Material requirements planning and lot sizing

Why it matters

A tractor or a pump has hundreds of parts, each with its own lead time. Ordering them by reorder points would leave some parts short and others piled up. Material requirements planning (MRP) works backwards from the master schedule to tell purchasing and the shop exactly which parts are needed, how many, and when each order must be released. Lot sizing then decides how to group those needs into economical orders.

Key ideas

Dependent vs independent demand. Demand for end items (and service spares) comes from the market and is forecast – independent demand. Demand for components, sub-assemblies and raw materials is calculated from the end-item schedule – dependent demand. MRP is meant for dependent demand, which is lumpy and known once the MPS is fixed; reorder-point methods suit independent demand.

Inputs to MRP.

• Master production schedule (MPS) – end-item quantities and due weeks.
• Bill of materials (BOM) – product structure: which components, how many per parent (usage quantity), and levels (end item = level 0). A component appearing at several levels is given its lowest level (low-level code) so that its total gross requirement is collected before netting.
• Inventory records – on-hand stock, scheduled receipts (open orders already released), lead times, lot-size rule, safety stock, scrap allowances.

The MRP record (for each item, period by period).

• Gross requirements – from the MPS (level 0) or from the planned order releases of all parents × usage quantity.
• Scheduled receipts – open orders due in.
• Projected on-hand (available) – stock expected at the end of the period.
• Net requirements = gross requirements − (projected on-hand from the previous period + scheduled receipts), plus safety stock if used, but not less than zero.
• Planned order receipts – net requirement adjusted by the lot-size rule.
• Planned order releases – planned receipts offset earlier by the lead time. These become the gross requirements of the children.

This "explode, net, lot-size, offset" cycle is repeated level by level from the top of the BOM down.

Outputs. Planned orders, release notices, reschedule (expedite/de-expedite) messages, cancellation notices, and inputs to capacity requirements planning (CRP). MRP II (manufacturing resource planning) extends MRP to capacity, shop-floor control, purchasing and finance; ERP extends it to the whole enterprise.

Regenerative vs net-change MRP. Regenerative MRP recalculates everything in a batch run (often weekly); net-change MRP updates only the records affected by a transaction.

Lot-sizing rules.

• Lot-for-lot (L4L) – order exactly the net requirement of each period. Least inventory, most orders; best when ordering/set-up cost is low.
• Fixed order quantity (FOQ) / EOQ – a fixed lot each time; the EOQ uses the average demand rate, which is a poor fit for lumpy MRP demand and often leaves remnants carried for many periods.
• Periodic order quantity (POQ) – order to cover a fixed number of periods, chosen as EOQ ÷ average demand per period, rounded to a whole number.
• Part-period balancing (PPB) – extend the order to cover future periods until the accumulated part-periods (units × periods carried) come as close as possible to the economic part-period EPP = S/h.
• Least unit cost (LUC), Silver–Meal (least period cost) – heuristics that stop adding periods when the cost per unit or per period starts to rise.
• Wagner–Whitin – dynamic programming that finds the optimum for the given horizon.

Formulas

Gross requirement (child, t) = Σ planned order release (parent, t) × usage per parent Net requirement(t) = max[0, GR(t) + SS − POH(t−1) − SR(t)] POH(t) = POH(t−1) + SR(t) + PORec(t) − GR(t) PORel(t − L) = PORec(t)

• GR = gross requirement (units), SS = safety stock (units), POH = projected on-hand (units), SR = scheduled receipt (units), PORec = planned order receipt (units), PORel = planned order release (units), L = lead time (periods).

EOQ = √(2 · D · S / h)

• D = demand per period (units/period), S = ordering or set-up cost (₹/order), h = holding cost (₹/unit·period). Units of D and h must use the same period.

POQ (periods) = EOQ / d̄

• d̄ = average demand per period (units/period); round to the nearest whole number of periods (at least 1).

EPP = S / h

• Economic part-period (unit·periods) for part-period balancing.

Total cost = (number of orders) · S + h · Σ (units carried × periods carried)

• Holding charged on stock carried from the receipt period to the period of use.

Worked examples

Example 1 (standard) – BOM explosion with lot-for-lot. One A needs 2 B and 3 C; one B needs 2 C. Lead times: A 1 week, B 2 weeks, C 1 week. On hand: A 20, B 50, C 100; no scheduled receipts. MPS for A: 100 in week 5 and 150 in week 7.

1. A: gross 100 (wk 5), 150 (wk 7). Net = 100 − 20 = 80 (wk 5) and 150 (wk 7). Releases (offset 1 week): 80 in wk 4, 150 in wk 6.
2. B: gross = 2 × A releases = 160 (wk 4), 300 (wk 6). Net = 160 − 50 = 110 (wk 4), 300 (wk 6). Releases (offset 2 weeks): 110 in wk 2, 300 in wk 4.
3. C: gross = 3 × A releases + 2 × B releases. Week 2: 2 × 110 = 220. Week 4: 3 × 80 + 2 × 300 = 240 + 600 = 840. Week 6: 3 × 150 = 450.
4. C net: 220 − 100 = 120 (wk 2), 840 (wk 4), 450 (wk 6). Releases (offset 1 week): 120 in wk 1, 840 in wk 3, 450 in wk 5. Notice C is needed both by A and by B; its gross requirement is collected from both parents before netting.

Example 2 (GATE level) – comparing lot-sizing rules. Net requirements for weeks 1–6: 50, 60, 70, 60, 95, 75 units. Ordering cost S = ₹200/order, holding cost h = ₹1 per unit per week, charged on units carried to a later week.

1. L4L: 6 orders, no carrying. Cost = 6 × 200 = ₹1200.
2. POQ: average demand = 410/6 = 68.33 units/week; EOQ = √(2 × 68.33 × 200/1) = 165.3 units; POQ = 165.3/68.33 = 2.42 → 2 weeks. Orders: 110 in wk 1, 130 in wk 3, 170 in wk 5. Carrying = 60 + 60 + 75 = 195 unit-weeks. Cost = 3 × 200 + 195 = ₹795.
3. PPB: EPP = 200/1 = 200 part-periods. From wk 1: covering wk 2 adds 60, covering wk 3 adds 2 × 70 = 140, total 200 = EPP, so the first lot covers wks 1–3 (180 units). From wk 4: covering wk 5 gives 95; adding wk 6 gives 95 + 150 = 245, which is closer to 200 (|245 − 200| = 45 < 105), so the second lot covers wks 4–6 (230 units). Cost = 2 × 200 + 200 + 245 = ₹845.
4. Wagner–Whitin (optimum) gives the same plan as POQ, ₹795.
5. Best rule here: POQ of 2 weeks, total cost ₹795; PPB is a heuristic and is not always optimal.

Common mistakes

• Offsetting by the lead time in the wrong direction: releases come earlier than receipts.
• Exploding a component from the parent's gross requirement or MPS instead of the parent's planned order releases.
• Forgetting to multiply by the usage quantity, or to add requirements from every parent that uses the component.
• Netting stock twice: on-hand is used once and then carried forward as projected on-hand.
• Using annual EOQ figures with weekly demand (mismatched periods).
• Charging holding cost on units used in the same week they arrive when the problem states holding on carried stock only.

For GATE PI

Expect a small product structure and an MPS, with a request for the gross or net requirement, or the planned order release, of a component in a given week; and lot-sizing tables asking for total cost under L4L, EOQ, POQ or part-period balancing. Conceptual items test dependent vs independent demand, inputs and outputs of MRP, and low-level coding. Practise drawing the MRP grid quickly and offsetting lead times carefully.

Quick check

1. One X uses 4 Y. Planned order releases of X are 30 units in week 3. What is the gross requirement of Y, and in which week?
2. Gross requirement 200, previous projected on-hand 70, scheduled receipt 50, no safety stock. What is the net requirement?
3. A planned order receipt in week 9 has a lead time of 3 weeks. When is it released?
4. S = ₹150 per order, h = ₹2 per unit per week. What is the economic part-period?

Answers: 1. 120 units of Y in week 3. 2. 200 − 70 − 50 = 80 units. 3. Week 6. 4. EPP = 150/2 = 75 unit-weeks.