12.2 Aggregate Planning, Master Production Scheduling (MPS), and MRP

Manufacturing operations rely on a hierarchical production planning architecture to convert corporate business goals into shop-floor fabrication and assembly schedules. Strategic planning dictates multi-year capacity; aggregate planning optimizes monthly workforce and inventory levels; the Master Production Schedule (MPS) establishes specific finished goods delivery targets; and Material Requirements Planning (MRP) coordinates the purchasing and release of every subcomponent.

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1. The Production Planning Hierarchy

Production Planning Hierarchy
 ├── Strategic Business Plan (1–5+ Years, Corporate Strategy & Facility Capital)
 ├── Aggregate Production Plan (3–18 Months, Product Families & Monthly Labor/Inventory)
 │    ├── Resource Requirements Planning (RRP / Rough-Cut Capacity)
 ├── Master Production Schedule (Weeks–Months, Specific Finished SKUs & ATP Quantities)
 │    ├── Rough-Cut Capacity Planning (RCCP / Bottleneck Work Centers)
 ├── Material Requirements Planning (Days–Weeks, Dependent Demand Components & BOM Explosion)
 │    ├── Capacity Requirements Planning (CRP / Machine & Labor Workload)
 └── Shop Floor Control & Purchasing (Hours–Days, Dispatch Lists, POs, Vendor Expediting)

• Independent Demand: Demand for finished goods, replacement spare parts, or service components that originates directly from external customers. Must be forecasted.
• Dependent Demand: Demand for raw materials, subassemblies, and fabricated components that is directly calculated from the production schedule of parent assemblies. Governed strictly by MRP and BOM relationships, never forecasted independently.

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2. Aggregate Production Planning Strategies

Aggregate Planning addresses intermediate-range operations (typically 3 to 18 months in monthly or quarterly buckets). Demand is aggregated into broad product families (e.g., "total gallons of paint" or "total automotive chassis") rather than individual SKUs, aiming to minimize total production costs while satisfying anticipated demand.

Pure Aggregate Planning Strategies

Mathematical Formulation of Aggregate Planning Costs

Total aggregate planning cost over planning horizon $T$ is formulated as:

$\text{TC} = \sum_{t=1}^T \left[ C_{\text{reg}} W_t + C_{\text{OT}} O_t + C_{\text{sub}} S_t + C_{\text{hire}} H_t + C_{\text{lay}} L_t + C_{\text{hold}} I_t + C_{\text{back}} B_t \right]$

where:

• $W_t$ = regular workforce hours (or workers) in period $t$
• $O_t$ = overtime hours worked
• $S_t$ = units subcontracted
• $H_t, L_t$ = number of workers hired and laid off
• $I_t, B_t$ = ending inventory and backorder units in period $t$

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3. The Master Production Schedule (MPS) and Available-to-Promise (ATP)

The Master Production Schedule (MPS) disaggregates the aggregate plan into specific finished end items, exact batch quantities, and weekly time buckets. The MPS forms the binding contract between marketing/sales and manufacturing operations.

Available-to-Promise (ATP) Logic

Available-to-Promise (ATP) represents the uncommitted portion of finished goods inventory and scheduled production maintained in the master schedule. Sales and customer service personnel use ATP to promise realistic delivery dates for incoming customer orders without disrupting the shop floor.

ATP Calculation Convention (Non-Cumulative / Discrete Method)

• For the First Period ($t = 1$): $\text{ATP}_1 = (I_0 + \text{MPS}_1) - \sum_{\tau=1}^{k-1} \text{Booked Orders}_\tau$ where $I_0$ is the beginning on-hand inventory, $\text{MPS}_1$ is the planned production completion in period 1, and booked orders are summed across all periods up to (but not including) the next period $k$ that has a scheduled MPS receipt.

• For Subsequent Periods ($t > 1$ with $\text{MPS}_t > 0$): $\text{ATP}_t = \text{MPS}_t - \sum_{\tau=t}^{m-1} \text{Booked Orders}_\tau$ where booked orders are summed from period $t$ until the next scheduled MPS replenishment period $m$.

• If $\text{MPS}_t = 0$, ATP is typically not calculated for that period (or defined as zero).

MPS Time Fences and Zones

To balance schedule stability against customer responsiveness, companies establish time fences:

Time Fences & Planning Zones
 ├────── Frozen Zone ──────┼────── Slushy Zone ──────┼────── Liquid Zone ──────>
 Current                 Demand                   Planning                  Future
 Time                   Time Fence               Time Fence                 Horizon
 (No changes allowed)   (Trade-offs allowed)     (System auto-generates)

1. Frozen Zone (Inside Demand Time Fence): Near-term schedule. Capacity and materials are committed. No modifications permitted without executive authorization; expediting causes severe shop chaos.
2. Slushy Zone (Between Demand and Planning Time Fences): Intermediate term. Minor volume and product mix trade-offs are permissible if raw materials and capacity constraints permit.
3. Liquid / Open Zone (Beyond Planning Time Fence): Long term. The MRP computer algorithm can freely reschedule, increase, or cancel planned orders based on changing demand forecasts.

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4. Material Requirements Planning (MRP) Structure and Inputs

Material Requirements Planning (MRP) is a computer-based computational engine that explodes the independent demand of the MPS into time-phased dependent demand schedules for every subassembly, component, and raw material required.

MRP System Architecture
 ┌─────────────────────────┐  ┌─────────────────────────┐  ┌─────────────────────────┐
 │ Master Production       │  │ Bill of Materials (BOM) │  │ Inventory Records File  │
 │ Schedule (MPS)          │  │ (Product Structure Tree)│  │ (On-Hand, Lead Times, SS)│
 └───────────┬─────────────┘  └───────────┬─────────────┘  └───────────┬─────────────┘
             │                            │                            │
             └───────────────────────┐    │    ┌───────────────────────┘
                                     ▼    ▼    ▼
                               ┌───────────────────────┐
                               │   MRP Computer Engine  │
                               │  (Explosion & Offsets) │
                               └───────────┬───────────┘
                                           │
                     ┌─────────────────────┴─────────────────────┐
                     ▼                                           ▼
       ┌───────────────────────────┐               ┌───────────────────────────┐
       │ Planned Order Releases    │               │ Secondary Exception       │
       │ (Purchase & Shop Orders)  │               │ Reports (Expedites, Resch)│
       └───────────────────────────┘               └───────────────────────────┘

The Three Core MRP Inputs

1. Master Production Schedule (MPS): Specifies which finished end items will be completed, in what quantities, and in which time buckets.
2. Bill of Materials (BOM): An engineering document detailing the complete hierarchical list of raw materials, parts, and subassemblies required to manufacture one unit of an end item, including precise quantities per assembly.
3. Inventory Records File (Item Master File): Contains real-time inventory status for every part number: physical on-hand inventory, scheduled receipts (open purchase orders already placed), safety stock, purchasing/manufacturing lead time ($L$), and assigned lot-sizing rules.

Product Structure Trees and Low-Level Coding

In a product structure tree, finished end items reside at Level 0. Direct subassemblies reside at Level 1, their child components at Level 2, and basic raw materials at the lowest leaf nodes.

• Low-Level Coding Rule: If an identical part number appears at multiple distinct levels within one product tree—or across several different product trees—it is assigned a low-level code equal to the lowest level (highest numeric index) at which it appears anywhere in the system.
• Why Low-Level Coding is Mandatory: The MRP processing engine explodes requirements level-by-level (Level 0, then Level 1, then Level 2). By assigning a component its lowest level code, the algorithm guarantees that all gross requirements generated by every parent assembly are fully compiled before the system calculates net requirements and releases orders for that component. Without low-level coding, duplicate, disjointed orders would be triggered for the same component.

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5. MRP Record Mechanics and Grid Formulations

For every item in the inventory file, the MRP system maintains a standardized time-phased grid. The row definitions and computational formulas for each period $t$ are:

1. Gross Requirements ($GR_t$): Total anticipated demand for the item during period $t$. For end items, this comes directly from the MPS; for components, it equals the sum of $(PORel \times \text{usage quantity})$ across all parent items.
2. Scheduled Receipts ($SR_t$): Open orders previously released to the shop floor or purchase orders dispatched to outside vendors, legally due to arrive at the beginning of period $t$.
3. Projected Available Balance ($PAB_t$): The expected physical inventory on hand at the end of period $t$: $PAB_t = PAB_{t-1} + SR_t + PORec_t - GR_t$ (where $PAB_0$ is initial on-hand inventory).
4. Net Requirements ($NR_t$): The actual shortage that must be fulfilled in period $t$ to satisfy demand and maintain the mandated safety stock ($SS$): $NR_t = \max\left(0, \; GR_t - PAB_{t-1} - SR_t + SS\right)$
5. Planned Order Receipts ($PORec_t$): The replenishment batch quantity scheduled to arrive at the start of period $t$. If $NR_t > 0$, $PORec_t \ge NR_t$, dictated by the item's lot-sizing rule.
6. Planned Order Releases ($PORel_{t-L}$): The replenishment quantity that must be launched or ordered $L$ periods earlier (where $L$ is lead time) so that it arrives exactly when needed: $PORel_{t-L} = PORec_t$

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6. Lot-Sizing Techniques in MRP

When net requirements are positive ($NR_t > 0$), the lot-sizing rule dictates the order quantity ($PORec_t$):

• Lot-for-Lot (L4L): $PORec_t = NR_t$ Orders exactly what is needed in each period. Eliminates ending inventory ($PAB_t = SS$), driving inventory holding costs to zero. Highly advantageous when setup costs are minimal (Lean/JIT) or when components are expensive and subject to rapid obsolescence. However, if setup costs are significant, L4L incurs severe setup penalties.
• Economic Order Quantity (EOQ): Calculates a constant order quantity $Q^* = \sqrt{2DS/H}$ based on average annualized demand. Whenever $NR_t > 0$, an order of size $Q^$ (or integer multiples if $NR_t > Q^$) is placed. Produces substantial leftover inventory in non-uniform demand environments.
• Periodic Order Quantity (POQ): Converts the calculated EOQ into an equivalent number of periods $P$: $P = \text{round}\left(\frac{Q^*}{\bar{d}}\right)$ Whenever an order is triggered, $PORec_t$ is sized to cover the exact net requirements for the next $P$ periods. Eliminates leftover inventory between orders while reducing order frequency.

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7. Evolution: Closed-Loop MRP, MRP II, and ERP

Evolution of Manufacturing Enterprise Systems
 ┌───────────────────────────┐
 │ Basic MRP                 │ Time-phased material explosion (Materials only, infinite capacity assumption)
 └─────────────┬─────────────┘
               ▼
 ┌───────────────────────────┐ Adds Capacity Requirements Planning (CRP) feedback loop to verify work center
 │ Closed-Loop MRP           │ labor hours and machine capacity before finalizing shop releases
 └─────────────┬─────────────┘
               ▼
 ┌───────────────────────────┐ Integrates operational manufacturing with financial accounting, purchasing,
 │ MRP II (Mfg Resource Plan)│ master business planning, engineering design, and sales forecasting
 └─────────────┬─────────────┘
               ▼
 ┌───────────────────────────┐ Enterprise-wide relational database unifying manufacturing, global supply chains,
 │ ERP (Enterprise Resource) │ human capital, customer relationship management (CRM), and corporate financials
 └───────────────────────────┘

• Closed-Loop MRP: Adds a closed feedback loop via Capacity Requirements Planning (CRP). If planned order releases overload machine work centers, the master schedule is revised before release.
• Manufacturing Resource Planning (MRP II): Broadens closed-loop MRP to integrate all manufacturing resources: tooling, human resource capacity, direct cash flows, capital budgeting, and marketing sales plans.
• Enterprise Resource Planning (ERP): Modular, enterprise-spanning software platforms (SAP, Oracle) built upon unified central relational databases. ERP eliminates data silos across accounting, procurement, human resources, shop operations, and global logistics.

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8. Step-by-Step Worked Engineering Calculations

Worked Example 12.2.1: Aggregate Planning Cost Comparison (Chase vs. Level)

Problem: A manufacturer of commercial power equipment prepares an aggregate plan for the next 4 quarters. Demand forecasts are:

• Q1: 1,000 units
• Q2: 1,400 units
• Q3: 1,800 units
• Q4: 1,000 units

Total demand over the horizon is 5,200 units ($1,300\text{ units/quarter average}$). Initial inventory at the start of Q1 is 0 units, and desired ending inventory at the end of Q4 is 0 units.

Operating parameters:

• Each worker produces 100 units per quarter.
• Current workforce at $t = 0$: 10 workers (producing 1,000 units/quarter).
• Regular time labor cost: $3,000 per worker per quarter.
• Cost to hire a worker: $500.
• Cost to lay off a worker: $800.
• Inventory holding cost: $10 per unit remaining in inventory at the end of a quarter.
• Backorders are strictly prohibited.

Compare the total cost of a Pure Chase Strategy versus a Pure Level Strategy.

Solution:

Plan A: Pure Chase Strategy (Match Demand Exactly Each Quarter)

• Q1: Demand = 1,000 units. Workers needed = $1,000 / 100 = 10$. Current workforce = 10. Hires = 0, Layoffs = 0. Cost = $0$.
• Q2: Demand = 1,400 units. Workers needed = $1,400 / 100 = 14$. Must hire $14 - 10 = 4$ workers. Hiring cost = $4 \times 500 = $2,000$.
• Q3: Demand = 1,800 units. Workers needed = $1,800 / 100 = 18$. Must hire $18 - 14 = 4$ workers. Hiring cost = $4 \times 500 = $2,000$.
• Q4: Demand = 1,000 units. Workers needed = $1,000 / 100 = 10$. Must lay off $18 - 10 = 8$ workers. Layoff cost = $8 \times 800 = $6,400$.
• Total Workforce Adjustment Cost: $2,000 + 2,000 + 6,400 = $10,400$.
• Regular Labor Cost: Total worker-quarters = $10 + 14 + 18 + 10 = 52$ worker-quarters. $\text{Labor Cost} = 52 \times 3,000 = \$156,000$
• Inventory Holding Cost: Ending inventory is 0 at the end of every quarter $\implies $0$.
• Total Chase Cost: $\text{TC}_{\text{chase}} = \$156,000 + \$10,400 + \$0 = \$166,400$

Plan B: Pure Level Strategy (Constant Workforce & Output, Zero Backorders)

• Because backorders are prohibited, the level production rate must be set high enough that cumulative production never falls below cumulative demand. Let us evaluate cumulative demand:
  • End of Q1: 1,000 units
  • End of Q2: $1,000 + 1,400 = 2,400\text{ units}$
  • End of Q3: $2,400 + 1,800 = 4,200\text{ units}$
  • End of Q4: $4,200 + 1,000 = 5,200\text{ units}$
• If we produce the average demand of 1,300 units/quarter ($5,200 / 4$):
  • Cumulative production by Q3 = $3 \times 1,300 = 3,900\text{ units}$. But cumulative demand is 4,200 units! This would cause a 300-unit stockout in Q3.
• To prevent any stockout without backorders, peak cumulative demand occurs in Q3 (4,200 units over 3 quarters), requiring an output rate of at least $4,200 / 3 = 1,400\text{ units/quarter}$!
• Workers required = $1,400 / 100 = 14$ workers constant throughout all 4 quarters.
• Hiring / Layoff Cost: At start of Q1, hire $14 - 10 = 4$ workers: $4 \times 500 = $2,000$. Retained for all 4 quarters; 0 layoffs.
• Regular Labor Cost: $14 \times 4 \times 3,000 = 56 \times 3,000 = $168,000$.
• Quarterly Inventory Tracking:
  • Q1: Produce 1,400, Demand 1,000 $\implies$ Ending Inventory $I_1 = 0 + 1,400 - 1,000 = 400\text{ units}$.
  • Q2: Produce 1,400, Demand 1,400 $\implies$ Ending Inventory $I_2 = 400 + 1,400 - 1,400 = 400\text{ units}$.
  • Q3: Produce 1,400, Demand 1,800 $\implies$ Ending Inventory $I_3 = 400 + 1,400 - 1,800 = 0\text{ units}$.
  • Q4: Produce 1,400, Demand 1,000 $\implies$ Ending Inventory $I_4 = 0 + 1,400 - 1,000 = 400\text{ units}$.
• Inventory Holding Cost: $\text{Holding Cost} = (400 + 400 + 0 + 400) \times \$10 = 1,200 \times 10 = \$12,000$
• Total Level Cost: $\text{TC}_{\text{level}} = \$168,000 + \$2,000 + \$12,000 = \$182,000$
• Cost Difference: The Chase Strategy is more economical by $$182,000 - $166,400 = $15,600$ under these strict no-backorder conditions.

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Worked Example 12.2.2: Available-to-Promise (ATP) Calculation

Problem: An electronics plant schedules production for a high-end industrial router. The current on-hand inventory is 60 units. The master production schedule has planned completions of 200 units in Week 1 and 200 units in Week 4. Customer booked orders are logged as shown below:

Calculate the Available-to-Promise (ATP) quantities for Week 1 and Week 4.

Solution:

Step 1: Calculate ATP for Week 1

• For Week 1 ($t = 1$), ATP incorporates beginning on-hand inventory ($I_0 = 60$) plus the MPS receipt ($ ext{MPS}_1 = 200$).
• Booked customer orders are accumulated across all weeks up to, but not including, the next MPS replenishment week (Week 4). Thus, sum booked orders for Weeks 1, 2, and 3: $\sum \text{Orders} = 90 + 50 + 40 = 180\text{ units}$
• Calculate $\text{ATP}_1$: $\text{ATP}_1 = (I_0 + \text{MPS}_1) - \sum_{\tau=1}^3 \text{Orders}_\tau = (60 + 200) - 180 = 260 - 180 = 80\text{ units}$

Step 2: Calculate ATP for Week 4

• For Week 4 ($t = 4$), a new MPS replenishment of 200 units arrives. On-hand inventory is not added again because it was fully accounted for in Week 1.
• Sum booked customer orders from Week 4 up to the end of the horizon (Weeks 4, 5, and 6): $\sum \text{Orders} = 110 + 30 + 20 = 160\text{ units}$
• Calculate $\text{ATP}_4$: $\text{ATP}_4 = \text{MPS}_4 - \sum_{\tau=4}^6 \text{Orders}_\tau = 200 - 160 = 40\text{ units}$
• Operational Result: Sales representatives can immediately promise up to 80 additional units for delivery anytime in Weeks 1–3, and up to 40 additional units for delivery in Weeks 4–6.

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9. NCEES Reference Handbook Tips & Realistic Exam Traps

• ATP Lookahead Order Summing Trap: In discrete ATP calculations, remember to sum all booked customer orders between the current MPS replenishment and the next MPS replenishment. Do not subtract only the current week's order. For Week 1, subtract booked orders for Weeks 1, 2, and 3!
• On-Hand Inventory in ATP: Beginning on-hand inventory ($I_0$) is added only to the first ATP period ($ ext{ATP}_1$). Never add beginning inventory to subsequent MPS replenishment periods ($ ext{ATP}_4, \text{ATP}_7$, etc.).
• Lead Time Offsetting Direction: Planned Order Receipts occur when the material is needed ($t$). Planned Order Releases occur at $t - L$. A common exam error is adding lead time ($t + L$), which would schedule the release after the assembly is already due!
• Dependent vs. Independent Demand: Never apply statistical forecasting methods (SES, moving average) to subassemblies or component parts with dependent demand. Component demand is strictly exploded mathematically from parent Planned Order Releases via the BOM.
• Low-Level Code Numbering: Level 0 is the top-level finished product. The higher the numeric level code (Level 1, Level 2, Level 3), the lower the part is in the product hierarchy. Low-level coding assigns a shared component its highest numerical level index.