6.2 Aggregate Planning Strategies & Master Production Scheduling (MPS)

Aggregate Planning Strategies & Master Production Scheduling (MPS)

Core Principle: Industrial operations link high-level corporate strategy to day-to-day manufacturing through a multi-tiered planning hierarchy. Aggregate Sales & Operations Planning (S&OP) establishes intermediate capacity and workforce policies, which are disaggregated into end-item Master Production Schedules (MPS) and validated through Rough-Cut Capacity Planning (RCCP).

Manufacturing organizations cannot make optimal shop-floor operational decisions in isolation from strategic corporate plans. If an operations facility reacts to daily demand spikes without an intermediate aggregate plan, it faces oscillating hiring cycles, excessive overtime, elevated inventory carrying expenses, and frequent delivery stockouts. Aggregate planning coordinates marketing projections, financial targets, and operational capabilities across a rolling medium-term planning horizon.

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1. The Production Planning Hierarchy

Production planning operates across a structured, multi-echelon hierarchy where time horizons compress and product granularity increases as planning moves closer to shop-floor execution:

Production Planning & Execution Hierarchy

[Strategic Business Plan] (2-5 Years)
  │  Corporate strategy, capital investment, facility locations
  ▼
[Aggregate Sales & Operations Plan (S&OP)] (3-18 Months)
  │  Product families, aggregate labor hours, baseline output rates
  ▼
[Master Production Schedule (MPS)] (1-6 Months)
  │  Specific finished end-items (SKUs), weekly/daily buckets
  ├── [Rough-Cut Capacity Planning (RCCP)] (Checks bottleneck capacity)
  ▼
[Material Requirements Planning (MRP)] (1-12 Weeks)
  │  Component BOM explosion, purchase orders, shop work orders
  ├── [Capacity Requirements Planning (CRP)] (Validates work center loads)
  ▼
[Shop-Floor Dispatching & Execution] (Days / Hours)
  │  Priority dispatching rules (FIFO, SPT, EDD), machine loading

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2. Aggregate Planning Strategies: Chase, Level, and Hybrid

Aggregate planning balances anticipated demand against available operational capacity. When demand fluctuates across seasons, management selects from two pure boundary strategies or deploys a hybrid mixed strategy.

Chase vs Level Production Profiles

Units ^
      |              /\  <-- Customer Demand Profile
      |             /  \
      |   ---------/----
      |  |        /      \         [Chase Strategy: Matches Demand Exactly]
      |  |       /        \        [Level Strategy: Flat Output Rate (===)]
      |  |==========================  Level Production Rate (P_avg)
      |  |     /            \
      |  |    /              \   <-- Excess Inventory Accumulated (Holding Cost)
      |  |   /                \   <-- Backorders / Stockouts Incurred (Shortage Cost)
      +--+---------------------------------------------> Time (Months)

1. Pure Chase Strategy

In a Chase Strategy, production output in each period $t$ is set to equal forecasted demand $D_t$ exactly ($P_t = D_t$):

• Mechanisms: The workforce is dynamically adjusted through aggressive hiring and firing, or plant work hours are modulated via variable workweeks.
• Inventory Impact: Finished-goods inventory is held at or near zero ($I_t \approx 0$), eliminating inventory holding costs and warehouse space requirements.
• Cost Drivers: Severe hiring, onboarding, training, and severance expenses. High workforce turnover reduces operator morale, degrades process capability, and increases product defect rates.
• Application: Suitable for non-storable products (e.g., commercial airlines, fast food, custom made-to-order capital equipment) or industries where carrying costs are prohibitive.

2. Pure Level Strategy

In a Level Strategy, the production rate is held strictly constant in every period at the average demand rate ($P_t = \bar{P} = \frac{\sum D_t}{N}$), maintaining an entirely stable workforce:

• Mechanisms: The workforce remains unchanged. When demand is below $\bar{P}$ (demand troughs), the excess production accumulates as finished-goods inventory. When demand exceeds $\bar{P}$ (demand peaks), inventory buffers are depleted to fulfill customer orders.
• Inventory Impact: Significant inventory holding costs accumulate during off-peak periods. If demand exceeds accumulated stock, backorders, customer delays, or lost sales occur.
• Cost Drivers: Finished goods carrying costs, warehouse storage, insurance, capital costs, and potential shortage/stockout penalties.
• Application: High-capital, automated, or continuous-flow industries (e.g., petroleum refining, semiconductor fabrication, chemicals) where adjusting workforce size is impractical or specialized skilled labor cannot easily be hired.

3. Hybrid / Mixed Strategies

Real-world manufacturing systems utilize Hybrid (Mixed) Strategies, combining workforce stability with tactical flexibility:

• Maintaining a baseline core permanent workforce sized for minimum baseline demand.
• Utilizing scheduled overtime ($OT$) or undertime during moderate fluctuations.
• Engaging subcontractors ($SC$) or third-party contract manufacturers to absorb extreme peak surges without expanding permanent facility infrastructure.

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3. Mathematical Optimization of Aggregate Planning

Aggregate planning can be formulated as a Linear Programming (LP) model to identify the minimum-cost production plan over an $N$-period horizon.

LP Decision Variables (for Period $t = 1, \dots, N$)

• $W_t$: Workforce level (number of equivalent full-time workers).
• $H_t$: Number of workers hired at the start of period $t$.
• $L_t$: Number of workers laid off at the start of period $t$.
• $P_t$: Units produced on regular time.
• $O_t$: Units produced on overtime.
• $S_t$: Units acquired via subcontracting.
• $I_t$: Finished-goods inventory held at the end of period $t$.
• $B_t$: Unfulfilled backordered units at the end of period $t$.

Objective Function (Minimize Total System Cost)

$\min Z = \sum_{t=1}^N \left( c_r P_t + c_o O_t + c_s S_t + c_h H_t + c_l L_t + c_i I_t + c_b B_t \right)$

Where:

• $c_r$: Regular-time direct production cost per unit.
• $c_o$: Overtime production cost per unit.
• $c_s$: Subcontracting cost per unit.
• $c_h$: Cost to hire and train one worker.
• $c_l$: Cost to lay off one worker.
• $c_i$: Inventory holding cost per unit per period.
• $c_b$: Backorder shortage cost per unit per period.

System Constraints

1. Workforce Balance Constraint:

$W_t = W_{t-1} + H_t - L_t, \quad \forall t$

1. Regular-Time Production Capacity Constraint: (Assuming each worker contributes $K$ labor-hours per period and each product requires $k$ labor-hours):

$P_t \le \frac{K}{k} W_t, \quad \forall t$

1. Overtime Capacity Constraint: (Overtime is restricted to a fraction $\gamma$ of regular hours):

$O_t \le \gamma \left(\frac{K}{k} W_t\right), \quad \forall t$

1. Inventory & Backorder Flow Conservation:

$I_{t-1} - B_{t-1} + P_t + O_t + S_t - D_t = I_t - B_t, \quad \forall t$

1. Non-negativity Bounds:

$W_t, H_t, L_t, P_t, O_t, S_t, I_t, B_t \ge 0, \quad \forall t$

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4. Master Production Schedule (MPS) Mechanics & Time Fences

The Master Production Schedule (MPS) translates aggregate planning product family targets into specific, time-phased manufacturing batches for independent-demand finished items.

Time Fences and Planning Horizons

To balance manufacturing stability against market flexibility, the MPS planning horizon is divided into three distinct zones demarcated by time fences:

MPS Time Fences & Operational Zones

Today               Demand Time Fence (DTF)     Planning Time Fence (PTF)
  │                         │                           │
  ▼                         ▼                           ▼
┌───────────────────────────┬───────────────────────────┬───────────────────────────┐
│        FROZEN ZONE        │        SLUSHY ZONE        │        LIQUID ZONE        │
│  - Customer orders rule   │  - Trade-offs allowed     │  - Forecast rules         │
│  - Zero unauthorized mod  │  - Material committed     │  - Free optimization      │
│  - Emergency changes only │  - Mix changes permitted  │  - Long-range procurement │
└───────────────────────────┴───────────────────────────┴───────────────────────────┘
<------ Near-Term ---------> <------ Intermediate -----> <------- Long-Term -------->

1. Frozen Zone (Near-term, e.g., Weeks 1–3): Inside the Demand Time Fence (DTF). Production batches are already released to the shop floor or in setup. Demand is driven entirely by booked customer orders, not forecasts. Schedule changes are strictly prohibited without executive authorization because disruptions cause component shortages and scrap.
2. Slushy Zone (Intermediate, e.g., Weeks 4–8): Between the Demand Time Fence and the Planning Time Fence (PTF). Long lead-time raw materials are ordered, but capacity allocation can shift between product variations. Changes in product mix are allowed if total capacity is preserved.
3. Liquid Zone (Long-term, e.g., Weeks 9–24): Beyond the Planning Time Fence. The schedule is driven primarily by statistical forecasts. Schedulers have complete freedom to optimize batch sizes and reallocate capacity.

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5. Available-to-Promise (ATP) Mathematics

Available-to-Promise (ATP) is the uncommitted portion of a company's finished inventory and planned production, maintained in the MPS to support sales order promising. When a sales representative receives a customer order, the ATP value dictates whether delivery can be confirmed immediately without disrupting existing commitments.

Projected Available Balance (PAB)

Before calculating ATP, the Projected Available Balance (PAB) tracks anticipated inventory across time buckets:

• Prior to the Demand Time Fence (Inside Frozen Zone): Demand is determined strictly by committed Customer Orders ($CO$):

$PAB_t = PAB_{t-1} + MPS_t - CO_t$

• Beyond the Demand Time Fence (Slushy/Liquid Zones): Schedulers take the conservative maximum between forecast ($F_t$) and committed customer orders ($CO_t$):

$PAB_t = PAB_{t-1} + MPS_t - \max(F_t, CO_t)$

Discrete Available-to-Promise (ATP) Formulas

Under standard discrete ATP logic (without lookahead consumption):

1. For the First Period ($t = 1$): Includes starting on-hand inventory ($I_0$):

$ATP_1 = I_0 + MPS_1 - \sum_{k=1}^{m-1} CO_k$

Where $m$ is the index of the next period in which an $MPS$ replenishment receipt occurs ($MPS_m > 0$). Customer orders are summed across all periods up to the next replenishment.

1. For Subsequent Periods with an MPS Receipt ($MPS_t > 0$): Inventory carried from prior periods is already committed to earlier orders, so ATP depends solely on the new production batch:

$ATP_t = MPS_t - \sum_{k=t}^{m-1} CO_k$

Where customer orders $CO_k$ are summed from period $t$ up to, but not including, the next period $m$ with an $MPS$ receipt.

1. For Periods Without an MPS Receipt ($MPS_t = 0$):

$ATP_t = 0$

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6. Worked Numerical Example: MPS and ATP Calculation

An industrial manufacturer schedules production of an automated hydraulic manifold. The operational parameters are:

• Starting On-Hand Inventory: $I_0 = 60$ units.
• Fixed MPS Batch Lot Size: $150$ units.
• Demand Time Fence (DTF): End of Week 2.
• Planning Horizon: 6 Weeks.

Schedule Data

Step-by-Step Mathematical Calculation

1. Projected Available Balance (PAB):

• Week 1 (Inside DTF): $PAB_1 = I_0 + MPS_1 - CO_1 = 60 + 0 - 48 = 12$
• Week 2 (Inside DTF): $PAB_2 = PAB_1 + MPS_2 - CO_2 = 12 + 150 - 35 = 127$
• Week 3 (Beyond DTF): $\max(F_3, CO_3) = \max(60, 30) = 60$. $PAB_3 = PAB_2 + MPS_3 - \max(F_3, CO_3) = 127 + 0 - 60 = 67$
• Week 4 (Beyond DTF): $\max(F_4, CO_4) = \max(60, 18) = 60$. $PAB_4 = PAB_3 + MPS_4 - \max(F_4, CO_4) = 67 + 150 - 60 = 157$
• Week 5 (Beyond DTF): $\max(F_5, CO_5) = \max(50, 10) = 50$. $PAB_5 = PAB_4 + MPS_5 - \max(F_5, CO_5) = 157 + 0 - 50 = 107$
• Week 6 (Beyond DTF): $\max(F_6, CO_6) = \max(50, 5) = 50$. $PAB_6 = PAB_5 + MPS_6 - \max(F_6, CO_6) = 107 + 150 - 50 = 207$

2. Available-to-Promise (ATP):

• Week 1 ($t = 1$): Starting stock $I_0 = 60$. The next MPS receipt occurs at Week 2 ($m = 2$). $ATP_1 = I_0 + MPS_1 - CO_1 = 60 + 0 - 48 = 12 \text{ units}$
• Week 2 ($t = 2$): $MPS_2 = 150$. The next MPS receipt occurs at Week 4 ($m = 4$). We sum customer orders for Week 2 and Week 3: $ATP_2 = MPS_2 - (CO_2 + CO_3) = 150 - (35 + 30) = 150 - 65 = 85 \text{ units}$
• Week 3 ($t = 3$): No MPS replenishment ($MPS_3 = 0$), so $ATP_3 = 0$.
• Week 4 ($t = 4$): $MPS_4 = 150$. The next MPS replenishment occurs at Week 6 ($m = 6$). We sum customer orders for Week 4 and Week 5: $ATP_4 = MPS_4 - (CO_4 + CO_5) = 150 - (18 + 10) = 150 - 28 = 122 \text{ units}$
• Week 5 ($t = 5$): No MPS replenishment ($MPS_5 = 0$), so $ATP_5 = 0$.
• Week 6 ($t = 6$): $MPS_6 = 150$. No further replenishment is scheduled within the horizon. Subtract $CO_6$: $ATP_6 = MPS_6 - CO_6 = 150 - 5 = 145 \text{ units}$

Master Production Schedule Master Table

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7. Rough-Cut Capacity Planning (RCCP)

Before releasing the Master Production Schedule to MRP, the proposed schedule must be validated against critical facility constraints via Rough-Cut Capacity Planning (RCCP). RCCP prevents the company from committing to an infeasible MPS that would bottleneck key work centers.

Three RCCP Methodologies

1. Capacity Planning using Overall Factors (CPOF): The simplest macro-level method. Takes total direct labor or machine hours required per finished unit and allocates them across work centers based on historical percentage usage.
2. Bill of Resources (Capacity Bills): Utilizes the detailed engineering standard hours required at each specific bottleneck work center per unit of product, multiplying MPS batch sizes by work center standard hours. It assumes all capacity is consumed in the completion period (ignoring lead times).
3. Resource Profile Approach: The most sophisticated RCCP method. Incorporates operation lead-time offsets, mapping exactly when hours will hit each work center prior to final product delivery.

If RCCP detects that required load exceeds available rated capacity at a bottleneck resource, schedulers resolve the infeasibility by authorizing planned overtime, advancing lot production to earlier open periods, subcontracting components, or shifting mix within the slushy zone.