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Unit VIII · Statistics, operations and operations research
12 min readConcept sheetMCQ · match the layout, apply Johnson's rule, score locations

Operations management: location, layout, ERP and scheduling

Operations turns inputs into goods and services. Key choices: where to locate, how to lay out, how ERP links functions, and how jobs are loaded, sequenced and scheduled.

Transformation modelInputs (people, materials, machines, money, information) → conversion process → outputs, with feedback for control
Four basic layoutsProcess (functional), product (line), fixed-position, cellular (group technology)
ERP lineageMRP (1960s-70s) → MRP II (1980s) → ERP (1990s): one integrated database across functions
Johnson's rule (S. M. Johnson, 1954)Sequences n jobs on two machines, all in the same order, to minimise the total elapsed time (makespan)

Role and scope of operations management

  • Operations is the function that actually makes the product or delivers the service, converting inputs into outputs.
  • Strategic (long-term) decisions: product and service design, process choice, capacity, facility location and layout.
  • Tactical (medium-term) decisions: aggregate planning, workforce levels, materials planning (MRP or ERP), quality systems.
  • Operational (short-term) decisions: loading, sequencing, scheduling, inventory control and maintenance.
  • Productivity = output ÷ input. Services differ from goods: they are intangible and perishable, and are produced and consumed together, often with the customer present.

Facility location methods

MethodHow it works
Factor ratingWeight each factor, score each site, multiply and add; choose the highest total
Centre of gravityCx = Σ(xV) ÷ ΣV and Cy = Σ(yV) ÷ ΣV, where V is the volume shipped to each point; gives a low-cost distribution point
Locational break-even (cost-volume)Total cost = FC + VC × Q for each site; choose the cheapest site at the expected volume
Transportation methodChooses the plant or warehouse that gives the least total shipping cost across the network
Brown-Gibson modelCombines objective (cost) factors and subjective factors into one location measure

Worked example 1: factor rating

Problem

A firm compares Pune and Chennai. Weights: labour cost 0.5, market access 0.3, infrastructure 0.2. Scores out of 100 are Pune 80, 70, 60 and Chennai 70, 80, 90.

Working
  1. Pune = 0.5 × 80 + 0.3 × 70 + 0.2 × 60 = 40 + 21 + 12 = 73.
  2. Chennai = 0.5 × 70 + 0.3 × 80 + 0.2 × 90 = 35 + 24 + 18 = 77.
Answer

Choose Chennai (77 > 73).

Worked example 2: centre of gravity

Problem

A distributor serves three markets at grid points (2, 4), (6, 2) and (5, 8), shipping 200, 100 and 200 tonnes a month. Where should the warehouse be?

Working
  1. ΣV = 200 + 100 + 200 = 500.
  2. Cx = (2 × 200 + 6 × 100 + 5 × 200) ÷ 500 = (400 + 600 + 1,000) ÷ 500 = 2,000 ÷ 500 = 4.
  3. Cy = (4 × 200 + 2 × 100 + 8 × 200) ÷ 500 = (800 + 200 + 1,600) ÷ 500 = 2,600 ÷ 500 = 5.2.
Answer

Locate the warehouse near (4, 5.2).

Worked example 3: locational break-even

Problem

Site X: fixed cost ₹30 lakh a year, variable cost ₹150 a unit. Site Y: fixed cost ₹50 lakh, variable cost ₹100 a unit. Which site is cheaper at 30,000 units and at 50,000 units?

Working
  1. Equal cost: 30,00,000 + 150Q = 50,00,000 + 100Q, so 50Q = 20,00,000 and Q = 40,000 units.
  2. At 30,000 units: X = ₹30 lakh + ₹45 lakh = ₹75 lakh; Y = ₹50 lakh + ₹30 lakh = ₹80 lakh. X is cheaper.
  3. At 50,000 units: X = ₹30 lakh + ₹75 lakh = ₹105 lakh; Y = ₹50 lakh + ₹50 lakh = ₹100 lakh. Y is cheaper.
Answer

Below 40,000 units choose X (low fixed cost); above 40,000 units choose Y (low variable cost).

Types of layout

LayoutArrangementSuitsExampleTrade-off
Process (functional)Similar machines or skills grouped togetherLow volume, high variety (job shop)Hospital departments, a tool roomFlexible, but long material flows and high handling cost
Product (line)Machines in the sequence of operationsHigh volume, standard productsCar assembly line, bottling plantLow unit cost, but rigid; needs line balancing
Fixed-positionThe product stays put; workers and equipment come to itVery large, bulky or one-off productsShip-building, aircraft, dams, buildingsHard to schedule; crowded work sites
Cellular (group technology)Cells of different machines, each making a family of similar partsMedium volume, medium variety (batch)Engine-part cells in an auto-component plantCombines line efficiency with process flexibility

Common ERP modules

ModuleCovers
Finance and accountingGeneral ledger, payables, receivables, costing, budgeting
Human resourcesPersonnel records, payroll, attendance, training
Sales and distributionOrders, pricing, invoicing, shipping
Materials managementPurchasing, inventory, vendor evaluation
Production planningMRP, capacity planning, shop-floor control
Supply chain and CRMLogistics, demand planning, customer service

Implementing ERP

Vendors include SAP, Oracle and Microsoft Dynamics. Most ERP failures come from people and process issues, not from the software.

  1. 1★
    Assess readiness, set goals and secure top-management support.
  2. 2
    Select the package and vendor; run a gap analysis between the package and current processes.
  3. 3★
    Re-engineer processes (BPR) and configure the software, customising only where essential.
  4. 4
    Clean and migrate the data, then test the system.
  5. 5
    Train users and manage the change.
  6. 6★
    Go live: big bang (all at once), phased (module by module) or parallel (old and new systems together).
    parallel is safest but costliest
  7. 7
    Review, stabilise and support the system after go-live.

★ one-way, controls the pace

Loading, sequencing, scheduling and monitoring

LoadingAssigning jobs to work centres or machines. Tools: the Gantt load chart and the assignment (Hungarian) method.
SequencingDeciding the order of jobs at a work centre. Tools: priority rules and Johnson's rule.
SchedulingFixing start and finish times. Forward scheduling starts from today; backward scheduling works back from the due date.
MonitoringTracking progress against the plan: Gantt progress charts, input-output control and expediting late jobs.

Loading and monitoring tools

  • Infinite loading assigns work without checking capacity; finite loading never loads a work centre beyond its capacity.
  • Gantt load chart: shows how busy each machine or work centre is over time. Gantt schedule (progress) chart: shows each job's planned times and its actual progress.
  • Assignment (Hungarian) method: assigns n jobs to n machines, one job each, at the least total time or cost (H. W. Kuhn, 1955).
  • Dispatching releases jobs to the shop floor through a dispatch list ordered by a priority rule.
  • Input-output control compares planned and actual work entering and leaving a work centre. When input runs above output, a queue is building up.
  • Expediting (follow-up) chases late or urgent jobs so that they move ahead.

Priority (dispatching) rules

RuleOrder jobs byKnown for
FCFSOrder of arrivalSeen as fair; rarely the best on time measures
SPT (shortest processing time)Shortest job firstMinimises average flow time, average waiting time and average number of jobs in the system
EDD (earliest due date)Earliest due date firstMinimises the maximum lateness
LPT (longest processing time)Longest job firstUsually poor on flow time
Critical ratio (CR)Smallest CR first; CR = time left until the due date ÷ work time leftCR < 1 means the job is behind schedule

Worked example 4: comparing priority rules

Problem

Four jobs arrive in the order J1 to J4. Processing days and due days: J1 (6, 8), J2 (2, 6), J3 (8, 18), J4 (4, 10). Compare FCFS, SPT and EDD.

Working
  1. FCFS (J1, J2, J3, J4): completions 6, 8, 16, 20; total 50, average flow time 12.5 days. Tardiness 0, 2, 0, 10: total 12; maximum lateness 10.
  2. SPT (J2, J4, J1, J3): completions 2, 6, 12, 20; total 40, average 10 days. Tardiness 0, 0, 4, 2: total 6; maximum lateness 4.
  3. EDD (J2, J1, J4, J3): completions 2, 8, 12, 20; total 42, average 10.5 days. Tardiness 0, 0, 2, 2: total 4; maximum lateness 2.
Answer

SPT gives the lowest average flow time (10 days); EDD gives the lowest maximum lateness (2 days).

Worked example 5: Johnson's rule (n jobs, 2 machines)

Problem

Five jobs go through Machine 1 and then Machine 2. Times in hours (M1, M2): A (5, 2), B (1, 6), C (9, 7), D (3, 8), E (10, 4). Find the sequence and the makespan.

Working
  1. Rule: find the smallest time left. If it is on M1, place that job as early as possible; if on M2, as late as possible. Strike it out and repeat.
  2. The smallest is 1 (B on M1), so B goes first. Next is 2 (A on M2), so A goes last.
  3. Next is 3 (D on M1), so D goes second. Next is 4 (E on M2), so E goes fourth. C fills the third place.
  4. Sequence: B, D, C, E, A.
  5. M1 finishes the jobs at 1, 4, 13, 23 and 28. M2 runs B 1-7, D 7-15, C 15-22, E 23-27 and A 28-30.
  6. M2 is idle from 0-1, 22-23 and 27-28: 3 hours in all.
Answer

Sequence B-D-C-E-A; total elapsed time 30 hours.

How NET asks this

NET asks you to match layouts with industries, apply Johnson's rule to find a sequence or makespan, pick the priority rule that minimises flow time or lateness, and do quick factor-rating or location break-even sums. ERP questions test modules, evolution and go-live approaches.

Exam angle

Typical MCQ: “In Johnson's rule, the smallest time in the table is on Machine 2. Where does that job go?” As late as possible in the sequence. Trap: putting it first; only a Machine 1 minimum goes to the front.

Typical MCQ: “A job's critical ratio is 0.8. What does that mean?” It is behind schedule: the time left is less than the work left. CR = 1 is on time and CR > 1 is ahead. Trap: reading 0.8 as comfortable.

Typical MCQ: “What is the main design problem in a product layout?” Line balancing: dividing the work so that every station has nearly equal time and idle time is low. Trap: confusing it with the routing problem of a process layout.

Remember it

SPT cuts the average flow time; EDD cuts the worst lateness. Johnson: a small time on M1 goes to the front, a small time on M2 goes to the back.