Operations Planning: formula sheet

Key formulas

Three levels of operations planning

Strategic (long term) → Tactical (medium term) → Operational (short term)

Time horizon shortens and detail increases as you go down. Authority moves from top to supervisory management.

Core planning questions

What? How much? When? Where? How?

Use as a checklist to define operations planning in any answer.

Strategy to plan chain

Business strategy → Operations strategy → Operations plans → Execution and control

Shows the link between planning and strategy. Add a feedback arrow from control back to planning.

Simple moving average (n periods)

Forecast for next period = (sum of demand of last n periods) ÷ n

Every period in the window has equal weight. A larger n gives a smoother but slower-reacting forecast.

Weighted moving average

Forecast = Σ (weight × demand of that period)

Weights must add up to 1 (or divide by the sum of weights). Give the highest weight to the latest period unless told otherwise.

Exponential smoothing

Ft+1 = α × At + (1 − α) × Ft

α is the smoothing constant, between 0 and 1. At is actual demand and Ft is the earlier forecast for the same period. A higher α gives more weight to recent demand.

Forecast error

Error = Actual demand − Forecast

A positive error means demand was under-forecast.

Mean absolute deviation (MAD)

MAD = Σ |Actual − Forecast| ÷ number of periods

Ignore signs when adding. The method with the lower MAD is more accurate.

Linear regression trend line

Y = a + bX

Y is demand and X is the period or causal variable. a and b are found by the least squares method.

Capacity utilisation

Utilisation = (Actual output ÷ Design capacity) × 100

Shows use of the designed maximum. Always compare with design capacity.

Efficiency

Efficiency = (Actual output ÷ Effective capacity) × 100

Shows performance against the realistic maximum.

Order of capacities

Actual output ≤ Effective capacity ≤ Design capacity

Use this to check that your data and answers make sense.

Capacity from resources

Capacity = Number of machines × Hours available × Output per hour

Use available hours after deducting stated breaks or maintenance.

Capacity required

Capacity required = Forecast demand ÷ (1 − allowance for rejects or losses)

Use when a part of the output is expected to be rejected.

Capacity gap

Gap = Required capacity − Available capacity

A positive gap means shortage. A negative gap means surplus.

Layout matching rule

Low volume + high variety → Process layout; High volume + low variety → Product layout

Medium volume with part families points to cellular layout. Very large, immovable items point to fixed position.

Location choice rule

Choose the site with the lowest total cost and best fit with qualitative factors

Weigh economic factors first, then non-economic factors. Cost-led factors alone can mislead.

Weighted factor score

Score of a site = Σ (weight of factor × rating of site on that factor)

Pick the site with the highest total. Weights should add up to 1 or 100.

Closing inventory

Closing inventory = Opening inventory + Production − Demand

Use for each period under any strategy. If it goes negative, you have a shortage or backlog, unless the question allows it.

Level production per period

Level production = Total demand for the plan ÷ Number of periods

Adjust for opening and required closing stock: (Total demand + Closing stock − Opening stock) ÷ Periods.

Chase production per period

Production in period = Demand in period (adjusted for opening and target closing stock)

Workforce or overtime changes to follow demand.

Total plan cost

Total cost = Production cost + Hiring and layoff cost + Overtime cost + Inventory holding cost + Shortage or subcontracting cost

Include only cost heads the question gives. Compare totals across strategies.

Average inventory carried

Inventory cost = Σ (closing inventory of each period × holding cost per unit per period)

Charge holding cost on closing stock unless the question says to use average stock.

Projected available balance (MPS)

Projected available balance = Previous balance + MPS quantity − Higher of forecast and customer orders

Schedule an MPS lot when the balance would fall below zero (or below safety stock).

Available to promise (ATP)

ATP = Opening stock + MPS quantity − Customer orders until the next MPS receipt

Shows how much can still be promised to new orders.

Gross requirement of a component

Gross requirement = Parent quantity planned × Quantity of component per parent unit

Use this for each BOM level. At lower levels, the parent quantity is the planned order of the item above, not the finished-goods quantity.

Net requirement

Net requirement = Gross requirement − On-hand stock − Scheduled receipts

If the result is zero or negative, no order is needed. Add safety stock to the requirement if the question gives it.

Planned order release date

Order release period = Period the item is needed − Lead time

Offsetting for lead time is done period by period, working backwards from the due date.

MRP flow

MPS + BOM + Inventory records → MRP → Planned orders, reschedule notices, reports

The three inputs and the outputs are common short-answer points.

Flow time of a job

Flow time = Completion time − Arrival (release) time

If all jobs are available at time 0, flow time equals completion time.

Average flow time

Σ Flow times ÷ Number of jobs

SPT gives the minimum on a single machine.

Lateness

Lateness = Completion time − Due date

Negative means early. Tardiness = maximum of (lateness, 0).

Average number of jobs in the system

Σ Flow times ÷ Total processing time (makespan)

Valid when all jobs are available at time 0 and there is no idle time, on one machine. Useful for comparing rules on one machine.

Completion time of a job

Completion time = Sum of processing times of all jobs up to and including it

Valid for one machine with no idle time.

Quick revision

• Operations planning matches resources to expected demand over a stated time horizon.
• Forecasts are rarely exact, so check forecast error when comparing methods.
• Moving average gives equal weight to the chosen past periods; weighted moving average gives more weight to recent ones.
• Exponential smoothing: new forecast = old forecast + α × (actual demand − old forecast).
• Capacity is the maximum output possible in a period; utilisation compares actual output with capacity.
• Location decisions weigh cost, access to market, suppliers, labour and infrastructure.
• Product layout suits high-volume standard goods; process layout suits varied, low-volume work.
• Aggregate planning uses chase, level or mixed strategies to balance output and demand.
• The master production schedule states what to make, how many and when.
• MRP works from the master schedule, bill of materials and inventory records.
• MRP II extends MRP to cover capacity, finance and other resources.
• Sequencing rules such as FCFS, SPT and earliest due date decide job order.

Common mistakes

• Confusing operations planning with operations control. Fix: Planning is deciding in advance. Control is monitoring actual output against the plan and correcting deviations.
• Placing capacity or location decisions at the operational level. Fix: Capacity, location, technology and process choice are strategic. Aggregate plans are tactical. Scheduling and dispatching are operational.
• Treating Delphi and market survey as the same thing. Fix: Delphi uses a panel of experts, anonymous, in repeated rounds with feedback. A market survey asks customers or the market about buying intentions, usually once.
• Using the wrong periods in a moving average. Fix: The forecast for a period uses only the n periods immediately before it.
• Dividing actual output by effective capacity to get utilisation. Fix: Remember: utilisation goes with design capacity, efficiency goes with effective capacity.
• Using different time units for capacity and output. Fix: Convert everything to one period before calculating.
• Mixing up process layout and product layout. Fix: Remember: process layout groups machines by function; product layout arranges them in the sequence of one product.
• Listing location factors without linking them to the business. Fix: Pick the three or four factors that matter most for the case and explain why.
• Treating aggregate planning as item-wise scheduling. Fix: Remember: aggregate plan is for product families over months; the MPS is for specific end items over weeks.
• Showing inventory in a chase plan. Fix: In a pure chase plan, production equals demand, so inventory change is zero unless opening or target stock is given.

Exam tips

• Definition plus levels is the favourite combination. Draw a small three-row table in words: horizon, decision maker, examples.
• In MCQs, check the time horizon first. Long term means strategic, medium term means aggregate or tactical, short term means scheduling.
• Always write one line linking planning to business strategy. It earns marks that many answers miss.
• Use a short Indian business example. It makes a theory answer look applied.
• For 'discuss importance' questions, write separate headed points rather than one long paragraph.
• Theory questions often ask for the difference between Delphi and market survey. Write at least four points in a table-like list: participants, anonymity, rounds, use.
• In numerical questions, show the formula and each period's working. Step marks are given even if the final figure is wrong.
• Keep the roles of qualitative and quantitative methods clear: judgement for new or uncertain situations, data for stable patterns.