15.9 Material Requirements Planning, Scheduling & Sequencing

Dependent Versus Independent Demand

The single idea that justifies MRP is the distinction between two kinds of demand.

If a shovel bucket needs six teeth, then the demand for teeth is not a matter for forecasting. It is arithmetic: six times the number of buckets. Applying reorder-point logic to dependent items produces the classic symptom of holding stock of every component while still being short of the one required.

Inputs to MRP

The bill of materials is structured in levels, with the finished product at level 0, its major assemblies at level 1, their components at level 2, and so on. Where an item appears at more than one level, low-level coding assigns it the lowest level at which it occurs, so that all its requirements are accumulated before it is planned.

The MRP Logic

For each item, working down level by level:

1. Gross requirements — the total quantity needed in each period, taken from the parent's planned order releases.
2. Scheduled receipts — quantities already ordered and due to arrive.
3. Projected on hand — the balance carried forward.
4. Net requirements = Gross requirements minus scheduled receipts minus projected on hand available.
5. Planned order receipts — when the net requirement must arrive, adjusted for lot sizing.
6. Planned order releases — the receipt date offset backwards by the lead time.

The planned order releases at one level become the gross requirements at the next level down. This cascade is called the BOM explosion, and the backwards shift is lead time offsetting.

Worked example

A hydraulic cylinder assembly is required in quantity 100 in week 8. Each assembly uses 2 seal kits. Seal kits have a lead time of 3 weeks, 40 are in stock, and none are on order.

If the assembly's own lead time is 2 weeks, the seal kits are actually needed for assembly start in week 6, and the calculation would offset from there instead — a distinction that matters in practice and is a common source of error.

Lot Sizing Rules

MRP Outputs and Extensions

Outputs include planned order releases, rescheduling notices for existing orders, cancellation notices, and exception reports where a requirement cannot be met.

Limitations

MRP assumes fixed lead times independent of load, and infinite capacity unless capacity planning is added. Both assumptions fail in a congested shop, where lead time actually grows with queue length. It also depends critically on data accuracy: an inventory record error or an out-of-date bill of materials propagates through every dependent item. The commonly quoted requirement is inventory accuracy above 95% and bill of materials accuracy above 98% before MRP is worth implementing at all.

Scheduling and Sequencing

Scheduling assigns start and finish times to operations. Sequencing decides the order in which jobs waiting at a machine are processed. The two are related but distinct.

Key measures

Priority Sequencing Rules

Two results are worth memorising because they are provable and frequently examined:

• SPT minimises mean flow time on a single machine. Its weakness is that long jobs may be indefinitely postponed.
• EDD minimises maximum lateness on a single machine.

Note that SPT does not minimise the number of tardy jobs — that requires Moore's algorithm — and EDD does not minimise average lateness.

Johnson's Rule: Two Machines, n Jobs

For $n$ jobs that must pass through two machines in the same order, Johnson's rule finds the sequence that minimises makespan.

Procedure

1. List the processing times of every job on both machines.
2. Find the smallest processing time in the whole table.
3. If it lies on Machine 1, schedule that job as early as possible (leftmost free position). If it lies on Machine 2, schedule it as late as possible (rightmost free position).
4. Delete that job and repeat until every position is filled.
5. Break ties arbitrarily; the makespan is unaffected.

Worked example

Five jobs must be turned then milled:

Smallest overall is 1 (job B on M1) so B goes first. Next smallest is 2 (job A on M2) so A goes last. Next is 3 (job D on M1) so D goes second. Next is 4 (job E on M2) so E goes second-last. C takes the remaining middle slot.

$\text{Optimal sequence: } B \to D \to C \to E \to A$

Computing the makespan:

The makespan is 30, and machine 2 idle time totals 1 unit at the start plus 1 unit between C and E.

Extension to Three Machines

Johnson's rule extends to three machines only if at least one of the following holds:

$\min(M_1) \geq \max(M_2) \quad\text{or}\quad \min(M_3) \geq \max(M_2)$

That is, the middle machine must be dominated. When the condition holds, form two pseudo-machines:

$G = M_1 + M_2, \qquad H = M_2 + M_3$

and apply the two-machine rule to $G$ and $H$. If the condition fails, no simple optimal rule exists and heuristics or enumeration must be used.

Gantt Charts and Loading

The Gantt chart remains the standard visual scheduling tool, plotting machines or jobs against time as horizontal bars. A load chart shows the workload assigned to each machine against its available capacity, immediately revealing bottlenecks.

Finite loading respects capacity limits and schedules accordingly; infinite loading assigns work regardless of capacity and leaves overloads visible for the planner to resolve. Standard MRP uses infinite loading, which is precisely why capacity requirements planning has to be bolted on to make closed-loop MRP work.

Application to a coal workshop

In a subsidiary's central repair workshop, the mix is characteristically high variety and low volume, with urgent breakdown work interrupting planned overhauls. In that setting, pure SPT would starve the large overhauls indefinitely, while pure FCFS would delay urgent breakdowns. Practice generally uses a critical ratio or slack-based rule, which keeps due dates in view while remaining responsive, with genuine breakdown work given a separate expedite priority.