Infinite and Finite Capacity Planning and Scheduling

Introduction

Capacity Requirement Planning (CRP) translates the workload implied by a production plan, master production schedule, or material requirements plan into requirements for specific work centres. It asks whether machines, labour, tools, space, and other constrained resources can complete planned work within the required time. This chapter focuses on two fundamentally different approaches: infinite capacity planning, which loads work without initially restricting it by available capacity, and finite capacity planning, which explicitly limits assignment to the capacity that is actually available.

The distinction is managerial as well as mathematical. An infinite-capacity plan may be useful for identifying overloads and estimating resource requirements, but it is not automatically executable. A finite-capacity schedule is more realistic because it respects resource limits, yet it may require order delays, alternative routings, overtime, subcontracting, lot splitting, or priority decisions. Thus, a feasible capacity plan is a necessary condition for execution, but feasibility must be evaluated across all relevant constraints, including material availability, labour skills, tooling, maintenance, setup times, quality approvals, and due dates.

Learning Objectives

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

1. Explain infinite loading and finite loading and distinguish their purposes.
2. Calculate basic work-centre capacity and capacity requirements.
3. Apply forward and backward scheduling.
4. Compare common priority rules and identify their behavioural effects.
5. Explain overlapping, lot splitting, setup effects, and interrupted processing.
6. Analyse the difference between a capacity-feasible plan and an executable schedule.
7. Evaluate scheduling decisions using operational and managerial performance measures.

1. Capacity Planning and Scheduling: Related but Different

Capacity planning determines whether resources are sufficient for a set of expected requirements. Scheduling determines the sequence and timing of specific jobs. Capacity planning generally operates at an aggregate or period level, whereas scheduling operates at a detailed job-and-operation level.

A work centre is a production resource or group of resources performing similar operations. A work centre may be one machine, several interchangeable machines, a labour pool, or a department. A routing specifies the operations, work centres, processing times, setup requirements, and sequence needed to manufacture an item.

A useful hierarchy is:

The same order may therefore appear feasible in a monthly CRP report but become infeasible in a daily schedule because all jobs require the same machine on the same day.

2. Basic Capacity and Load Concepts

2.1 Available capacity

Available capacity is the productive time that a work centre can provide during a planning period. A simple deterministic expression is:

where:

• C_a = available productive capacity, usually in hours per period;
• N = number of identical resources;
• S = number of shifts per day;
• H = scheduled hours per shift per period;
• U = planned utilisation factor;
• E = efficiency factor relative to the standard rate.

The formula assumes that resources are sufficiently interchangeable and that utilisation and efficiency can be represented by stable factors. In practice, planned downtime, preventive maintenance, breaks, absenteeism, changeovers, micro-stoppages, and skill restrictions should be modelled explicitly where material.

For example, two machines operate two shifts per day, each shift lasting 8 hours, for five days. If planned utilisation is 0.85 and efficiency is 0.90:

C_a = 2 × 2 × 8 × 5 × 0.85 × 0.90 = 122.4 hours per week.

The result is not a guarantee of output. It is an estimate of usable time under stated assumptions.

2.2 Required capacity

For a set of operations, required capacity is commonly estimated as:

where:

• C_r = required capacity;
• Q_i = quantity of job or item i processed at the work centre;
• t_i = run time per unit for job i;
• s_i = setup time for job i;
• the summation includes all jobs assigned to the work centre.

If t_i is expressed in minutes per unit and s_i in minutes, the result must be divided by 60 to obtain hours. The formula assumes that processing and setup times are known and that all required work is included. It does not automatically include waiting, transport, rework, inspection, or breakdowns unless those elements are incorporated into the times.

The basic load ratio is:

where L is the load ratio. A value above 1 indicates that required work exceeds stated available capacity. A value below 1 does not prove that a schedule is feasible: poor sequencing, release timing, material shortages, or bottlenecks can still cause failure.

2.3 Capacity requirements profiles

A capacity requirements profile distributes load by period and work centre. It is more informative than a single total because it identifies when an overload occurs. A work centre may have adequate weekly capacity but be overloaded on Tuesday and idle on Friday. Such temporal imbalance creates queues and may cause late orders even when total weekly capacity appears sufficient.

3. Infinite Loading

3.1 Meaning and purpose

Under infinite loading, planned operations are assigned to their required work centres and time periods without initially limiting the amount of work assigned to the capacity available. The resulting load is compared with capacity after loading.

Infinite loading is valuable for:

• detecting bottlenecks;
• estimating additional labour, shifts, or equipment;
• evaluating a preliminary master production schedule;
• comparing alternative product mixes;
• exposing the consequences of demand changes;
• supporting rough-cut capacity planning.

It is not a promise that the resulting operation dates can be achieved.

3.2 Illustrative calculation

Suppose a work centre has 100 available hours in a week. Three planned orders require:

The infinite load is 114.5 hours. The overload is 14.5 hours and the load ratio is 114.5 ÷ 100 = 1.145, or 114.5%. Management may respond by adding overtime, moving an order, using another work centre, reducing setup time, subcontracting, or revising the production plan.

3.3 Strengths and limitations

Infinite loading is transparent and computationally simple. It shows the unconstrained consequences of a plan and is useful at medium planning horizons where exact sequencing is not yet known. Its central limitation is that it may place several operations in the same time interval or assume that all capacity can be used simultaneously. It can therefore generate impossible operation dates and misleading promise dates if users mistake requirements for commitments.

4. Finite Loading

4.1 Meaning and purpose

Finite loading assigns work only when the required resource has sufficient capacity in the relevant time interval. If capacity is unavailable, the operation is moved, delayed, split, routed to an alternative resource, or supported by an approved capacity expansion.

Finite loading seeks an executable schedule subject to defined constraints. Typical constraints include:

• machine and labour availability;
• operation precedence;
• setup and teardown times;
• material and tooling availability;
• calendars, holidays, and maintenance;
• batch and minimum-run requirements;
• operator qualifications;
• due dates and release restrictions.

4.2 Finite scheduling logic

A practical finite-loading procedure is:

1. Establish calendars and net available capacity.
2. Expand orders into operations using valid routings.
3. Select a scheduling direction and priority rule.
4. Identify the earliest or latest permissible time for each operation.
5. Search for a feasible interval on the required resource.
6. Reserve capacity and update predecessor or successor dates.
7. Recalculate loads and identify constraint violations.
8. Apply authorised alternatives such as overtime or alternate routing.
9. Release only operations that are materially, technically, and organisationally ready.

Finite loading does not eliminate trade-offs. It converts hidden overloads into visible decisions, such as lateness, overtime, work-in-process, or lost flexibility.

4.3 Finite versus infinite loading

5. Forward and Backward Scheduling

5.1 Forward scheduling

Forward scheduling begins with a job’s release date and places each operation as early as possible, subject to precedence and resource availability. If operation processing times are p₁, p₂, …, p_n and there are no waiting or setup complications, the completion time is approximately:

where R is the release time, p_j is processing time for operation j, and s_j is its setup time. The expression assumes a single routing, no interruptions, and no resource-induced waiting. In an actual finite schedule, waiting must be added whenever the next resource is unavailable.

Forward scheduling is appropriate when:

• materials are available now;
• early completion has value;
• due dates are uncertain or negotiable;
• the organisation wants to identify the earliest completion date;
• make-to-stock replenishment is important.

Its disadvantages include early completion, increased inventory, and excessive work-in-process when jobs are released too soon.

5.2 Backward scheduling

Backward scheduling begins with a required completion or due date and schedules each operation as late as possible while preserving precedence. For a final operation with completion time D, its start time is:

For preceding operations, the latest completion of operation j equals the start of its successor, so:

These relationships assume a linear routing and no unmodelled waiting, transfer, or material constraints. When finite capacity prevents a late placement, an earlier slot must be selected or the due date becomes infeasible.

Backward scheduling is useful for reducing premature production and work-in-process. It is especially suitable for make-to-order production with reliable due dates. However, it may create a fragile schedule with little protection against breakdowns, quality failures, or supplier delays.

5.3 Example of direction choice

A job has three operations with total planned times of 2, 4, and 1 hours, including setups. If released at hour 8, a simple forward schedule completes at hour 15, assuming no waiting. If the customer requires completion at hour 20, a simple backward schedule starts at hour 13. The seven-hour difference is available as slack only if capacity and material constraints permit it. It is not automatically free time; it may be needed for queueing, inspection, transport, or disruption recovery.

6. Priority Rules and Dispatching

A priority rule determines which waiting job is selected when several jobs compete for a resource. No single rule is best for every environment. The appropriate rule depends on strategic objectives, due-date reliability, setup economics, flow characteristics, and customer commitments.

The critical ratio is commonly represented as:

where D is the due date, t is the current time, and W is remaining work time. A value below 1 suggests that the job has less time remaining than the estimated work required. The measure assumes comparable time units and reasonably accurate remaining-work estimates. It does not include future queueing unless that is explicitly estimated.

Priority rules should not override safety, quality, legal, or material constraints. Nor should an urgent job be released when its predecessor is incomplete merely because its priority value is high.

7. Overlapping, Lot Splitting, and Interruptions

7.1 Overlapping operations

In a conventional routing, the entire lot completes operation 1 before operation 2 begins. Overlapping allows a successor operation to begin before the full lot has completed the predecessor, often by transferring a transfer batch.

If a lot of quantity Q is divided into transfer batches of b units, the number of batches is:

where ⌈x⌉ means rounding up to the next whole batch. If the predecessor run time per unit is t₁ and successor run time per unit is t₂, overlapping can reduce elapsed flow time, but the precise completion time depends on transfer, setup, handling, and whether either operation can process continuously. The simplified expressions must therefore not be treated as universal scheduling formulas.

For example, a batch of 100 units may be processed at operation 1 in transfer batches of 20. Operation 2 can begin after the first 20 units are complete and transported, rather than waiting for all 100. This reduces flow time and may reduce downstream starvation, but it increases material handling, tracking, and coordination requirements.

7.2 Lot splitting

Lot splitting divides a production order into sublots that may be processed simultaneously on alternative resources or sequentially through the same routing. It can reduce completion time and exploit parallel capacity. Its costs include additional setups, movement, inspection, identification, reconciliation, and risk of uneven quality or quantity.

Lot splitting is especially useful when:

• a bottleneck operation dominates total lead time;
• parallel machines are available;
• customer delivery is more important than minimum setup count;
• sublots can be independently controlled and reassembled.

7.3 Interruptions and pre-emption

A pre-emptive schedule allows a job to be interrupted and another job to run. Pre-emption may be justified for emergencies, high-priority medical products, or maintenance events. It is undesirable when setups are costly, work is fragile, or partially completed units require special protection. A scheduling system must explicitly state whether processing is interruptible; otherwise, calculated schedules may be operationally invalid.

8. Feasible Capacity Plans and Executable Schedules

A capacity-feasible plan demonstrates that aggregate requirements do not exceed specified capacity under stated assumptions. An executable schedule specifies actual operation start and finish times and satisfies all relevant constraints.

A plan may be capacity-feasible but not executable for several reasons:

1. Temporal concentration: total weekly hours fit, but too much work is required on one day.
2. Precedence conflict: a successor is scheduled before its predecessor finishes.
3. Material infeasibility: capacity exists, but components are unavailable.
4. Skill constraint: a machine is available, but no qualified operator is present.
5. Tooling constraint: several jobs require the same die, fixture, or test equipment.
6. Sequence-dependent setups: the assumed setup time changes with job sequence.
7. Calendar restrictions: maintenance, holidays, or approved working hours are omitted.
8. Quality or regulatory holds: inspection or release approval adds time.
9. Transfer and queue time: jobs cannot move instantly between operations.
10. Data error: standard times, yields, routings, or quantities are inaccurate.

A strong planning process therefore uses progressive validation:

• aggregate capacity check;
• work-centre and period load check;
• finite schedule check;
• material and tooling check;
• labour and skill check;
• execution-readiness review;
• real-time monitoring and rescheduling.

The distinction is central to management. Infinite loading may reveal that 120 hours are required. Finite scheduling may show that only 100 hours are available this week, while 20 hours are available next week. A feasible response could be to delay an order, use overtime, move work to another resource, or split the lot. The final decision depends on cost, customer impact, risk, and strategic priorities.

9. Performance Measures and Trade-offs

Scheduling performance should be measured using more than utilisation. Important measures include:

• Makespan: elapsed time from the beginning of the first job to completion of the last job.
• Flow time: time a job spends in the system from release to completion.
• Lateness: completion time minus due date; it may be negative for early completion.
• Tardiness: maximum of lateness and zero, so early jobs have zero tardiness.
• On-time delivery: proportion of jobs completed by their promised dates.
• Work-in-process: jobs or units released but not completed.
• Queue time: time waiting rather than being processed.
• Setup hours: time consumed by changeovers.
• Bottleneck utilisation: productive use of the constraining resource.

High utilisation is not always desirable. When a bottleneck is loaded near 100%, small disruptions can create long queues and substantial lateness. A capacity plan should preserve strategically justified protective capacity, particularly at bottlenecks and resources with volatile processing times.

10. Worked Application: Finite Scheduling of Three Jobs

Consider one machine available from hour 0 to hour 16. Three jobs are ready at hour 0:

Assume no setup time, no pre-emption, and one machine. Under EDD, the sequence is B, A, C because their due dates are 7, 12, and 16.

• B runs from 0 to 3 and is completed 4 hours before its due date.
• A runs from 3 to 8 and is completed 4 hours before its due date.
• C runs from 8 to 12 and is completed 4 hours before its due date.

All jobs are on time. The machine is occupied for 12 of the 16 available hours, so utilisation is 75% for this horizon. The unused four hours do not necessarily represent waste: they may provide resilience, support maintenance, or accommodate additional work.

Now suppose Job A requires a two-hour setup and Job C requires a three-hour setup. If setup times are included in total machine occupation, the sequence requires 3 + 5 + 2 + 4 + 3 = 17 hours and cannot complete by hour 16. The plan is therefore not executable even though processing time alone totals 12 hours. Possible responses include reducing setups, using an alternate machine, authorising overtime, changing sequence, or renegotiating a due date. This illustrates why CRP must include setup and calendar assumptions rather than relying only on nominal run time.

11. Illustrative Case: Precision Components Ltd.

Background

Precision Components Ltd. manufactures machined housings for industrial pumps. Its master production schedule releases several customer orders each week. The company has two CNC machines, one heat-treatment furnace, and a shared inspection station. Management traditionally used infinite loading in a weekly spreadsheet.

Problem

The spreadsheet showed that weekly CNC and furnace requirements were below available hours. Nevertheless, customer orders were frequently late. Investigation found that all three major orders required heat treatment on Wednesday and inspection immediately afterward. The weekly totals concealed a severe midweek overload. In addition, a special fixture was shared by two product families, and the inspection station operated only on one shift.

Analysis

The planning team developed finite schedules using earliest due date as the initial rule. They added setup times, furnace batch restrictions, fixture availability, inspection calendars, and a two-hour material-release delay. The finite schedule showed that the furnace, not the CNC machines, was the effective bottleneck. Two orders could not meet their original dates without overtime or an alternative batch sequence.

Approach and solution

The company adopted four measures:

1. It retained infinite loading for monthly scenario analysis and bottleneck identification.
2. It used finite loading for weekly release and dispatch decisions.
3. It grouped compatible furnace loads to reduce cleaning and temperature-change setups.
4. It split one large order into transfer batches so that inspection could begin before the entire order completed machining.

The company also introduced a rule that no job could be released solely because machine capacity appeared available; materials, fixtures, operator skills, and inspection capacity had to be confirmed.

Outcome

The revised process reduced hidden queueing and made delivery risks visible earlier. Some orders were deliberately rescheduled before production began, while a limited amount of overtime was directed to the furnace bottleneck. Although average machine utilisation did not increase substantially, schedule reliability improved because the plan reflected actual constraints.

Learning points

The case demonstrates that aggregate capacity sufficiency does not guarantee temporal or operational feasibility. Bottleneck identification, finite scheduling, setup management, and release discipline are complementary practices. It also shows that a lower utilisation figure may accompany better performance when protective capacity reduces disruption propagation.

12. Technology, Data, and Governance

Modern advanced planning and scheduling systems use finite-capacity engines, constraint programming, mixed-integer optimisation, simulation, and heuristic search. Artificial intelligence can assist with demand forecasts, estimated processing times, anomaly detection, and schedule recommendations. However, an algorithm cannot compensate for inaccurate routings, missing calendars, unreliable standard times, or unrecorded skill restrictions.

AI-supported scheduling should therefore include:

• traceable input data and version control;
• human approval for major schedule changes;
• explanation of priority and constraint decisions;
• safeguards against systematically disadvantaging particular customers or shifts;
• protection of production, employee, and customer data;
• monitoring for model drift and changing process conditions.

A schedule is a managerial commitment as well as a computational output. Responsibility for safety, legal compliance, worker welfare, quality, and customer communication remains with accountable managers, not with software alone.

13. Best Practices

Effective capacity planning and scheduling generally follow these principles:

1. Separate requirement calculation from executable scheduling.
2. Maintain accurate routings, standard times, calendars, and setup data.
3. Model bottlenecks and shared tools explicitly.
4. Use infinite loading for diagnosis and scenario analysis, not as a promise date.
5. Use finite loading when releasing detailed work.
6. Select priority rules according to the performance objective.
7. Protect bottlenecks from avoidable starvation and excessive variability.
8. Include material, skill, inspection, maintenance, and quality constraints.
9. Use lot splitting and overlapping only when control costs are acceptable.
10. Review schedule adherence and update parameters using actual performance.
11. Preserve some capacity for uncertainty where lateness costs are high.
12. Communicate exceptions early rather than hiding overloads through unrealistic dates.

Chapter Summary

Infinite loading assigns planned work without initially restricting it by available capacity. It is useful for revealing overloads, evaluating scenarios, and supporting medium-term planning, but its dates may be infeasible. Finite loading explicitly respects resource limits and produces a more realistic schedule, although it requires richer data and creates visible trade-offs among lateness, overtime, inventory, and flexibility.

Available capacity depends on resources, shifts, scheduled hours, utilisation, efficiency, maintenance, and calendars. Required capacity includes quantity, processing time, and setup time. Forward scheduling identifies the earliest possible completion, whereas backward scheduling starts from a due date and places work as late as possible. Priority rules such as FCFS, SPT, EDD, least slack, and critical ratio influence flow time, fairness, utilisation, and due-date performance.

Overlapping and lot splitting can reduce lead time but introduce additional handling, tracking, and setup requirements. A capacity-feasible plan is not necessarily an executable schedule because temporal concentration, precedence, materials, tools, skills, quality approvals, and calendars may invalidate it. Professional CRP therefore combines aggregate analysis, finite scheduling, constraint verification, disciplined release, performance measurement, and continuous feedback.

Key Terms

Capacity Requirement Planning: The process of translating planned production into resource requirements by work centre and time period.

Available capacity: Productive time that a resource can provide during a defined period.

Required capacity: Time needed to complete specified processing and setup work.

Work centre: A machine, labour pool, department, or group of similar resources.

Infinite loading: Assigning work without initially enforcing capacity limits.

Finite loading: Assigning work while enforcing resource and calendar limits.

Load ratio: Required capacity divided by available capacity.

Capacity profile: Time-phased representation of load and capacity.

Forward scheduling: Scheduling from a release date toward the earliest completion.

Backward scheduling: Scheduling from a due date toward the latest permissible start.

Priority rule: A method for selecting the next job from a waiting queue.

Critical ratio: Time remaining until due date divided by remaining work.

Slack: Time available before a job becomes late after considering remaining work.

Overlapping: Starting a successor operation before the full predecessor lot is complete.

Lot splitting: Dividing an order into sublots for parallel or sequential processing.

Pre-emption: Interrupting one job to process another job.

Setup time: Time required to prepare a resource for a job or product.

Bottleneck: A resource whose limited capacity constrains system output.

Executable schedule: A schedule satisfying resource, precedence, material, calendar, and operational constraints.

Work-in-process: Jobs or units released into production but not yet completed.

Review Questions

5 Short Answer Questions

1. What is the principal difference between infinite loading and finite loading?
2. Define available capacity and identify two factors that reduce nominal capacity.
3. When is backward scheduling generally preferable to forward scheduling?
4. What is the purpose of a priority rule?
5. State two disadvantages of lot splitting.

5 Long Answer Questions

1. Explain how a capacity-feasible plan can fail to become an executable schedule. Use at least four operational constraints.
2. Compare forward and backward scheduling, including their advantages, risks, and appropriate applications.
3. Discuss the strengths and limitations of infinite loading for production management.
4. Compare EDD, SPT, FCFS, least slack, and critical ratio as dispatching rules.
5. Explain how setup times, overlapping, and lot splitting affect capacity and lead time.

3 Analytical / Application Questions

1. A work centre has two machines, one 8-hour shift per day, five days per week, utilisation of 0.80, and efficiency of 0.90. Calculate its weekly productive capacity. If planned work requires 62 hours, calculate the load ratio and interpret the result.
2. Three jobs require 6, 3, and 4 hours and have due dates of 14, 8, and 11 hours from now. Construct an EDD sequence, calculate each completion time, and identify any tardiness.
3. A weekly capacity report shows no overload, but jobs are repeatedly late. Develop a diagnostic approach that tests temporal concentration, setups, material availability, bottlenecks, shared tooling, skills, and inspection constraints.

Multiple Choice Questions with Answers

Question 1

Which statement best describes infinite loading?

A. It assigns work only when capacity is available

B. It assigns work without initially enforcing capacity limits

C. It schedules every job backward from its due date

D. It excludes all setup and processing times

Correct Answer: B. It assigns work without initially enforcing capacity limits

Question 2

A work centre has 120 hours of available capacity and 150 hours of required load. What is its load ratio?

A. 0.80

B. 1.00

C. 1.25

D. 1.50

Correct Answer: C. 1.25

Question 3

Which scheduling approach begins with a job’s release date and places operations as early as possible?

A. Backward scheduling

B. Forward scheduling

C. Critical-ratio scheduling

D. Reverse loading

Correct Answer: B. Forward scheduling

Question 4

Which priority rule selects the job with the nearest due date?

A. SPT

B. FCFS

C. EDD

D. Longest processing time

Correct Answer: C. EDD

Question 5

If a job’s critical ratio is below 1, what does this generally indicate?

A. The job has more time remaining than work remaining

B. The job has less time remaining than estimated work remaining

C. The job has already been completed early

D. The job requires no further processing

Correct Answer: B. The job has less time remaining than estimated work remaining

Question 6

What is the main purpose of overlapping operations?

A. To increase the size of every production lot

B. To allow a successor operation to begin before the whole predecessor lot is complete

C. To eliminate all setup requirements

D. To prevent material movement between work centres

Correct Answer: B. To allow a successor operation to begin before the whole predecessor lot is complete

Question 7

Which condition can make a capacity-feasible plan non-executable?

A. All jobs have documented routings

B. The plan includes a valid work-centre calendar

C. A required component is unavailable when production is scheduled

D. The schedule includes setup times

Correct Answer: C. A required component is unavailable when production is scheduled

Question 8

A job has a due date at time 20 and 6 hours of remaining work. Under simple backward scheduling, when should it start?

A. At time 6

B. At time 14

C. At time 20

D. At time 26

Correct Answer: B. At time 14

Question 9

Which rule is most directly associated with reducing average flow time in many single-machine settings?

A. Shortest processing time

B. Longest processing time

C. Random selection

D. Latest due date

Correct Answer: A. Shortest processing time

Question 10

Why may high bottleneck utilisation increase lateness?

A. It guarantees excess spare capacity

B. It leaves little protection against variability and disruption

C. It eliminates queue formation

D. It reduces the need for accurate routings

Correct Answer: B. It leaves little protection against variability and disruption