Demand, Inventory and Distribution Planning

Introduction and context

Packaging and distribution systems must deliver the right product, in the right quantity and condition, to the right location and time. These requirements create a managerial tension. High inventory improves availability and protects against uncertainty, but increases capital, storage, obsolescence, insurance and handling costs. Low inventory releases working capital but increases stockout risk, production disruption and customer dissatisfaction.

Demand, inventory and distribution planning provides the analytical foundation for resolving this tension. Demand forecasting estimates future requirements; inventory planning determines where and how much stock should be held; distribution planning positions inventory across a network; and sales and operations planning (S&OP) aligns commercial demand with operational capacity and financial objectives. In packaging management, these decisions are especially important because packaging materials may be bulky, have long procurement lead times, require special storage, or become obsolete when product design, regulation or branding changes.

The objective is not to minimise inventory in isolation. It is to optimise total supply-chain performance subject to service, cost, capacity, quality and risk constraints.

Learning objectives

After studying this chapter, the learner should be able to:

1. Explain the relationship among demand forecasts, inventory policies and distribution plans.
2. Select and evaluate forecasting methods using appropriate accuracy measures.
3. Calculate safety stock, reorder points and economic order quantities under stated assumptions.
4. Apply service-level analysis, ABC classification and multi-echelon logic.
5. Explain distribution requirements planning and the S&OP process.
6. Evaluate trade-offs among availability, working capital, responsiveness and uncertainty.
7. Design governance controls for data, algorithms, inventory decisions and supply risk.

1. The planning architecture

A useful planning architecture has four linked horizons:

Planning should be performed at the appropriate level of aggregation. A monthly S&OP plan may use product families and distribution regions, whereas a replenishment system uses individual stock-keeping units (SKUs), locations and time periods. Confusing these levels produces false precision: a detailed forecast is not necessarily an accurate forecast.

The principal stock measures are:

• On-hand inventory: physically available stock.
• Allocated or committed inventory: stock reserved for known requirements.
• Available inventory: stock that can be promised after considering commitments and restrictions.
• Pipeline inventory: stock ordered or in transit but not yet received.
• Inventory position: on-hand stock plus on-order stock minus backorders or commitments, according to the policy definition.
• Cycle stock: inventory used between replenishment arrivals.
• Safety stock: additional inventory held to protect against demand or supply uncertainty.
• Obsolete or excess stock: inventory unlikely to be consumed within its economic or usable life.

For packaging, inventory records should also include dimensions, pallet configuration, lot or batch information, shelf life, print version, regulatory status and compatibility with filling or handling equipment.

2. Demand forecasting

A forecast is a structured estimate of future demand based on historical observations, causal information and managerial judgement. It is not a promise and should not be treated as an unquestionable input. Forecast quality depends on the demand signal: shipments may reflect stockouts, allocation rules or sales incentives rather than true customer consumption.

2.1 Demand patterns

Four patterns are particularly important:

• Level: demand fluctuates around a stable mean.
• Trend: demand rises or falls over time.
• Seasonality: a repeating pattern occurs at a known frequency.
• Intermittency: many periods have zero demand, interrupted by irregular transactions; this is common for spare packaging components and slow-moving SKUs.

Promotional uplift, product launches, cannibalisation, substitution, price changes and regulatory events may create structural breaks. A statistical model based only on history can perform poorly after such a change.

2.2 Forecasting methods

A simple moving average of the most recent n observations is:

where D_t is actual demand in period t, F_t+1 is the forecast for the next period, and n is the number of observations. The method assumes that recent observations are equally relevant and that no strong trend exists.

A weighted moving average is:

where w_i are non-negative weights. Greater weight on recent observations improves responsiveness but may amplify random noise.

Exponential smoothing with a level-only model is:

Here α is the smoothing constant. A high value responds rapidly to changes; a low value produces a smoother forecast. Trend and seasonal methods, such as Holt and Holt–Winters models, should be used when the data support those structures. Intermittent demand may require specialised approaches such as Croston-type methods, but these must be validated because their error properties differ from ordinary time-series methods.

Judgemental adjustments are appropriate when information is not present in history, such as a confirmed customer contract or a new packaging regulation. However, every override should have a documented reason, owner, date and subsequent accuracy review.

2.3 Measuring forecast performance

Forecast accuracy should be evaluated out of sample and at the level at which decisions are made. Common measures include:

MAD is expressed in demand units, RMSE penalises large errors more heavily, and MAPE is easy to communicate as a percentage. MAPE is undefined when actual demand is zero and unstable when actual demand is very small; weighted or scaled measures are often preferable for intermittent demand. Forecast bias should also be monitored:

A persistent positive bias indicates systematic under-forecasting; a persistent negative bias indicates over-forecasting. Forecast value added analysis can test whether human intervention improves the statistical baseline or merely introduces optimism.

Worked example 1: smoothing and error

Suppose demand for the last three months was 100, 120 and 110 units. A three-month moving-average forecast for month 4 is:

If the actual demand in month 4 is 130 units, the absolute error is 20 units. The forecast is therefore useful as a baseline, but it has not captured a possible upward change. A planner should investigate whether the increase reflects a sustained trend, a promotion or random variation before changing the policy.

3. Service levels and uncertainty

A service level expresses the probability or extent to which demand is met. The cycle service level (CSL) is the probability that no stockout occurs during a replenishment cycle. The fill rate is the proportion of total demand supplied immediately from stock. These are not equivalent: a system may have a high CSL but a low fill rate if occasional stockouts are severe.

Uncertainty arises from demand, lead time, supply quantity, transport, quality release and master-data errors. Safety stock should therefore be based on the uncertainty relevant to the replenishment decision, rather than on an arbitrary number of days of supply.

If demand during lead time is approximately normally distributed and lead time is constant, safety stock is:

where SS is safety stock in units, z is the standard-normal factor corresponding to the target CSL, and σ_LT is the standard deviation of demand during lead time. The reorder point is:

where μ_LT is mean demand during lead time. For example, a 95% CSL corresponds approximately to z = 1.645 under the normality assumption.

If demand per period has standard deviation σ_D and lead time is L periods, independent demand implies:

If both demand and lead time vary, a commonly used approximation is:

where μ_D is mean demand per period and σ_L is the standard deviation of lead time. This expression assumes independence between demand and lead time and uses a normal approximation. If demand and lead time are correlated, or distributions are highly skewed, simulation or empirical quantiles are safer.

Worked example 2: reorder point

Daily demand has mean 50 units and standard deviation 10 units. Lead time is constant at 4 days. For a 95% CSL, use z = 1.645. Mean lead-time demand is:

The standard deviation during lead time is:

Therefore:

When inventory position falls to approximately 233 units, a replenishment order should be triggered. This calculation does not include order quantity; it only establishes the trigger point. If lead time is not constant, the variable-lead-time expression should be used or an empirical percentile should be calculated.

4. Replenishment policies and EOQ

A continuous-review (Q, R) policy orders a fixed quantity Q when inventory position reaches reorder point R. A periodic-review (P, S) policy reviews stock every P periods and orders enough to raise inventory position to an order-up-to level S. Continuous review requires reliable, timely transaction data; periodic review is simpler and can coordinate reviews across many SKUs.

The basic economic order quantity (EOQ) balances annual ordering and holding costs:

where D is annual demand in units per year, S is ordering or setup cost per order, and H is annual holding cost per unit. The classical model assumes constant demand, fixed lead time, instantaneous replenishment, no shortages, fixed ordering cost and constant unit price. It is a cost benchmark, not an automatic order instruction.

Annual relevant cost is:

The first term is annual ordering cost and the second is average cycle-stock holding cost. Purchase cost is excluded when unit price is constant because it does not change with Q.

Worked example 3: EOQ

Annual demand for a standard carton is 24,000 units, ordering cost is 500 currency units per order, and annual holding cost is 20 currency units per unit. Then:

The approximate order frequency is 24,000 ÷ 1,095 ≈ 21.9 orders per year. If supplier minimums, pallet quantities or quantity discounts apply, the planner must compare feasible quantities and total cost rather than blindly use 1,095 units. With planned safety stock, average inventory is approximately cycle stock Q ÷ 2 plus safety stock, although pipeline and in-transit inventory must be considered separately for working-capital analysis.

5. ABC classification and differentiated control

ABC analysis ranks items by annual usage value:

Items are ordered from highest to lowest value and classified cumulatively. A common, but not universal, policy is A items representing roughly 70–80% of value, B items the next 15–25%, and C items the remainder. The percentages are managerial conventions, not natural laws.

ABC should not be the sole control method. A low-value item can be critical if its absence stops a filling line; a high-value item may be easy to replenish. A useful extension combines value with criticality, lead time, demand variability, obsolescence risk and supply risk. Such a matrix may classify items as high-value/high-criticality, low-value/high-criticality and so forth, leading to different review frequencies, approval limits and supplier strategies.

Typical controls include:

6. Multi-echelon inventory planning

In a multi-echelon network, inventory is held at several connected levels, such as supplier, plant, regional distribution centre and customer-facing warehouse. Local optimisation can increase total inventory. For example, every facility may independently hold safety stock even though upstream stock could protect several downstream locations.

An echelon inventory position includes inventory at a location and all downstream inventory for which that location is responsible. Echelon policies allocate service targets and inventory buffers across the network. Centralisation often reduces safety stock through risk pooling when customer demands are not perfectly correlated, but it may increase transport time and last-mile cost.

Key design questions include:

• Where should decoupling stock be held?
• Which location has the best demand visibility?
• Can postponement delay final packaging or labelling until demand is known?
• Which node owns the service-level commitment?
• Are transport lead times and customs risks included in the policy?

Network models should evaluate total landed cost, not merely warehouse inventory. Total cost may include purchasing, handling, storage, transport, stockout, obsolescence, quality and carbon-related costs. Simulation or optimisation is often necessary where lead times, capacities and demand correlations are complex.

7. Distribution Requirements Planning

Distribution Requirements Planning (DRP) translates a distribution forecast into time-phased replenishment requirements. It generally begins with gross requirements at each stocking location, subtracts available inventory and scheduled receipts, applies safety-stock rules, and determines planned order receipts and releases. Planned releases are offset by transport or replenishment lead time.

A simplified DRP record contains:

This illustrative schedule assumes a two-period replenishment lead time and a policy that prevents negative projected availability. In a complete system, beginning inventory, safety stock, lot sizing, minimum shipment quantities, transport calendars and allocation rules must be shown explicitly. DRP must be integrated with master production scheduling and supplier capacity; otherwise it simply transfers shortages upstream.

The distinction between push and pull is also important. A forecast-based DRP plan is largely anticipatory, while a consumption signal or kanban replenishes in response to actual use. Most professional systems are hybrid: strategic and tactical plans use forecasts, while execution uses actual consumption and exception signals.

8. Sales and operations planning

S&OP is a cross-functional, recurring process that reconciles market demand, supply capability and financial plans. A robust cycle typically includes:

1. Data and portfolio review: cleanse history, identify events, product changes and forecast bias.
2. Demand review: develop an unconstrained demand plan with sales and marketing.
3. Supply review: test capacity, labour, materials, suppliers, inventory and logistics.
4. Reconciliation: evaluate scenarios, trade-offs and risks.
5. Executive review: approve decisions, priorities and escalations.
6. Execution and learning: communicate the plan and measure outcomes.

S&OP should not be reduced to a meeting or a forecast number. It is a decision-rights system. Participants must know who can approve overtime, change service targets, allocate scarce packaging, accept a stockout or discontinue a slow-moving SKU.

Useful measures include forecast bias, forecast accuracy, case fill rate, on-time-in-full delivery, inventory turns, days of supply, stockout frequency, aged inventory, schedule adherence and working-capital value. Metrics should be balanced: rewarding only inventory reduction can encourage shortages; rewarding only service can create excessive stock.

9. Illustrative case: packaging supply for a seasonal beverage

Background. The following is a fictional illustrative case. A beverage company supplies three regional markets. Its printed cartons have a 20-day supplier lead time, a minimum order quantity of 10,000 units and a six-month artwork life. Demand rises sharply before a summer campaign. Historically, the company forecast from shipments, although two regions experienced frequent stockouts.

Problem. The company held 1.8 million currency units of packaging inventory, yet achieved only 91% case fill. Obsolete cartons after artwork changes represented 6% of annual packaging spend. Sales wanted a high service level, procurement wanted large orders, and finance wanted lower working capital.

Analysis. A cross-functional team separated true consumption from stock-constrained shipments. It segmented SKUs using annual usage value and criticality. The main carton was an A-class, high-criticality item. Daily demand during the campaign had a mean of 2,000 cartons and standard deviation of 350 cartons. Supplier lead time was approximately constant at 20 days. The team selected a 97.5% cycle service target, using z ≈ 1.96.

Mean lead-time demand was 40,000 cartons. The standard deviation was:

Safety stock was:

The reorder point was therefore approximately:

The result was reviewed rather than adopted mechanically. Because the supplier minimum was 10,000 cartons, the company used a feasible order multiple of 10,000 and negotiated a reserved-capacity agreement for the campaign. It also introduced a weekly DRP review, regional inventory pooling where transport allowed, and a postponement design using a generic base carton with late-stage labels for lower-volume variants.

Solution and outcome. S&OP approved one campaign demand scenario, one downside scenario and a trigger for revising artwork orders. Procurement orders were released against the approved time-phased plan rather than sales optimism. Aged inventory was reported separately from usable stock. In the subsequent campaign, case fill improved to 97%, average packaging inventory fell by 12%, and obsolete printed cartons fell materially. The improvement was not attributed to safety stock alone: it resulted from better demand data, segmentation, postponement, supplier collaboration and governance.

Learning points. First, inventory availability cannot compensate indefinitely for a defective demand signal. Second, service targets must be differentiated by customer and item criticality. Third, packaging design and artwork decisions are inventory decisions. Finally, a mathematically calculated policy must be reconciled with minimum order quantities, capacity, shelf life and commercial realities.

10. Technology, AI and governance

Enterprise resource planning, warehouse-management and transport-management systems provide transaction visibility, while advanced planning systems support scenario modelling and multi-echelon optimisation. Barcode, RFID, electronic proof of delivery and IoT monitoring can improve inventory accuracy and condition visibility. Digital twins can test network policies before implementation.

AI and machine learning may improve forecasts by incorporating promotions, weather, web traffic, customer signals and external events. However, they do not eliminate the need for causal reasoning. Risks include data leakage, unstable relationships, hidden bias, poor handling of new products, unexplained recommendations and automation of erroneous master data. A responsible control framework should require:

• documented data lineage and ownership;
• version-controlled models and reproducible forecasts;
• comparison with simple statistical baselines;
• human review of material overrides;
• monitoring for drift, bias and service impact;
• access controls and audit trails;
• contingency procedures when systems or data fail.

Ethically, planners should not manipulate forecasts to secure scarce supply or meet performance targets. Allocation rules during shortages should be transparent, consistent and attentive to safety, contractual commitments and vulnerable customers. Personal or commercially sensitive demand data must be protected. Environmental governance should include packaging waste, reverse logistics, carbon from expedited transport and the consequences of overproduction.

11. Challenges and limitations

No inventory formula captures every managerial reality. Normal approximations may be poor for intermittent or highly skewed demand. Forecast accuracy can be misleading when aggregation hides SKU-level shortages. EOQ ignores supplier constraints unless the model is extended. ABC classes become stale when prices or demand change. Safety stock calculated from historical variation may fail during disruption, geopolitical events or regulatory change. Multi-echelon optimisation can produce recommendations that are mathematically sound but operationally infeasible.

Best practice is therefore to combine quantitative models with scenario analysis, supplier intelligence, exception management and periodic policy review. Planners should maintain a clear distinction between model output, management judgement and approved decision. Sensitivity analysis is particularly valuable: test how results change when demand, lead time, service targets, prices or capacity vary.

Best-practice checklist

1. Establish a clean item-location calendar, unit of measure and lead-time definition.
2. Forecast consumption where possible, not merely shipments.
3. Segment products by value, criticality, variability, life cycle and supply risk.
4. Set service targets explicitly and distinguish CSL from fill rate.
5. Calculate safety stock from measured uncertainty and review distributional assumptions.
6. Treat EOQ as a benchmark subject to minimums, capacity, shelf life and discounts.
7. Integrate DRP with production, purchasing and transport capacity.
8. Use S&OP to resolve cross-functional trade-offs and document decisions.
9. Measure total cost, working capital, availability, obsolescence and sustainability together.
10. Audit master data, overrides, algorithms and allocation decisions.

Chapter Summary

Demand, inventory and distribution planning balances customer availability against working capital and uncertainty. Forecasts provide an informed view of future requirements, but must be tested for accuracy, bias, structural change and the difference between consumption and shipments. Moving averages and exponential smoothing are useful baselines; more complex methods are justified only when their assumptions and performance are demonstrated.

Service-level decisions determine safety stock and reorder points. Under stated normality and independence assumptions, safety stock equals a service-factor multiplier times the standard deviation of lead-time demand. EOQ balances ordering and holding costs but must be adapted to practical constraints. ABC analysis focuses attention on high-value items, while criticality and supply risk prevent low-value but essential items from being neglected.

Multi-echelon planning considers the location and ownership of inventory across a network, and DRP converts distribution requirements into time-phased replenishment actions. S&OP integrates demand, supply, finance and executive decisions. Technology and AI can improve visibility and analysis, but require data governance, transparency and human accountability. The effective planner combines quantitative discipline with commercial understanding, scenario analysis and ethical decision-making.

Key Terms

Forecast: A structured estimate of future demand.

Forecast bias: Persistent tendency to over-forecast or under-forecast.

Safety stock: Buffer inventory held against uncertainty.

Cycle service level: Probability of avoiding a stockout during a replenishment cycle.

Fill rate: Proportion of demand supplied immediately from available stock.

Reorder point: Inventory position at which replenishment is triggered.

Inventory position: Stock available plus relevant pipeline stock minus outstanding requirements.

EOQ: Order quantity that balances relevant ordering and holding costs under stated assumptions.

Cycle stock: Inventory consumed between replenishment receipts.

ABC analysis: Classification based primarily on cumulative annual usage value.

Criticality: Consequence of an item being unavailable.

Lead time: Time between initiating and receiving replenishment.

Multi-echelon inventory: Inventory distributed across connected supply-chain levels.

Echelon inventory position: Inventory at a node plus downstream inventory under its responsibility.

DRP: Time-phased planning of replenishment for distribution locations.

S&OP: Cross-functional process for reconciling demand, supply and financial plans.

Postponement: Delaying final configuration, labelling or packaging until demand is clearer.

Obsolescence: Loss of usability or economic value before inventory is consumed.

Review Questions

Short Answer Questions

1. Distinguish cycle service level from fill rate.
2. State the assumptions of the basic EOQ model.
3. Why can shipment history differ from true customer consumption?
4. What is the purpose of a reorder point?
5. Explain why a low-value packaging item may still require high-priority control.

Long Answer Questions

1. Explain how forecasting, safety stock and replenishment policy interact in a packaging supply chain.
2. Compare continuous-review and periodic-review inventory systems, including their data and operational requirements.
3. Discuss the strengths and limitations of ABC analysis and propose a multidimensional segmentation approach.
4. Explain how multi-echelon inventory planning can reduce total stock while maintaining service.
5. Describe the S&OP process and evaluate its role in balancing commercial, operational and financial objectives.

Analytical / Application Questions

1. Daily demand has a mean of 80 units and standard deviation of 15 units. Lead time is constant at 9 days. Calculate safety stock and reorder point for a 95% cycle service level using z = 1.645. State the assumptions.
2. Annual demand is 36,000 units, ordering cost is 300 currency units per order and annual holding cost is 12 currency units per unit. Calculate EOQ and explain two practical reasons why the recommended order quantity might differ.
3. A distribution centre has rising fill-rate failures despite high inventory. Design an investigation using forecast bias, inventory accuracy, allocation rules, lead-time variability, SKU segmentation and DRP data. Recommend at least three corrective actions.

Multiple Choice Questions with Answers

Question 1

Which measure is most directly associated with the probability of avoiding a stockout during a replenishment cycle?

A. Cycle service level

B. Inventory turnover

C. Forecast bias

D. Annual usage value

Correct Answer: A. Cycle service level

Question 2

Daily demand has a standard deviation of 10 units and constant lead time is 4 days. Under independent demand, what is the standard deviation of lead-time demand?

A. 10 units

B. 14 units

C. 20 units

D. 40 units

Correct Answer: C. 20 units

Question 3

In the basic EOQ model, which cost is balanced against annual ordering cost?

A. Annual holding cost

B. Sales commission

C. Transport damage cost only

D. Forecast bias cost

Correct Answer: A. Annual holding cost

Question 4

What is a principal limitation of MAPE?

A. It cannot be expressed as a percentage

B. It is undefined when actual demand is zero

C. It always penalises large errors most heavily

D. It measures inventory position directly

Correct Answer: B. It is undefined when actual demand is zero

Question 5

Which item would most likely require differentiated control despite a low annual usage value?

A. A noncritical office label

B. A critical component whose absence stops production

C. A widely available commodity with no lead time

D. An item with no customer or operational consequence

Correct Answer: B. A critical component whose absence stops production

Question 6

What does DRP primarily convert into time-phased replenishment requirements?

A. Distribution-location demand and inventory information

B. Employee performance ratings

C. Supplier financial statements

D. Product artwork specifications only

Correct Answer: A. Distribution-location demand and inventory information

Question 7

What is the main purpose of safety stock?

A. To eliminate all ordering costs

B. To protect against uncertainty in demand or supply

C. To replace cycle counting

D. To guarantee zero obsolete inventory

Correct Answer: B. To protect against uncertainty in demand or supply

Question 8

Which statement best describes S&OP?

A. A warehouse picking method

B. A cross-functional process reconciling demand, supply and finance

C. A formula for calculating EOQ

D. A barcode standard

Correct Answer: B. A cross-functional process reconciling demand, supply and finance

Question 9

If annual demand is 24,000 units, ordering cost is 500 currency units and holding cost is 20 currency units per unit-year, the EOQ is approximately:

A. 500 units

B. 775 units

C. 1,095 units

D. 2,400 units

Correct Answer: C. 1,095 units

Question 10

What is a key advantage of postponement in packaging operations?

A. It increases the need for obsolete printed stock

B. It delays final configuration until demand is clearer

C. It removes the need for demand planning

D. It guarantees constant lead time

Correct Answer: B. It delays final configuration until demand is clearer