Aggregate Planning, Scheduling and Revenue Management

Introduction

Operations managers rarely make decisions at a single time horizon. Strategic decisions determine facilities, technology and long-term capacity; tactical decisions translate expected demand into workforce, inventory and resource plans; operational decisions assign specific jobs, employees and machines to particular times. Aggregate planning, master scheduling, sequencing, finite-capacity scheduling and revenue management connect these horizons.

The central managerial problem is one of balance. A plan must provide sufficient capacity and customer service without creating excessive inventory, overtime, idle time or employee instability. It must also remain flexible when forecasts are wrong. In services, the equivalent problem is often to allocate scarce, perishable capacity—such as hotel rooms, airline seats or consulting hours—to customers with different willingness to pay.

This chapter treats planning and scheduling as integrated decision processes rather than isolated techniques. Quantitative models are useful, but managerial judgment, labor agreements, ethics, data quality and organizational capability determine whether a plan can be implemented.

Learning Objectives

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

1. Distinguish aggregate planning, the master production schedule and detailed scheduling.
2. Construct and evaluate level, chase and hybrid workforce plans.
3. Formulate basic aggregate-planning and scheduling models.
4. Apply sequencing rules and explain their limitations.
5. Use finite-capacity logic to identify overloads and bottlenecks.
6. Explain yield management and revenue-management decisions.
7. Evaluate trade-offs involving cost, service, flexibility, employees and ethics.
8. Recommend an integrated planning approach for a realistic operating system.

1. Planning Hierarchy and Time Horizons

Operations planning is hierarchical. At the strategic level, managers decide facility location, process technology and broad capacity. Aggregate planning usually covers several months to approximately two years and uses product families, labor categories and broad capacity measures. The master production schedule (MPS) converts the aggregate plan into end-item quantities and time buckets, often weeks. Material requirements planning and detailed scheduling then determine components, jobs, machines and labor assignments.

The hierarchy reduces complexity. A factory may produce hundreds of stock-keeping units, but aggregate planning may treat them as three families measured in standard labor hours. This abstraction is useful only if the conversion factors and capacity assumptions are credible.

Important terms include:

• Demand forecast: an estimate of future customer requirements.
• Aggregate plan: a medium-term plan for production, workforce, inventory, backlog and subcontracting.
• Master production schedule: a time-phased statement of which end items will be produced and when.
• Available-to-promise (ATP): uncommitted inventory and scheduled production that can be promised to customers.
• Capacity: the maximum feasible output under specified resources, time and operating conditions.
• Bottleneck: a resource whose effective capacity limits system throughput.
• Time fence: a period within which schedule changes are restricted.

A sound process uses feedback. Forecast error, absenteeism, supplier disruption and machine failure should be compared with plan assumptions, and the plan should be revised through a controlled sales and operations planning (S&OP) process.

2. Aggregate Planning

2.1 Objectives and decision variables

Aggregate planning seeks a feasible and economical response to medium-term demand. Typical decisions include:

• regular-time production;
• overtime production;
• subcontracting;
• inventory and planned backlog;
• hiring, layoffs and cross-training;
• temporary labor and shift patterns;
• use of alternative processes or facilities.

The relevant costs include regular labor, overtime premiums, hiring, separation, inventory holding, backorder, subcontracting and sometimes lost sales. A plan minimizing accounting cost alone may damage quality, safety, retention or long-term capability.

2.2 Basic inventory balance

For period t, the fundamental balance is:

where I_t is ending inventory (units), P_t is production (units), and D_t is demand (units). If backorders are permitted, I_t may be negative; alternatively, inventory and backlog may be represented by separate nonnegative variables. The equation assumes that units produced and demanded are comparable and that losses, returns and quality rejects are either negligible or incorporated into the variables.

With workforce and capacity constraints, a simplified model is:

where W_t is regular workforce, a is regular output per worker per period, o_t is overtime output and s_t is subcontracted output. The units must be consistent—for example, all output terms may be measured in units per month.

A linear aggregate-planning model can be written as:

Here, P_t is regular production, O_t overtime production, S_t subcontracting, I_t ending inventory, B_t ending backlog, H_t hires and F_t separations. The coefficients are their respective unit costs. A common balance with separate inventory and backlog is:

All decision variables are nonnegative. Additional constraints specify workforce transitions, capacity, minimum staffing, subcontracting limits and service requirements. This is a planning model, not a precise description of reality; its value depends on realistic costs and constraints.

2.3 Level, chase and hybrid strategies

A level strategy maintains a relatively stable workforce and production rate. Demand variation is absorbed through inventory, backlog, overtime or temporary capacity. It supports employment stability and learning but may create inventory costs, obsolescence and cash-flow exposure.

A chase strategy adjusts production or workforce to follow demand. It can reduce inventory but may incur hiring, separation, training, morale and quality costs. It is more feasible where labor is flexible and skills are transferable.

A hybrid strategy combines regular production with selective overtime, inventory, temporary labor or subcontracting. In practice, hybrid plans are common because demand and capacity rarely behave in a perfectly regular manner.

The choice depends on product perishability, labor law, union agreements, skill scarcity, demand volatility, customer tolerance for waiting, supplier reliability and strategic priorities. For perishable services, inventory is often impossible, so managers use appointments, reservations, flexible staffing and demand-shifting prices instead.

2.4 Worked example: comparing simple plans

An illustrative manufacturer faces demand of 800, 1,200 and 1,000 units in three consecutive months. Initial inventory is 200 units. Each worker produces 100 units per month. The firm begins with 10 workers, so regular capacity is 1,000 units per month. Ignore hiring, separation and overtime costs for this comparison.

Under a level plan, production is 1,000 units each month:

The plan ends with 200 units and never backorders. If holding cost is $2 per unit per month, the illustrative holding cost based on ending inventories is $2(400 + 200 + 200) = $1,600.

A chase-like plan could produce 600 units in month 1, 1,200 in month 2 and 1,000 in month 3, assuming workforce changes are feasible. Inventory would be 0, 0 and 0, but the plan requires substantial capacity changes. If the workforce cannot be changed quickly, the plan is infeasible even though its inventory cost is lower. This illustrates why cost comparisons must include transition and implementation costs.

3. Master Scheduling and Available-to-Promise

The MPS disaggregates aggregate quantities into end items and dates. It must reconcile three requirements: customer demand, material availability and capacity. An MPS that ignores bottleneck capacity is not a plan; it is an aspiration.

A simplified projected available balance is:

where PAB_t is projected available balance and MPS_t is scheduled production in period t. In a more detailed system, forecast demand, actual orders, safety stock and time fences are incorporated.

ATP helps customer-facing employees make reliable promises. For the first MPS receipt, a typical calculation is:

For later receipts, ATP generally equals the MPS receipt minus orders until the next receipt. Exact definitions vary by system, and safety stock may be protected rather than promised.

The MPS should be stable enough for execution but responsive enough to reflect material changes. Rolling schedules, frozen zones and formal change authorization prevent constant rescheduling from disrupting suppliers and employees.

4. Workforce and Resource Strategies

Workforce planning is not merely a numerical capacity exercise. It affects safety, equity, motivation, skill retention and organizational reputation. Options include cross-training, flexible shifts, part-time work, temporary labor, overtime, job rotation, remote work for suitable service activities and postponement of final customization.

A useful capacity measure is effective capacity rather than theoretical capacity. If a machine is available for 160 hours per month, but planned maintenance consumes 12 hours and expected downtime is 8 hours, practical available time is 140 hours before considering product mix. Utilization should therefore be interpreted against effective capacity, not an unrealistic 160-hour maximum.

Cross-training increases flexibility but has costs: training time, competency maintenance and possible loss of specialization. Overtime provides rapid response but can increase fatigue, accidents, absenteeism and defects. Subcontracting adds capacity but may expose intellectual property, quality and supply continuity risks.

Managers should evaluate workforce plans using both quantitative and human indicators: overtime hours, turnover, absence, injury rates, engagement, training completion, service level and quality yield. A plan that achieves output by systematically overloading employees is operationally and ethically defective.

5. Sequencing and Detailed Scheduling

Scheduling assigns jobs to resources and times. The decision may be made for a single machine, parallel machines, a flow shop, a job shop, a project network or a service workforce. Common performance measures include completion time, flow time, lateness, tardiness, number of late jobs, makespan and utilization.

For job j, if processing starts at S_j and takes p_j time units:

where C_j is completion time. If the due date is d_j, lateness is:

and tardiness is:

Lateness can be negative when a job is early; tardiness cannot. These formulas assume a single completion time and a known processing duration.

5.1 Priority rules

• First come, first served (FCFS): supports perceived fairness and simple administration, but may create long waits for short jobs.
• Shortest processing time (SPT): often minimizes average flow time on a single machine when all jobs are available and preemption is not used. It may delay long jobs.
• Earliest due date (EDD): orders jobs by due date and is useful for controlling maximum lateness under classic single-machine assumptions.
• Critical ratio:

where t is current time. Lower ratios indicate greater urgency. The rule is dynamic but can oscillate as conditions change.

• Slack per remaining operation: prioritizes jobs with little time relative to remaining work in multi-operation environments.

No rule is universally best. A hospital may prioritize clinical urgency; a repair center may prioritize safety-critical equipment; a premium customer may have contractual priority. Rules must be aligned with the service promise and governance policy.

5.2 Worked sequencing example

Three jobs are available at time zero:

SPT produces B–C–A. Completion times are B = 2, C = 6 and A = 12. Tardiness is 0, 0 and 2, respectively; total tardiness is 2. EDD produces B–A–C. Completion times are 2, 8 and 12, with tardiness 0, 0 and 0. In this small example, EDD achieves zero tardiness, while SPT produces a lower average completion time: (2 + 6 + 12) ÷ 3 = 6.67 time units. The preferred rule depends on whether the organization values average flow or due-date performance more strongly.

6. Finite-Capacity Scheduling

Infinite-capacity planning loads work without checking whether resources can actually perform it. Finite-capacity scheduling explicitly limits assignments to available labor, machine, room, vehicle or specialist hours. It may use dispatching rules, constraint programming, mixed-integer optimization, simulation or commercial scheduling systems.

For resource r in period t, a basic capacity constraint is:

where x_{jt} is the quantity of job or activity j scheduled in period t, a_{jr} is the resource requirement per unit and Cap_{rt} is available capacity. Setup times, sequence-dependent changeovers, maintenance and breaks must be included when material.

A schedule should be evaluated for bottleneck load, due-date performance, setup frequency, work-in-process, labor feasibility and robustness. An apparently optimal schedule can fail when processing times vary. Robust scheduling protects time or capacity buffers around bottlenecks and high-uncertainty operations.

The theory of constraints emphasizes five recurring actions: identify the constraint, exploit it, subordinate other resources, elevate the constraint and repeat. Local utilization should not be maximized if it creates excessive queues before the bottleneck.

7. Yield Management and Revenue Management

Yield management originated in industries with fixed, perishable capacity and variable demand, especially airlines. Revenue management extends the idea through forecasting, customer segmentation, pricing, booking controls and capacity allocation. The objective is not simply to charge the highest price; it is to maximize contribution while protecting long-term customer relationships and fairness.

A service seat, hotel room or appointment lost today often cannot be stored and sold tomorrow. This creates an opportunity cost. Accepting a low-price booking may prevent a later high-price booking. Conversely, rejecting current demand can leave capacity unused.

For a simple two-class decision, accept a low-fare request if its revenue exceeds the expected value of protecting capacity for future high-fare demand. If the high-fare price is p_H and future high-fare demand exceeds protected capacity with probability q, a simplified expected opportunity value is q × p_H. The low fare p_L should be accepted when:

This is a simplified rule. It assumes one unit of capacity, known prices, no cancellation or no-show complications, and a particular interpretation of q. Real systems use demand distributions, nested booking limits, overbooking models and network optimization.

For a single resource with stochastic demand, the newsvendor critical fractile is often used conceptually:

where D is demand, y* is the target capacity or booking protection level, C_u is underage cost and C_o* is overage cost. The formula applies to a one-period decision with specified cost assumptions and a continuous or appropriately discretized demand distribution. It should not be applied mechanically to complex networks or repeated bookings.

Revenue-management tools include:

• fare fences, such as advance-purchase or cancellation restrictions;
• booking limits and protection levels;
• dynamic prices based on demand and remaining capacity;
• overbooking to offset predictable cancellations and no-shows;
• customer segmentation and differentiated packages;
• network optimization when one resource supports several products.

Overbooking creates a risk of denied service. Ethical and regulatory requirements may mandate compensation, transparent terms and nondiscriminatory treatment. Dynamic pricing may also produce public concern if customers cannot understand why prices differ or if essential services become inaccessible.

8. Integrated Case: Aurora Medical Equipment Services

Background

Aurora Medical Equipment Services repairs diagnostic devices for hospitals. Demand is seasonal, emergency repairs receive priority and certified technicians are scarce. The company promises standard repairs within five working days and emergency repairs within 24 hours. It has technicians, a calibration laboratory and outsourced capacity for selected routine work.

Problem

Monthly demand for the next quarter is forecast at 420, 600 and 480 repair units. Beginning backlog is 60 units. The company has eight technicians, each capable of 60 standard-equivalent units per month under normal hours. Emergency work consumes 1.5 standard units of capacity per repair, while routine work consumes 1 unit. Management is considering overtime and subcontracting, but technician fatigue and calibration quality have recently deteriorated.

Analysis

Normal monthly capacity is 8 × 60 = 480 standard-equivalent units. In month two, forecast demand alone is 600 units, before considering the 60-unit backlog. The bottleneck is certified technician capacity, not merely total labor hours. A chase strategy would require rapid hiring of certified staff, which is unrealistic. A level strategy without additional capacity would create a growing backlog.

The operations team therefore separates emergency and routine work, reserves capacity for emergency cases, and uses finite-capacity scheduling in the calibration laboratory. Routine jobs are sequenced by due date and processing time, while emergency work is inserted under a documented priority rule. Overtime is capped and assigned only to trained technicians. Selected routine repairs are subcontracted to an approved provider after quality validation.

Approach and solution

The integrated plan includes:

1. a monthly aggregate plan using regular capacity, limited overtime and approved subcontracting;
2. an MPS for repair families rather than individual device models;
3. a weekly finite-capacity schedule for certified technicians and calibration equipment;
4. a protected emergency-capacity buffer;
5. cross-training of two technicians in calibration procedures;
6. a customer communication policy that distinguishes promised, estimated and expedited dates;
7. dashboard metrics covering backlog age, emergency response, first-pass yield, overtime and safety.

Revenue management is used cautiously. Hospitals with emergency needs may purchase expedited service, but emergency access is not auctioned to the highest bidder. Prices reflect additional resources and contractual terms, while clinical urgency and safety remain protected.

Outcome

In this illustrative case, the plan reduces old backlog without making overtime the default response. Subcontracting absorbs routine peaks, while internal technicians retain control of safety-critical repairs. The company accepts that utilization will be below the theoretical maximum in some weeks because the buffer protects emergency response and quality.

Learning points

The case demonstrates that aggregate planning, scheduling and revenue decisions must share assumptions. A price decision that ignores technician capacity creates service failure; a schedule that ignores fatigue creates quality risk; and a capacity plan that ignores customer priority may violate the service promise.

9. Technology, Analytics and Contemporary Developments

Enterprise resource planning and advanced planning systems integrate forecasts, orders, inventory and capacity. Optimization engines can solve mixed-integer models, while simulation evaluates variability and alternative policies. Machine-learning forecasts may improve demand estimates, but forecast accuracy does not automatically produce good plans. The model must represent constraints, lead times, cancellations, promotions and behavioral responses.

Artificial intelligence can support demand sensing, anomaly detection, schedule repair and natural-language explanations. Human oversight remains essential because training data may encode historical discrimination, optimization may prioritize profitable customers unfairly, and automated schedules may violate labor rules. Good governance includes data lineage, access controls, explainability appropriate to the decision, monitoring for bias and a process for human override.

Digital twins can link real-time equipment, labor and order data to scenario analysis. Their value depends on calibration and disciplined change management. A highly sophisticated model with unreliable master data is less useful than a transparent model based on validated assumptions.

10. Limitations, Ethics and Best Practices

Forecasts are uncertain, costs are often nonlinear and capacity is not perfectly substitutable. Linear models may understate setup effects, congestion, learning, fatigue and service interactions. Sequencing rules can create systematic disadvantage for long jobs or less profitable customers. Revenue-management systems can reduce perceived fairness when prices change frequently or when restrictions are opaque.

Managers should:

• define service priorities before optimizing cost;
• validate units, assumptions and data ownership;
• distinguish theoretical, practical and effective capacity;
• model bottlenecks and changeover time explicitly;
• use scenario and sensitivity analysis rather than one forecast;
• protect employee health, legal rights and predictable scheduling;
• communicate booking rules and price conditions clearly;
• monitor outcomes, not merely plan adherence;
• retain human accountability for high-impact decisions;
• review whether optimization supports organizational purpose.

A useful sensitivity analysis changes demand, processing time, absence, supplier reliability and cost assumptions one at a time or in coherent scenarios. If a recommendation changes under small deviations, management should prefer flexibility and contingencies over false precision.

Chapter Summary

Aggregate planning converts medium-term demand and capacity information into decisions about production, workforce, inventory, backlog, overtime and subcontracting. Level, chase and hybrid strategies differ in their treatment of stability, inventory and labor flexibility. The MPS disaggregates aggregate plans into end-item schedules, while ATP supports credible customer promises.

Scheduling assigns work to resources and times. FCFS, SPT, EDD and critical-ratio rules offer useful priorities, but each reflects different performance objectives. Finite-capacity scheduling recognizes bottlenecks, setups, maintenance and labor limits. Revenue management allocates perishable capacity among demand segments through prices, booking controls and protection levels. Its use must be balanced with transparency, nondiscrimination, service obligations and employee welfare.

The most effective operating systems integrate planning horizons, use validated data, protect bottlenecks, incorporate uncertainty and maintain human accountability. Cost efficiency is important, but service reliability, resilience, quality, fairness and sustainable work design are equally significant measures of operational performance.

Key Terms

Aggregate plan: Medium-term plan for production, workforce, inventory and capacity.

Available-to-promise: Quantity that can be reliably promised after considering existing commitments.

Backlog: Demand not yet fulfilled and carried into a later period.

Bottleneck: Resource that constrains system throughput.

Capacity: Feasible output of a resource under stated conditions.

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

Critical ratio: Priority index comparing remaining time to remaining processing work.

Finite-capacity scheduling: Scheduling that does not assign more work than available resource capacity.

Forecast: Estimate of future demand or operating conditions.

Level strategy: Plan maintaining relatively stable workforce or production.

Lateness: Difference between completion time and due date.

Master production schedule: Time-phased plan for end-item production.

Overbooking: Accepting reservations beyond nominal capacity to offset expected cancellations or no-shows.

Revenue management: Coordinated use of pricing, forecasting and capacity allocation to maximize contribution from perishable capacity.

Sequencing: Determining the order in which jobs are processed.

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

Tardiness: Positive lateness; delay beyond the due date.

Time fence: Period restricting schedule changes.

Yield management: Allocation of limited capacity among customer segments to improve revenue yield.

Review Questions

Short Answer Questions

1. What is the difference between an aggregate plan and a master production schedule?
2. Explain one advantage and one disadvantage of a level strategy.
3. Distinguish lateness from tardiness.
4. Why is finite-capacity scheduling preferable to infinite-capacity loading when bottlenecks exist?
5. What problem does revenue management address in a service with perishable capacity?

Long Answer Questions

1. Compare level, chase and hybrid aggregate-planning strategies, including their effects on cost, service, flexibility and employees.
2. Explain how an MPS, ATP calculation and time fences support reliable customer promises.
3. Discuss the assumptions and limitations of SPT, EDD and critical-ratio sequencing rules.
4. Explain how bottleneck management and finite-capacity scheduling can improve system performance without maximizing every resource’s utilization.
5. Evaluate the ethical and governance issues associated with dynamic pricing and overbooking.

Analytical / Application Questions

1. A firm has monthly demand of 900, 1,300 and 1,000 units, beginning inventory of 100 units and regular capacity of 1,000 units per month. Construct the ending-inventory balance under constant production of 1,000 units and identify whether backlog occurs.
2. Three jobs require 3, 7 and 4 hours and have due dates of 9, 12 and 10 hours, respectively. Sequence them using SPT and EDD, calculate each completion time and compare total tardiness.
3. A hotel has one room left. A current customer offers $120. A future high-rate booking would generate $250 and has a 0.6 probability of arriving. Using the simplified protection rule in this chapter, should the hotel accept the current booking? State the assumptions and explain limitations.

Multiple Choice Questions with Answers

Question 1

Which plan generally maintains a relatively stable workforce and uses inventory or backlog to absorb demand variation?

A. Chase strategy

B. Level strategy

C. Pure subcontracting strategy

D. Random dispatching strategy

Correct Answer: B. Level strategy

Question 2

For a period t, which equation represents the basic inventory balance?

A. I_t = I_t-1 + P_t - D_t

B. I_t = D_t - P_t - I_t-1

C. I_t = P_t + D_t + I_t-1

D. I_t = I_t-1 ÷ P_t - D_t

Correct Answer: A. I_t = I_t-1 + P_t - D_t

Question 3

Which sequencing rule orders jobs by increasing processing time?

A. EDD

B. FCFS

C. SPT

D. Critical ratio

Correct Answer: C. SPT

Question 4

If a job finishes at time 18 and its due date is 15, what is its tardiness?

A. −3

B. 0

C. 15

D. 3

Correct Answer: D. 3

Question 5

What is the defining feature of finite-capacity scheduling?

A. It ignores bottleneck resources.

B. It assigns work without exceeding available resource capacity.

C. It always maximizes overtime.

D. It schedules only customer orders with the highest price.

Correct Answer: B. It assigns work without exceeding available resource capacity.

Question 6

A bottleneck is best defined as:

A. A resource with unlimited capacity

B. A resource that constrains system throughput

C. The least expensive resource

D. A finished-goods inventory location

Correct Answer: B. A resource that constrains system throughput

Question 7

Revenue management is especially relevant when capacity is:

A. Perishable and difficult to store

B. Unlimited and costless

C. Independent of demand

D. Used only for internal activities

Correct Answer: A. Perishable and difficult to store

Question 8

Using the simplified rule p_L ≥ q × p_H, should a $120 booking be accepted when q = 0.6 and p_H = $250?

A. Yes, because $120 ≥ $150

B. Yes, because $120 ≤ $150

C. No, because $120 < $150

D. No, because $120 > $150

Correct Answer: C. No, because $120 < $150

Question 9

What is the primary purpose of a master production schedule?

A. To determine corporate tax liability

B. To disaggregate aggregate plans into time-phased end-item production

C. To eliminate all forecast error

D. To calculate employee satisfaction

Correct Answer: B. To disaggregate aggregate plans into time-phased end-item production

Question 10

Which issue is a significant ethical risk in automated revenue-management systems?

A. Perfectly stable demand

B. Excessive physical inventory

C. Opaque or discriminatory customer treatment

D. Guaranteed zero cancellations

Correct Answer: C. Opaque or discriminatory customer treatment