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Qwestrum Engineering360 · Industrial & Production · Production Planning & Control

Scheduling and Sequencing

Scheduling decides job timing and order to meet due dates with minimum delay and flow time.
Exam tip: keep SI units consistent end-to-end, write the governing relation symbolically before substituting, and sanity-check magnitude and sign.

Key formulas & points

Skim these first — then read the full notes below.

  • FCFS, SPT, EDD dispatch rules
  • Critical ratio (due date − now)/remaining ops
  • Gantt chart visualises machine loading

Topic details

Introduction

Sequencing is a high-frequency exam topic because it combines simple rules with strong managerial consequences. Chase and Buffa compare dispatch rules under different objective functions.

Key relations & formulas

Formulas (Indian textbook notation)

  • makespanCmax=maxcompletiontimemakespan C_{max} = max completion time

Formulas (Indian textbook notation)

  • flowshopJohnson′sruleminimisesCmaxfor2machinesflow shop Johnson's rule minimises C_{max} for 2 machines

Formulas (Indian textbook notation)

  • weightedmeanflowtimeΣwiCi/Σwiweighted mean flow time Σ w_{i} C_{i} / Σ w_{i}

Notation and sign conventions

Relation 1 —
makespanCmax=maxcompletiontimemakespan C_{max} = max completion time

Formulas (Indian textbook notation)

  • makespanCmax=maxcompletiontimemakespan C_{max} = max completion time
Write this relation with symbols exactly as in Martand Telsang Ppc — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 2 —
flowshopJohnson′sruleminimisesCmaxfor2machinesflow shop Johnson's rule minimises C_{max} for 2 machines

Formulas (Indian textbook notation)

  • flowshopJohnson′sruleminimisesCmaxfor2machinesflow shop Johnson's rule minimises C_{max} for 2 machines
Write this relation with symbols exactly as in Martand Telsang Ppc — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.
Relation 3 —
weightedmeanflowtimeΣwiCi/Σwiweighted mean flow time Σ w_{i} C_{i} / Σ w_{i}

Formulas (Indian textbook notation)

  • weightedmeanflowtimeΣwiCi/Σwiweighted mean flow time Σ w_{i} C_{i} / Σ w_{i}
Write this relation with symbols exactly as in Martand Telsang Ppc — Standard reference before substituting numbers. Examiners award partial marks for a correct setup even when arithmetic slips.

Concept in depth

SPT usually minimizes average flow time, EDD improves due-date performance, and Johnson rule gives optimal sequence for two-machine flow shop assumptions. In practice, planners also consider setup families and bottleneck stability. Groover links sequencing quality with WIP and throughput behavior.

Assumptions and validity limits

State assumptions explicitly before using any relation for scheduling and sequencing — steady state, uniform properties, linear elastic material, ideal gas, incompressible flow, etc., as applicable.
Wrong assumptions invalidate the entire solution even when the formula is correct. In Production Planning viva and GATE descriptive questions, listing valid assumptions often earns separate marks.

Step-by-step problem approach

1. Read the question and list given data with SI units (common in Production Planning papers).
2. Draw a neat labelled diagram where applicable — examiners in Indian universities award diagram marks even when arithmetic slips.
3. Identify which relation from this topic applies to scheduling and sequencing.
4. Use equation 1:
makespanCmax=maxcompletiontimemakespan C_{max} = max completion time
.
5. Use equation 2:
flowshopJohnson′sruleminimisesCmaxfor2machinesflow shop Johnson's rule minimises C_{max} for 2 machines
.
6. Substitute values, compute, and verify units and sign (direction).
7. State conclusion in one line — e.g. safe/unsafe, stable/unstable, feasible/infeasible.

Applications & exam relevance

Scheduling and Sequencing appears in manufacturing plants. In Indian industrial curricula this topic is tested because it connects theory to MRP, scheduling, and capacity.
GATE and semester exams often combine scheduling and sequencing with earlier units — revise prerequisites before attempting mixed problems.
Industry interview panels sometimes ask: "Where did you use scheduling and sequencing?" — answer with a lab, mini-project, or plant visit example if possible.

Common mistakes in exams

Common errors include applying Johnson rule to more than two machines without checking reducibility conditions. Many answers also skip Gantt chart completion times needed for marks.

Quick revision checklist

Before attempting scheduling and sequencing problems, confirm you can:
1. FCFS, SPT, EDD dispatch rules
2. Critical ratio (due date − now)/remaining ops
3. Gantt chart visualises machine loading
Revise the solved examples in Martand Telsang Ppc — Standard reference and one previous-year GATE or university paper for this unit.

Worked examples

Try the problem first — open the solution when you are ready to check.

Johnson priority choice

Problem

For two-machine flow shop, Job A has (M1,M2)=(3,8), Job B=(6,2), Job C=(4,5). Which job gets first position by Johnson rule?

Solution

Global minimum processing time is 2 on M2 for Job B, so Job B is assigned to the last available position. Next minimum among remaining is 3 on M1 for Job A, so Job A goes to first.

Conceptual check — Scheduling and Sequencing

Problem

In a Production Planning semester or GATE paper you are asked: "State the main assumption, the governing relation, and one practical consequence of scheduling and sequencing." What should a complete answer include?

📖 Standard books (India)

  • Martand Telsang Ppc — Standard reference

    Read: Syllabus unit

    Referenced in Indian B.Tech syllabus

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