CMA Intermediate · Operations Management and Strategic Management
Scheduling and Queuing Models for CMA Inter
Scheduling decides when each job or task runs on each resource, using rules like FCFS, SPT and Johnson's rule. Queuing theory studies waiting lines using arrival rate (λ) and service rate (μ). To solve problems, list the data, pick the right rule or model, apply the formulas step by step, and interpret the result.
What this chapter covers
This chapter has two halves. The first half is scheduling: how you set the order and timing of jobs on machines or workers. You learn the meaning and objectives of scheduling, priority dispatching rules, Johnson's rule for sequencing jobs through two machines, and Gantt charts for loading and tracking work.
The second half is queuing theory. Here you study waiting lines: customers at a bank counter, vehicles at a toll plaza, machines waiting for a repair technician. You learn the vocabulary (arrival rate, service rate, queue discipline, channels and phases) and then apply formulas for the single-channel model (M/M/1) and the multi-channel model (M/M/s).
The chapter links to the rest of Operations Management through capacity planning, production planning and control, and service operations. Both halves answer the same question: how do you use limited capacity so that waiting and idle time stay low? Expect a mix of theory questions, short MCQs and numerical problems.
This chapter is one of the more scoring parts of the operations side of the paper, because most questions are rule-based and numerical. If you learn a few procedures well, such as Johnson's rule and the M/M/1 formulas, you can reach full step marks without long theory. The same procedures also appear as standalone MCQs in Section A, where there is no negative marking, so a quick calculation can earn 2 marks. Because the formulas are short and the logic is mechanical, the effort you put in gives a strong return compared with heavy descriptive chapters.
Scheduling and Queuing Models: topics in the order to study them
- 1Scheduling: Meaning, Objectives and TypesStart here to learn the vocabulary and purpose of scheduling before you meet any rule or calculation.
- 2Scheduling Rules and Priority DispatchingRules like FCFS, SPT, EDD and critical ratio are the first calculations and build the idea of ranking jobs by a measure.
- 3Johnson's Rule and Job SequencingIt builds on dispatching rules and adds the main numerical procedure of the scheduling half: minimising total time over two machines.
- 4Gantt Charts and LoadingGantt charts let you show a sequence visually, so study them after you can produce a sequence.
- 5Queuing Theory: Concepts and StructureMove to the second half only after scheduling is settled; you need the terms and symbols before any formula.
- 6Single-Channel Queuing Model (M/M/1)This is the simplest model, with short formulas based on λ and μ, and it is the base for the multi-channel case.
- 7Multi-Channel Queuing Model (M/M/s)Study it last because it extends M/M/1 to several servers and is the most formula-heavy topic.
How to prepare Scheduling and Queuing Models
Treat the chapter as two skill sets: sequencing by rules, and calculating queue measures by formula. Practise the procedures on paper until you can do them without the book.
- Read the meaning, objectives and types of scheduling once, and write a short list of objectives in your own words for theory answers.
- Learn each dispatching rule as a one-line instruction (for example, SPT means shortest processing time first). Then solve one small example per rule and compute average flow time and average lateness.
- Practise Johnson's rule in fixed steps: find the smallest time among all jobs; if it is on machine 1, place the job as early as possible; if on machine 2, place it as late as possible; remove the job and repeat. Then work out the total elapsed time and idle time using a table.
- Draw Gantt charts on graph paper or a ruled page with a time axis, labelled machines and clearly marked jobs. Neat charts earn presentation marks.
- Write the queuing symbols and formulas on one page: λ, μ, ρ = λ ÷ μ, Ls, Lq, Ws, Wq and the probability of n units. Check that the units of λ and μ match (both per hour, for example) before using them.
- Solve M/M/1 problems first, then M/M/s. Always check the stability condition (λ < μ for one channel, λ < sμ for s channels) and finish with a one-line interpretation, such as whether adding a server is justified.
- Finish with a timed set of Section A style MCQs on both halves, then two full written problems, one from each half.
Common mistakes in Scheduling and Queuing Models
Using different time units for arrival and service rates, such as λ per hour and μ per minute.
Fix: Convert both to the same unit first and write the units next to each value before calculating.
Applying Johnson's rule when the conditions do not hold, or breaking ties carelessly.
Fix: Check the conditions first. For ties, pick any one and state it. Cross out each assigned job so none is used twice.
Not computing idle time and total elapsed time correctly after sequencing.
Fix: Build a table with start and end times for each job on each machine. A job starts on machine 2 only when machine 1 has finished it and machine 2 is free.
Mixing up Ls and Lq, or Ws and Wq.
Fix: Remember that s means in the system (waiting plus being served) and q means in the queue only. Check with Ls − Lq = λ ÷ μ for M/M/1.
Ignoring the stability condition and giving answers for a queue that never settles.
Fix: Write the check as the first line of every answer. If it fails, say the queue grows without limit.
Drawing untidy Gantt charts or giving theory answers with no structure.
Fix: Use a ruler, a scale, labels and a heading. For theory, write short points with a heading and a one-line example.
Last-day revision: Scheduling and Queuing Models
- Scheduling sets the timing and order of jobs on resources to meet due dates and use capacity well.
- FCFS serves jobs in order of arrival; SPT serves the job with the shortest processing time first.
- EDD sequences jobs by earliest due date; it helps reduce maximum lateness.
- SPT generally gives the lowest average flow time among simple single-machine rules.
- Johnson's rule gives the minimum total elapsed time for n jobs on two machines in the same order.
- Johnson's rule: smallest time on machine 1 goes first; smallest time on machine 2 goes last.
- Gantt chart: time on the horizontal axis, machines or jobs on the vertical axis.
- Queue measures need λ (arrival rate) and μ (service rate) in the same time unit.
- M/M/1 utilisation: ρ = λ ÷ μ, and the model needs λ < μ.
- M/M/1: Ls = λ ÷ (μ − λ); Ws = 1 ÷ (μ − λ); Lq = λ² ÷ [μ(μ − λ)]; Wq = λ ÷ [μ(μ − λ)].
- Little's relations: Ls = λ × Ws and Lq = λ × Wq.
- M/M/s needs λ < sμ; the formulas use the probability of an empty system, P0.
Scheduling and Queuing Models practice questions
- Johnson's rule gives an optimal sequence for which of the following situations?
- At a toll plaza lane modelled as M/M/1, vehicles arrive at an average of 40 per hour and the booth serves an average of 50 per hour. What is…
- Which of the following is a typical objective of scheduling in an operations system?
- In the standard multi-channel queuing model (M/M/s), which assumption about the service channels is made?
- Which statement best distinguishes a Gantt progress chart from a Gantt load chart?
- A customer arrives at a restaurant, sees a long line and leaves without joining it. In queuing terminology this behaviour is called:
- Four jobs with processing times A = 5, B = 2, C = 4, D = 3 days are loaded on one machine from time zero. Their due dates are A = 14, B = 4,…
- Mehta Fabricators receives an order that must be delivered on 30 June. The planner starts from 30 June and works back through each operation…
Scheduling and Queuing Models in other exams
The same ground in other exams, if you are preparing for more than one or want another angle on it.
Scheduling and Queuing Models: frequently asked questions
Is this chapter more theory or numerical?
Both appear. Scheduling and queuing concepts can be asked as short theory or MCQs, while Johnson's rule, dispatching rules and queuing models are asked as numericals. Prepare the procedures well because they are the quickest way to earn step marks.
Do I need to memorise the M/M/s formulas?
Yes, learn the formulas you may need and practise them with numbers. Start with M/M/1, where the formulas are short, and then learn the extra P0 term for M/M/s. Write the formula first in your answer, since that earns marks even if arithmetic slips.
How do I answer a Johnson's rule question for full marks?
State that you are using Johnson's rule, show the selection steps, write the final sequence, and then give a time table for both machines. End with the total elapsed time and the idle time of each machine.
Can MCQs come from this chapter in Section A?
Yes, any topic can form a standalone MCQ. Typical ones ask for the first job in a sequence, the value of ρ, or the average number in a system. There is no negative marking, so attempt every one.