Aggregate Planning and Master Production Scheduling

Introduction and Context

Production planning converts market demand into a coordinated plan for materials, labour, equipment and time. Two linked planning levels are especially important. Aggregate planning establishes the overall production, workforce and inventory strategy for a medium-term horizon, usually three to eighteen months. Master production scheduling (MPS) translates that aggregate plan into a time-phased statement of which end items will be produced, in what quantities and when.

Aggregate planning is concerned with product families and broad capacity. An MPS is concerned with specific finished products and usually operates over weekly or daily periods. The aggregate plan must therefore be sufficiently realistic to support the MPS, while the MPS must remain consistent with the aggregate quantities and capacity decisions.

The central managerial problem is balancing uncertain demand against limited and costly resources. Managers must decide whether to build inventory before demand occurs, vary the workforce, use overtime, subcontract production, or allow backorders. No single strategy is universally best; the appropriate choice depends on cost, service requirements, labour regulations, product characteristics and operational risk.

Learning Objectives

By the end of this chapter, the learner should be able to:

1. Explain the relationship between aggregate planning, MPS, material requirements planning and capacity planning.
2. Construct and evaluate level, chase and mixed aggregate plans.
3. Calculate production, inventory, workforce, overtime and subcontracting requirements.
4. Prepare a feasible MPS using forecasts, customer orders and inventory records.
5. Calculate projected available balance and available-to-promise quantities.
6. Apply rough-cut capacity planning to test MPS feasibility.
7. Evaluate operational, financial, ethical and strategic trade-offs.

1. The Planning Hierarchy

Production planning is hierarchical. Decisions made at a higher level constrain decisions below them.

The aggregate plan is expressed in common units such as tonnes, standard hours, litres or equivalent units. The MPS is expressed in end-item units, for example 200 Model A pumps and 150 Model B pumps in a particular week.

A useful planning flow is:

Demand information → Aggregate plan → MPS → Material requirements plan → Purchasing and shop-floor control

Feedback also moves upward. If the MPS cannot be produced with available capacity, the aggregate plan, customer promise dates or capacity assumptions must be revised.

2. Aggregate Planning Concepts

2.1 Planning inputs

An aggregate plan normally uses:

• demand forecasts and confirmed customer orders;
• opening inventory and desired ending inventory;
• regular-time production capacity;
• workforce size, productivity and working-time rules;
• overtime and subcontracting limits;
• costs of hiring, training, layoffs, inventory, shortage and changeover;
• service-level, safety, regulatory and environmental requirements.

Demand is often uncertain. Consequently, a plan is not a prediction of exactly what will happen. It is a policy for responding to expected demand under stated assumptions.

2.2 Decision variables and balance equation

For period t, define:

• D_t = demand in units;
• P_t = regular-time production;
• O_t = overtime production;
• S_t = subcontracted production;
• I_t = ending inventory;
• B_t = ending backorders or shortage;
• I_t-1 and B_t-1 = opening inventory and backorders.

If inventory and backorders are not simultaneously permitted, the flow balance is:

The equation is expressed in product units. It assumes that production is available during the period in which it is recorded and that losses, scrap and yield effects have either been included in production quantities or modelled separately. A positive result represents inventory; a negative result represents a shortage.

When shortages are prohibited, the usual service constraint is:

2.3 Relevant cost structure

A simplified total planning cost can be written as:

where c_P, c_O and c_S are unit costs of regular, overtime and subcontract production; c_I and c_B are per-unit inventory and shortage costs per period; c_H and c_L are hiring and layoff costs; and H_t and L_t are hires and layoffs. The summation covers all planning periods. This is a decision-support model, not a complete accounting statement: transport, setup, quality, tax and disruption costs may also be relevant.

All terms must be stated in the same monetary units. If inventory cost is quoted per unit per month, the planning periods must be months or the rate must be converted appropriately.

3. Aggregate Planning Strategies

3.1 Level strategy

A level strategy maintains a relatively constant workforce and production rate. Demand variation is absorbed by inventory, backlog or a combination of both.

Advantages include stable employment, predictable production, lower hiring and training disruption, and efficient learning. Disadvantages include inventory carrying cost, risk of obsolescence, working-capital requirements and possible shortages during demand peaks.

If total forecast demand over n periods is ∑D_t and the desired ending inventory is I_n, a simple constant production rate, assuming opening inventory I₀ and no shortages, is:

This is an average rate. It is feasible only if the resulting inventory never violates storage, cash-flow or service constraints and if the constant rate is within capacity.

3.2 Chase strategy

A chase strategy changes production to follow demand. Workforce, hours, subcontracting or other capacity mechanisms are adjusted so that production approximately equals demand in each period.

Advantages include low finished-goods inventory and reduced obsolescence. Disadvantages include hiring and layoff costs, morale effects, training requirements, unstable supplier relationships and possible quality problems. A pure chase plan may be inappropriate where skilled labour is scarce or employment protection is strong.

3.3 Mixed strategy

A mixed plan combines stable regular-time production with selected use of overtime, inventory, temporary labour, subcontracting or controlled backorders. In practice, mixed strategies are common because they offer a compromise between cost and responsiveness.

Typical policies include:

• maintain a core workforce;
• build inventory before a predictable seasonal peak;
• use overtime for short peaks;
• subcontract only when internal capacity is exceeded;
• maintain a safety-stock target for important products;
• prohibit backorders for strategic customers but permit them for low-priority orders.

3.4 Comparison of strategies

4. Workforce and Capacity Calculations

If each worker produces r units per period and W_t workers are available, regular capacity is:

If working time is measured in hours, the equivalent form is:

where h_t is available productive hours per worker and p_t is units per productive hour. Breaks, planned maintenance, absenteeism and efficiency losses should be excluded from productive hours or represented through an efficiency factor.

If a firm starts with W_t-1 workers, then:

where H_t and L_t are hires and layoffs. Overtime capacity may be represented as:

Subcontracting similarly has a limit:

These limits are essential. A plan that balances demand mathematically but exceeds available overtime, supplier capability or labour law limits is not feasible.

Worked example: comparing level and chase plans

An appliance plant forecasts quarterly demand of 900, 1,200 and 1,500 units. Opening inventory is 100 units and desired ending inventory is 100 units. One worker produces 100 units per quarter. The plant starts with 12 workers. Ignore overtime, subcontracting and shortages.

Total demand is 3,600 units. The required production is:

3,600 + 100 - 100 = 3,600 units.

A level plan therefore produces 1,200 units per quarter, requiring 12 workers. Inventory evolves as follows:

The plan is feasible if 12 workers can produce 1,200 units each quarter. It carries a maximum inventory of 400 units.

A chase plan produces 800, 1,200 and 1,600 units respectively if the desired ending inventory is 100 units and opening inventory is 100 units. Workforce requirements are 8, 12 and 16 workers. Thus the plant would need to hire four workers before quarter 3, while possibly reducing the workforce after quarter 1. This plan reduces inventory but creates workforce-change costs and execution risk.

5. Master Production Scheduling

The MPS is the formal statement of planned production for specific end items. It serves three purposes:

1. It translates aggregate quantities into product and period detail.
2. It provides a basis for promising delivery dates.
3. It drives material requirements planning and capacity checks.

An MPS should distinguish among:

• customer orders already accepted;
• forecast demand not yet ordered;
• scheduled receipts from earlier decisions;
• planned production receipts;
• projected available balance;
• available-to-promise inventory.

The MPS horizon is normally divided into time fences. In a frozen zone, changes are highly restricted because materials and labour have been committed. A slushy zone permits controlled changes, while a liquid zone allows greater replanning. Time fences reduce nervousness, which is the disruptive effect of frequent schedule changes.

5.1 Projected available balance

For period t, projected available balance (PAB) can be calculated as:

where SR_t is a scheduled receipt and D_t is the demand used for that period. In an MPS table, demand may be the larger of forecast and customer orders, depending on the organisation’s demand policy. The choice must be documented to avoid double counting.

A feasible schedule normally requires:

where SS_t is the required safety stock. If this condition fails, the planner must move production earlier, increase quantity, revise the promise date or formally accept a shortage.

5.2 Available-to-promise

Available-to-promise (ATP) identifies uncommitted supply that can be promised to new customers. For the first MPS period, a common calculation is:

For a later period containing an MPS receipt:

The first-period formula includes beginning available inventory; later receipts include only the MPS receipt because earlier inventory has already been allocated. ATP calculations must use confirmed customer orders, not an unqualified mixture of forecasts and orders. The precise convention can vary by system, so the organisation’s allocation rules must be explicit.

Worked MPS example

A product has beginning available inventory of 80 units. The MPS contains receipts of 100 units in weeks 2 and 4. Forecast demand is 40 units per week. Confirmed customer orders are 30, 60, 20 and 70 units in weeks 1–4. Assume demand for the PAB calculation is the greater of forecast and order.

If safety stock is 30 units, the schedule is feasible because every PAB is at least 30. The first ATP quantity, before the next MPS receipt in week 2, is:

ATP₁ = 80 - 30 = 50 units.

For week 2, the next MPS receipt is week 4, so:

ATP₂ = 100 - (60 + 20) = 20 units.

For week 4, assuming no later MPS receipt within the horizon:

ATP₄ = 100 - 70 = 30 units.

ATP is not simply the PAB. PAB protects the projected stock position across all demand, whereas ATP protects uncommitted supply for new orders.

6. Rough-Cut Capacity Planning

Rough-cut capacity planning (RCCP) tests whether an MPS is broadly compatible with critical resources. It is less detailed than capacity requirements planning, but it detects overloads before detailed material and shop-floor schedules are released.

If product j requires a_j hours on a critical work centre and the MPS quantity is Q_{jt, required load is:

Capacity is available hours after considering working time, maintenance, efficiency and other commitments. Utilisation is:

The ratio is dimensionless because both numerator and denominator are hours. A utilisation above 100% indicates overload. Even utilisation near 100% may be risky because variability, downtime and urgent work require practical capacity cushions.

RCCP example

In week 2, the MPS calls for 120 units of Product A and 80 units of Product B. A requires 1.5 hours on the bottleneck; B requires 2 hours. Available capacity is 360 hours.

Load = (120 × 1.5) + (80 × 2) = 340 hours.

Thus utilisation is:

340 ÷ 360 × 100% ≈ 94.4%.

The schedule passes the broad capacity check, but the 20-hour margin may be insufficient if absenteeism or breakdowns are common. Options include moving work, reducing lot sizes, authorising limited overtime or revising customer promises.

7. Integrated Applied Case: Northstar Pumps

The following is an illustrative case, created for educational use.

Background

Northstar Pumps produces a family of industrial pumps. Demand for the next four months is forecast at 700, 900, 1,100 and 800 units. Beginning inventory is 100 units, and management requires 100 units at the end of month 4. Each worker produces 100 units per month. The company begins with nine workers. Regular production costs £40 per unit, overtime costs £55, inventory carrying cost is £3 per unit per month, and subcontracting costs £65 per unit. Hiring costs £1,000 per worker and layoff costs £700 per worker. Overtime is limited to 100 units per month, and subcontracting is limited to 150 units per month.

Problem

Management wants to avoid lost sales while limiting workforce disruption and inventory. A pure chase plan would require substantial changes in the workforce. A pure level plan may create high inventory before the peak.

Analysis and approach

Total demand is 3,500 units. Required production is:

3,500 + 100 - 100 = 3,500 units, or an average of 875 units per month.

A level plan of 900 units per month requires nine workers and produces the following inventory:

The ending inventory is 200 rather than the target 100, so regular production in month 4 could be reduced to 800 units, assuming the production system permits this adjustment. The revised schedule maintains nine workers and ends at 100 units. It avoids overtime and subcontracting but carries inventory into the peak.

A mixed alternative could produce 800 units in month 1, 900 in month 2, 1,000 regular units plus 100 overtime units in month 3, and 800 in month 4. Starting with 100 units, the ending inventories are 200, 200, 200 and 200 units; production would need to be reduced by 100 units in one period to meet the desired ending inventory. This illustrates an important planning discipline: every proposed plan must be reconciled period by period, not judged only by total production.

Recommended solution

Northstar should initially adopt a stable nine-worker plan with a controlled production adjustment in the final month, then use RCCP to confirm bottleneck capacity. If the peak month creates a bottleneck, 100 units of authorised overtime is preferable to permanent workforce expansion, provided fatigue, safety and quality controls remain acceptable. Subcontracting should be reserved for capacity emergencies or products that can be quality-assured externally.

Outcome and learning points

The case demonstrates that:

• total production sufficiency does not guarantee period feasibility;
• inventory can act as a buffer between stable capacity and variable demand;
• workforce stability has value beyond direct cost;
• overtime and subcontracting require explicit limits;
• MPS and RCCP are necessary after aggregate planning;
• a plan should be evaluated using cost, service, risk and strategic capability rather than cost alone.

8. Implementation, Governance and Contemporary Practice

Effective planning requires cross-functional participation. Sales and operations planning (S&OP) or integrated business planning brings together sales, marketing, finance, operations, procurement and senior management. The process should use a single set of demand and capacity assumptions, documented decision rules and a regular review calendar.

Enterprise resource planning and advanced planning systems can calculate PAB, ATP, capacity loads and alternative scenarios rapidly. Artificial intelligence can improve demand sensing, anomaly detection and scenario analysis, but it does not remove the need for managerial judgement. Forecast models may reproduce historical bias, especially where data reflect stockouts rather than true demand. Human review is required for promotions, new products, disruptions and ethical workforce consequences.

Governance issues include:

• compliance with working-time, overtime, safety and employment legislation;
• fair treatment during hiring, scheduling and layoffs;
• transparent allocation of scarce products among customers;
• responsible supplier qualification when subcontracting;
• avoidance of deceptive delivery promises;
• protection of commercially sensitive demand and capacity data;
• consideration of energy use, emissions, waste and supplier labour conditions.

Contemporary planners increasingly use scenario planning, postponement, modular products, collaborative forecasts and finite-capacity scheduling. These practices improve responsiveness, but they also increase data, coordination and change-management requirements.

9. Challenges and Limitations

Aggregate plans depend on forecasts that may be wrong. Costs are often nonlinear: hiring a tenth worker may be easy, while hiring the eleventh may require a second shift. Capacity may be constrained by a bottleneck rather than total labour. Inventory may be technically available but unusable because of quality, configuration or location. Subcontracting may reduce internal load while increasing lead-time and quality risk.

Linear cost models can also hide important realities. They may assume constant productivity, unlimited material availability, stable supplier performance and no setup sequence effects. Therefore, a mathematically optimal plan is not automatically operationally optimal. Sensitivity analysis should test demand increases, supply delays, absenteeism, downtime and changes in overtime or subcontracting limits.

Best practice is to maintain explicit assumptions, use rolling horizons, freeze near-term commitments, measure forecast error and schedule adherence, and review both financial and nonfinancial outcomes.

Chapter Summary

Aggregate planning determines medium-term production, workforce and inventory policies for product families. Level plans stabilise production and employment but may require inventory; chase plans follow demand closely but can create workforce and quality problems; mixed plans combine buffers and flexibility mechanisms. The fundamental inventory balance links opening stock, production, receipts, demand and ending stock.

The MPS converts aggregate decisions into specific end-item quantities by period. Projected available balance tests whether inventory remains adequate, while available-to-promise identifies uncommitted supply that can be offered to new customers. Rough-cut capacity planning compares MPS requirements with critical-resource capacity and detects overloads before detailed scheduling. Good planning integrates cost, service, capacity, workforce, supplier, ethical and sustainability considerations. Digital systems and AI support analysis, but reliable assumptions, governance and managerial judgement remain essential.

Key Terms

Aggregate plan: Medium-term plan for product-family output, workforce and inventory.

Available-to-promise: Uncommitted supply that can be promised to new customer orders.

Chase strategy: Policy that adjusts production or capacity to follow demand.

Demand fence: Boundary separating periods with different rules for schedule changes.

Finite capacity: Capacity limited by actual resources, time and operating constraints.

Forecast: Estimate of future demand based on information and assumptions.

Inventory balance: Relationship among opening stock, supply, demand and ending stock.

Level strategy: Policy maintaining a relatively stable production rate and workforce.

Master production schedule: Time-phased plan for producing specific finished products.

Mixed strategy: Aggregate plan combining level and chase mechanisms.

Projected available balance: Expected inventory position after planned supply and demand.

Rough-cut capacity planning: Broad capacity test of an MPS against key resources.

Safety stock: Inventory held to protect against uncertainty or variation.

Sales and operations planning: Cross-functional process aligning demand, supply and business objectives.

Scheduled receipt: Supply already planned or released for a specified period.

Subcontracting: Obtaining production from an external supplier.

Time fence: Planning boundary restricting or controlling schedule changes.

Utilisation: Required resource load expressed as a percentage of available capacity.

Workforce flexibility: Ability to vary labour quantity, hours or skills in response to demand.

Review Questions

5 Short Answer Questions

1. What is the principal difference between aggregate planning and master production scheduling?
2. Define a level strategy and identify one major advantage and one disadvantage.
3. What information does projected available balance provide?
4. Why is a time fence used in an MPS?
5. What does an RCCP overload indicate?

5 Long Answer Questions

1. Explain the relationship among aggregate planning, MPS, MRP and shop-floor control.
2. Compare level, chase and mixed strategies using cost, workforce, inventory and service criteria.
3. Explain how overtime, subcontracting and inventory can be used as capacity buffers.
4. Describe the assumptions and limitations of a cost-based aggregate planning model.
5. Explain how governance, labour standards and sustainability should influence production planning.

3 Analytical / Application Questions

1. A factory begins with 200 units, forecasts demand of 500, 800 and 600 units, and wants 100 units at the end of the horizon. Calculate total required production and propose a constant monthly production rate. State whether the result is feasible if monthly capacity is 650 units.
2. Prepare a four-week MPS PAB table for a product with beginning inventory of 60 units, weekly demand of 30 units, and MPS receipts of 80 units in weeks 2 and 4. Determine whether a safety stock of 20 units is maintained.
3. A bottleneck requires 1.2 hours for Product A and 2.5 hours for Product B. An MPS schedules 200 A units and 100 B units in one week, while available capacity is 500 hours. Calculate load and utilisation, then recommend two managerial responses if a 90% practical-utilisation limit applies.

Multiple Choice Questions with Answers

Question 1

Which planning level specifies quantities of particular finished products by time period?

A. Strategic capacity planning

B. Aggregate planning

C. Master production scheduling

D. Supplier development planning

Correct Answer: C. Master production scheduling

Question 2

A level strategy primarily absorbs demand variation through which mechanism?

A. Inventory changes

B. Frequent layoffs only

C. Elimination of forecasts

D. Permanent subcontracting

Correct Answer: A. Inventory changes

Question 3

A firm has demand of 900 units over three periods, opening inventory of 60 units and desired ending inventory of 30 units. What constant production rate is required?

A. 270 units per period

B. 290 units per period

C. 300 units per period

D. 330 units per period

Correct Answer: B. 290 units per period

Question 4

If opening inventory is 50, production is 120 and demand is 140, what is ending inventory assuming no backorders?

A. 10 units

B. 20 units

C. 30 units

D. 310 units

Correct Answer: C. 30 units

Question 5

What is the main purpose of available-to-promise?

A. To calculate employee productivity

B. To identify supply available for new customer commitments

C. To determine depreciation expense

D. To measure supplier defect rates

Correct Answer: B. To identify supply available for new customer commitments

Question 6

An MPS schedules 100 units of Product A requiring 2 hours each and 50 units of Product B requiring 1 hour each. What is the total bottleneck load?

A. 150 hours

B. 200 hours

C. 250 hours

D. 300 hours

Correct Answer: C. 250 hours

Question 7

A chase strategy generally creates which trade-off?

A. Lower inventory but greater workforce adjustment

B. Higher inventory and no workforce adjustment

C. No capacity variation and no cost

D. Lower responsiveness and fixed production

Correct Answer: A. Lower inventory but greater workforce adjustment

Question 8

If required capacity is 340 hours and available capacity is 400 hours, utilisation is:

A. 60%

B. 75%

C. 85%

D. 117.6%

Correct Answer: C. 85%

Question 9

Which document normally provides the input for material requirements planning?

A. Master production schedule

B. Annual financial statement

C. Employee appraisal form

D. Finished-goods quality certificate

Correct Answer: A. Master production schedule

Question 10

Why should a schedule with total sufficient production still be checked period by period?

A. Because total production can hide interim shortages or capacity overloads

B. Because inventory is never allowed in manufacturing

C. Because forecasts cannot be used in planning

D. Because overtime always costs less than regular production

Correct Answer: A. Because total production can hide interim shortages or capacity overloads