Aggregate planning, MRP and scheduling

Planning hierarchy, level/chase aggregate plans, MPS and MRP gross-to-net logic, and sequencing by SPT, EDD and Johnson's rule, with cost, MRP and makespan numericals.

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Why it matters

A vehicle plant must decide months ahead how many cars to build each month and with how many people, then weeks ahead exactly which parts to order or make and when, and finally each day in what order to run jobs on each machine. Aggregate planning, MRP and scheduling are these three levels of the same planning chain. Gross-to-net MRP calculations, level-versus-chase costs and sequencing rules (SPT, EDD, Johnson's rule) are standard GATE numericals.

Key ideas

The planning hierarchy. Business plan → aggregate production plan (3–18 months, product families, total output and workforce) → master production schedule (MPS) (weekly quantities of each end item, e.g. each car variant) → MRP (when and how many of every part to order or make) → shop-floor scheduling and sequencing (the order of jobs on each machine, hour by hour).

Aggregate planning. Demand varies by month; capacity is changed or demand is absorbed using:

  • Inventory build-up in slack months, overtime or under-time, hiring and layoffs, part-time or temporary labour, subcontracting, and backorders.
  • Level strategy: constant production and workforce; inventory absorbs the variation (holding and possibly shortage costs).
  • Chase strategy: production follows demand each period by hiring/firing or overtime (workforce-change costs, little inventory).
  • Mixed (hybrid) strategy: a combination, usually the cheapest in practice. Plans are compared by total cost; methods range from trial-and-error spreadsheets to linear programming (transportation formulation).

Master production schedule. Converts the aggregate plan into specific end items and weeks. Near-term weeks are usually frozen to keep the shop stable.

Material Requirements Planning (MRP). For dependent-demand items (parts whose demand follows from the end item — a car needs exactly four road wheels and one spare), forecasting each part separately is wrong; their needs are calculated.

  • Inputs: MPS, bill of materials (BOM) (product structure with quantity per parent and levels), inventory status file (on-hand, scheduled receipts, lead times, lot-sizing rule).
  • Logic for each item, level by level: gross requirements → subtract on-hand and scheduled receipts → net requirements → apply lot sizing (lot-for-lot, fixed quantity, EOQ) → planned order receipts → offset by lead time → planned order releases. A parent's planned order release becomes the gross requirement of each child (times quantity per).
  • Outputs: planned orders (purchase and work orders), reschedule notices, exception reports.
  • Low-level coding: an item appearing at several levels is processed at its lowest level, so all its gross requirements are collected first.
  • MRP II adds capacity requirements planning and finance; ERP extends this to the whole company.

Scheduling and sequencing.

  • Single machine, n jobs: SPT (shortest processing time first) minimises mean flow time, mean waiting time and mean number of jobs in the system. EDD (earliest due date first) minimises maximum lateness. Other rules: FCFS, critical ratio (time to due date ÷ remaining work).
  • Two machines in series, n jobs (flow shop): Johnson's rule minimises makespan. Pick the smallest remaining time; if it is on machine 1, put the job as early as possible; if on machine 2, as late as possible; remove the job and repeat.
  • Gantt charts show jobs on each machine against time.

Formulas

P_level = (Σ D_t + I_end − I_0) / T

  • Level production rate (units/period); D_t = demand in period t; I_0 = starting inventory; I_end = desired ending inventory; T = number of periods.

I_t = I_(t−1) + P_t − D_t

  • Inventory at the end of period t (units); negative means backorders.

NR_t = max(0, GR_t − OH_(t−1) − SR_t)

  • Net requirement (units); GR = gross requirement; OH = projected on-hand carried in; SR = scheduled receipt in that period.

POR_t = POReceipt_(t + LT)

  • Planned order release is placed LT periods before the planned receipt; LT = lead time (periods).

GR_child = POR_parent × q

  • q = quantity of the child per parent (from the BOM).

F_j = Σ p_i (i up to j), L_j = F_j − d_j, T_j = max(0, L_j)

  • Flow (completion) time, lateness and tardiness of job j (h); p = processing time; d = due date.

Worked examples

Example 1 (standard) — level versus chase. Given: demand for four months 800, 1,000, 1,200, 1,000 units; no starting or ending inventory; previous production rate 1,000 units/month. Holding cost ₹50 per unit per month on ending inventory; changing the rate costs ₹300 per unit increased (hiring) and ₹400 per unit decreased (layoffs).

  1. Level: P = (4,000 + 0 − 0) / 4 = 1,000 per month
  2. Ending inventories: 1,000 − 800 = 200; 200 + 0 = 200; 200 − 200 = 0; 0. Holding cost = (200 + 200) × 50 = ₹20,000. No rate change.
  3. Chase: rates 800, 1,000, 1,200, 1,000. Changes: −200, +200, +200, −200.
  4. Chase cost = 400 × 300 + 400 × 400 = ₹1,20,000 + ₹1,60,000 = ₹2,80,000.

Answer: level ₹20,000 versus chase ₹2,80,000 — the level plan is much cheaper here.

Example 2 (GATE level) — MRP gross-to-net with lead-time offset. Given: MPS calls for 300 seat assemblies in week 6. Each seat needs 2 recliner mechanisms. Seats: on hand 50, assembly lead time 1 week. Recliners: on hand 150, scheduled receipt 100 in week 3, purchase lead time 2 weeks, lot-for-lot.

  1. Seat: NR₆ = 300 − 50 = 250 → planned receipt week 6, planned release week 5 (250).
  2. Recliner gross requirement: GR₅ = 250 × 2 = 500 in week 5.
  3. Available by week 5 = 150 + 100 = 250 → NR₅ = 500 − 250 = 250.
  4. Offset 2 weeks → release a purchase order for 250 recliners in week 3.

Answer: seats: release 250 in week 5; recliners: order 250 in week 3.

Example 3 (GATE level) — Johnson's rule. Given: five jobs on M1 then M2 (h): J1 (5, 2), J2 (1, 6), J3 (9, 7), J4 (3, 8), J5 (10, 4).

  1. Smallest = 1 (J2 on M1) → first. Next 2 (J1 on M2) → last. Next 3 (J4 on M1) → second. Next 4 (J5 on M2) → fourth. J3 fills the middle.
  2. Sequence: J2 – J4 – J3 – J5 – J1.
  3. M1 finishes: 1, 4, 13, 23, 28. M2 finishes: max(1,0)+6 = 7; max(4,7)+8 = 15; max(13,15)+7 = 22; max(23,22)+4 = 27; max(28,27)+2 = 30.

Answer: makespan = 30 h (equal to the lower bound ΣM1 + last M2 time = 28 + 2, so it is optimal).

Example 4 — SPT versus EDD on one machine. Jobs (p, due) in h: A (6, 10), B (2, 6), C (8, 24), D (3, 8), E (5, 15).

  • SPT order B, D, E, A, C: completions 2, 5, 10, 16, 24 → mean flow time = 57/5 = 11.4 h; maximum lateness = 16 − 10 = 6 h.
  • EDD order B, D, A, E, C: completions 2, 5, 11, 16, 24 → mean flow time 11.6 h; maximum lateness = 1 h.

Common mistakes

  • Forecasting dependent-demand parts independently instead of exploding the BOM.
  • Forgetting to multiply by the quantity per parent, or exploding before netting the parent's own stock.
  • Placing the planned order release in the same week as the requirement instead of offsetting by lead time.
  • In Johnson's rule, putting a job whose minimum is on M2 at the front — it goes to the back.
  • Taking SPT as minimising lateness; SPT minimises mean flow time, EDD minimises maximum lateness.
  • Missing the ending-inventory requirement in the level production rate.

For GATE ME

Expect MRP netting with lead-time offset, level and chase plan cost comparison, single-machine sequencing (mean flow time, lateness, tardiness under SPT/EDD) and two-machine makespan by Johnson's rule. Conceptual questions ask about MRP inputs and outputs and which rule optimises which measure. Practise building the MRP table and the Gantt chart cleanly.

Quick check

  1. Which three inputs does MRP need?
  2. Gross requirement 400, on hand 120, scheduled receipt 80. Net requirement?
  3. Which single-machine rule minimises mean flow time?
  4. In Johnson's rule the smallest time is on machine 2. Where does that job go?
  5. Demand over 3 months is 1,500, opening stock 200, desired closing stock 100. Level rate?

Answers: 1. MPS, BOM, inventory status file. 2. 200. 3. SPT. 4. As late as possible in the sequence. 5. (1,500 + 100 − 200)/3 = 466.7 units/month.

Interview questions

All Production, Maintenance & Industrial Engineering interview questions

Try answering each one aloud before you open it.

  1. 1.What is aggregate planning in production management?Concept

    Aggregate planning is a process used in production management to determine the optimal production levels, inventory levels, and workforce levels to meet fluctuating demand over a medium-term horizon. It aims to balance supply and demand in a cost-effective manner by considering factors such as production rates, labor levels, inventory levels, and backorder levels.

  2. 2.Explain the concept of Material Requirements Planning (MRP).Concept

    MRP calculates how many of each dependent-demand item (components, sub-assemblies, raw material) is needed and when, so that end items in the master production schedule can be built on time. It explodes the bill of materials, nets gross requirements against on-hand stock and scheduled receipts, applies a lot-sizing rule and offsets each planned order by its lead time. The outputs are planned purchase and work orders and reschedule notices.

  3. 3.What is the purpose of scheduling in production management?Concept

    Scheduling in production management is the process of arranging, controlling, and optimizing work and workloads in a production process. Its purpose is to ensure that production processes are efficient, resources are used effectively, and customer demands are met on time. It involves planning the timing of tasks, allocating resources, and setting priorities.

  4. 4.Why is aggregate planning important in manufacturing?Application

    Aggregate planning is important in manufacturing because it helps companies balance supply and demand, optimize resource utilization, and minimize costs. By planning production levels, inventory, and workforce in advance, companies can avoid overproduction or underproduction, reduce inventory holding costs, and ensure timely delivery of products to customers.

  5. 5.How does MRP help in reducing inventory costs?Application

    MRP orders dependent-demand parts only in the quantities and periods the master schedule actually needs, instead of holding safety stocks of every part against independent forecasts. Netting against on-hand stock and scheduled receipts avoids duplicate orders, and lead-time offsetting makes material arrive just before it is used. The result is lower work-in-process and raw-material inventory, provided the BOM, inventory records and lead times are accurate.

  6. 6.What happens if scheduling is not properly managed in a production process?Application

    If scheduling is not properly managed, it can lead to several issues such as production delays, inefficient use of resources, increased operational costs, and failure to meet customer delivery deadlines. Poor scheduling can result in bottlenecks, idle time, and increased lead times, ultimately affecting the overall productivity and profitability of the manufacturing process.

  7. 7.Explain how aggregate planning can be used to manage seasonal demand fluctuations.Application

    Aggregate planning can manage seasonal demand fluctuations by adjusting production rates, workforce levels, and inventory levels to match the expected changes in demand. Companies can use strategies such as hiring temporary workers, building up inventory during low-demand periods, or using overtime during peak demand periods to ensure that they can meet customer needs without incurring excessive costs.

  8. 8.What are the key inputs required for an MRP system to function effectively?Concept

    The key inputs required for an MRP system to function effectively include the master production schedule, which outlines what products need to be produced and when; the bill of materials, which lists the raw materials and components needed for production; and inventory records, which provide information on the current stock levels and lead times for materials.

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