Inventory Analytics

Roberto Rossi’s Inventory Analytics combines inventory theory, forecasting, optimisation and Python-based simulation. The book explains how ordering decisions depend on system structure, cost assumptions, uncertainty and lead times, then extends the analysis from a single stock point to connected inventory systems.

How to study this book

Reproduce the small examples before changing parameters. Keep a consistent record of demand units, time units, ordering costs, holding costs and lead times, and distinguish stock on hand from inventory position. For simulation work, record random seeds and compare more than one run. Use the mathematical policy conditions and the computational results to check one another.

Chapter and section guide

Introduction — From Inventory Problems to Analytics

The introduction places inventory decisions within a practical tradition of recording resources and managing flows. Analytics brings together descriptive understanding, prediction and decision-making, but these activities answer different questions. Start by describing a real stock problem before choosing a familiar formula. The right model depends on what is observed, what can be controlled and which costs or service requirements matter.

Study task: Describe an inventory decision and separate the available data, the uncertain quantities and the controllable action.

Inventory Systems

The system description distinguishes physical flows from information flows and introduces the accounting needed for simulation. Demand, replenishment and lead times can separate stock on hand, inventory level and inventory position. Those differences matter when orders are outstanding or demand is backordered. The Python examples turn the definitions into explicit event sequences, helping readers discover mistakes hidden by an informal warehouse narrative.

Study task: Simulate a short sequence with demand and a delayed delivery, reporting on-hand stock, backorders and inventory position at each step.

Deterministic Inventory Control

With demand treated as known, the analysis develops economic order quantity and related replenishment problems. Extensions include discounts, planned backorders, production, coordinated ordering and finite-horizon planning. Each modification changes a cost structure or constraint, so a formula should be tied to its assumptions. The examples and optimisation methods show why the best decision depends on the entire relevant cost rather than purchase price alone.

Study task: Compare two candidate order quantities under one stated model, then change an assumption such as a quantity discount or finite planning horizon.

Demand Forecasting

Time-series methods connect observed demand to predictions used in replenishment decisions. Moving averages, naïve methods, exponential smoothing and ARIMA-style models embody different assumptions about persistence, trend and seasonality. Residual analysis and out-of-sample evaluation are central: a close fit to historical observations does not guarantee useful forecasts. Distinguish uncertainty about a mean from uncertainty in a future demand observation.

Study task: Split a series into training and test periods, compare a simple baseline with another forecasting method and inspect the errors.

Stochastic Inventory Control

Uncertain demand requires a decision about the balance between shortage and excess inventory. The newsvendor problem introduces this trade-off, while multi-period policies connect replenishment to stock state, review timing and ordering costs. Base-stock, reorder-point and order-up-to ideas must be matched to their information and cost assumptions. Optimisation and simulation then provide complementary ways to evaluate expected cost and service behaviour.

Study task: Explain how a higher shortage penalty changes a newsvendor target, then compare two replenishment policies across repeated simulated demand paths.

Multi-echelon Inventory Systems

Connected stock points create dependencies that a collection of separate single-location calculations can miss. In a serial system, upstream and downstream decisions influence one another through replenishment and shortages. Echelon-stock concepts help account for inventory across stages, while assembly and distribution structures broaden the network picture. Track both physical resources and the information used by each decision-maker before discussing a coordinated policy.

Study task: Draw a warehouse–retailer system and explain how changing a downstream target can alter upstream demand and total system cost.

Appendix — Stochastic Processes and Discrete-Event Simulation

The appendix supports the computational examples with probability-process and simulation foundations. Bernoulli, binomial and Poisson ideas describe different random mechanisms, while queueing examples make event timing concrete. A correct event sequence matters as much as a plausible plot: arrivals, service, demand and deliveries must update the system consistently. Use these foundations to audit the main chapters’ code rather than treating simulation as a black box.

Study task: Write an event log for a small queue or replenishment system and show that the state updates respect the order of events.

Applied assignment

Build a reproducible inventory experiment for one product with a stated demand process and lead time. Compare a baseline policy with an alternative, report expected cost and a clearly defined service measure across repeated runs, and vary one uncertain input. Explain why the preferred policy might change when the demand model or cost estimates change.

Suggested reading plan

Begin with the introduction and system accounting, then reproduce a deterministic example. Spend a separate session on forecasting and validation before stochastic control. Finish with a two-stage network and revisit the appendix whenever random processes or event timing are unclear.

Questions for reflection

• Why can stock on hand and inventory position recommend different actions?
• When does a forecast with smaller statistical error fail to produce a lower inventory cost?
• Which benefits of coordination disappear if each stock point is optimised independently?

Edition and source notes

Based on Rossi’s 2021 Open Book Publishers edition. The guide follows the introduction, five main thematic sections and technical appendix; the source does not present these as a conventional numbered chapter sequence. Explanations and tasks are original. Python examples should be checked against the packages and versions used in your working environment.

Consult the official source and full text.