatment.
• Data tables make a run inspectable; multiple deterministic tests catch timing and boundary errors before random demand is introduced.

Previous: Inventory Policies with Safety Stock.

Next: Beyond Normality — assess skewed demand and gamma-based inventory buffers.