Aggregate planning, MRP and scheduling

Why it matters

Planning works top-down. The aggregate plan sets monthly output, workforce and inventory for a whole product family. The master production schedule (MPS) breaks that into end items by week. MRP turns the MPS into dated orders for every part and raw material, and scheduling decides the order of jobs on each machine. Errors at any level show up as missed deliveries, idle machines or excess stock, so planners and production engineers use these tools every day.

Key ideas

Aggregate planning (horizon of about 3–18 months, in aggregate units such as tonnes or standard hours)

• Supply-side options: vary the workforce (hire or lay off), overtime and idle time, inventory build-up, backorders, subcontracting, part-time labour.
• Demand-side options: pricing, promotion, complementary products, reservations.
• Pure strategies: a level plan keeps production constant and absorbs demand changes with inventory or backorders; a chase plan matches production to demand each period by changing the workforce or using overtime. A mixed (hybrid) plan combines them.
• Costs compared: regular-time and overtime production, hiring and lay-off, inventory holding, backorder or shortage, and subcontracting. Methods range from trial-and-error tables to linear programming and the transportation method.

Master production schedule (MPS): the quantity of each end item to finish in each week, consistent with the aggregate plan. Rough-cut capacity planning checks it against key resources.

Material requirements planning (MRP)

• Inputs: the MPS, the bill of materials (BOM) (product structure with quantities per parent, organised in levels) and inventory status records (on hand, scheduled receipts, lead times, lot-sizing rules).
• Logic for each item, level by level: gross requirements come from the parent's planned order releases × quantity per parent; net requirement = gross − on hand − scheduled receipts (+ safety stock); a planned order receipt covers the net requirement using the lot-sizing rule (lot-for-lot, fixed quantity, EOQ, period order quantity); the planned order release is offset earlier by the lead time.
• Outputs: planned order releases (which become purchase and work orders), reschedule notices and exception reports.
• MRP suits dependent demand (components whose need follows from the end-item schedule); EOQ and reorder points suit independent demand.
• MRP II adds capacity requirements planning, shop-floor control and finance; ERP extends it across the whole business. MRP is a push system; JIT/kanban is a pull system.

Scheduling and sequencing

• Single-machine rules: FCFS (first come, first served), SPT (shortest processing time, which minimises mean flow time, mean waiting time and average number of jobs in the system), EDD (earliest due date, which minimises maximum lateness and maximum tardiness), LPT, and critical ratio CR = time remaining to due date / processing time remaining (CR < 1 means the job is behind).
• Performance measures: flow (completion) time, lateness = completion − due date (may be negative), tardiness = max(0, lateness), makespan, utilisation.
• Johnson's rule for n jobs on two machines in the same order (M1 then M2) minimises makespan: pick the smallest time in the table; if it is on M1, place that job as early as possible; if on M2, as late as possible; remove the job and repeat (break ties arbitrarily).
• Gantt charts show the schedule against time.

Formulas

Level production rate = (Σ demand + desired ending inventory − beginning inventory) / number of periods

• In units per period.

Ending inventory: I(t) = I(t−1) + P(t) − D(t)

• I = inventory (units), P = production (units), D = demand (units); a negative value is a backorder.

Net requirement = max(0, gross requirement − on-hand − scheduled receipts + safety stock)

Planned order release (period t − L) = planned order receipt (period t)

• L = lead time (periods).

Flow time Fᵢ = completion time Cᵢ − release time; Lateness Lᵢ = Cᵢ − dᵢ; Tardiness Tᵢ = max(0, Lᵢ)

• dᵢ = due date. Times in days or hours.

Mean flow time = ΣFᵢ / n; Average number of jobs in system = ΣFᵢ / makespan

Worked examples

Example 1 (standard): level versus chase. Demand for four months: 800, 1000, 1200, 1000 units; beginning inventory 0; production last month 1000. Holding cost ₹20 per unit per month on ending inventory; increasing the rate costs ₹30 per unit, decreasing it ₹25 per unit.

1. Level rate = (800 + 1000 + 1200 + 1000 + 0 − 0)/4 = 1000 units/month.
2. Ending inventories: 0 + 1000 − 800 = 200; 200 + 1000 − 1000 = 200; 200 + 1000 − 1200 = 0; 0 + 1000 − 1000 = 0. Holding cost = (200 + 200 + 0 + 0) × 20 = ₹8000 (no rate change from last month's 1000).
3. Chase: the rate changes 1000 → 800 (−200), → 1000 (+200), → 1200 (+200), → 1000 (−200). Cost = 400 × 30 + 400 × 25 = 12 000 + 10 000 = ₹22 000.
4. The level plan is cheaper here because holding is cheap compared with rate changes.

Example 2 (standard): MRP explosion. End item X needs 2 units of component A. MPS: 100 X due in week 5. X: on hand 20, lead time 1 week, lot-for-lot. A: on hand 50, scheduled receipt 30 in week 3, lead time 1 week, lot-for-lot.

1. X: net requirement in week 5 = 100 − 20 = 80; planned order receipt 80 in week 5, release 80 X in week 4.
2. A: gross requirement in week 4 = 2 × 80 = 160 (it is driven by X's release, not its due date).
3. Available by week 4 = 50 + 30 = 80, so net requirement = 160 − 80 = 80.
4. Planned order receipt 80 in week 4, released 80 A in week 3.

Example 3 (GATE level): Johnson's rule. Five jobs pass through M1 then M2 (times in h): J1 (5, 2), J2 (1, 6), J3 (9, 7), J4 (3, 8), J5 (10, 4).

1. Smallest time 1 (J2 on M1): J2 first. Next 2 (J1 on M2): J1 last. Next 3 (J4 on M1): J4 second. Next 4 (J5 on M2): J5 fourth. J3 fills the middle. Sequence J2–J4–J3–J5–J1.
2. M1 completion times: 1, 4, 13, 23, 28.
3. M2: J2 1→7; J4 starts max(4, 7) = 7 → 15; J3 starts max(13, 15) = 15 → 22; J5 starts max(23, 22) = 23 → 27; J1 starts max(28, 27) = 28 → 30.
4. Makespan = 30 h (a check of all 120 sequences confirms this is the minimum). M2 is idle 0–1, 22–23 and 27–28.

Common mistakes

• Offsetting the parent's due date instead of its planned order release when computing component gross requirements.
• Forgetting scheduled receipts or on-hand stock in gross-to-net, or subtracting on-hand stock twice in later periods.
• Placing a job at the end in Johnson's rule when its minimum is on M1 (it goes first) or vice versa.
• Computing M2 start times without checking that M1 has finished that job.
• Mixing up SPT (minimises mean flow time) and EDD (minimises maximum lateness).
• Reporting negative tardiness; tardiness is never negative, lateness can be.

For GATE ME

Sequencing is a favourite: Johnson's rule makespan, SPT or EDD with mean flow time, lateness or tardiness. Expect MCQs on MRP inputs and outputs, dependent versus independent demand, and level versus chase strategies, and occasional short aggregate-planning cost tables. Practise Johnson's rule with five or six jobs and draw the Gantt chart to get idle times.

Quick check

1. Which sequencing rule minimises mean flow time on a single machine?
2. Name the three inputs to MRP.
3. Jobs with processing times 4, 2 and 6 days are sequenced by SPT. What is the mean flow time?
4. In Johnson's rule, where does a job go if its smallest time is on the second machine?
5. Which aggregate strategy keeps the workforce constant and uses inventory as a buffer?

Answers: 1. SPT. 2. MPS, bill of materials, inventory status records. 3. (2 + 6 + 12)/3 = 6.67 days. 4. As late as possible in the sequence. 5. Level strategy.