Calculation Questions: Inventory, Capacity & Cost, Solved
Can a business sell out every day and still be badly managed? Yes - if it runs with excess safety stock, an overloaded bottleneck, or a cost structure that only looks profitable at high volume.
Inventory, capacity and cost questions are not about “doing maths fast”. They test whether you can turn messy operations language into the right variable, the right formula and a sensible business decision.
- Inventory questions usually ask “how much to order” or “when to reorder”: use EOQ, reorder point and safety stock logic.
- Capacity questions ask “can the system meet demand”: calculate takt time, bottleneck capacity, utilization and required resources.
- Cost questions ask “which option is cheaper or viable”: use contribution, break-even, relevant cost and make-or-buy comparison.
- Always align units first: per day, per month, per year, per unit, per batch and per machine-hour must not be mixed.
- The answer is not the number alone: say the decision implied by the number - order, add capacity, outsource, reject or renegotiate.
- The safest structure: classify the question, list variables, choose formula, calculate cleanly, sanity-check and recommend.
Big Picture: Three Calculations, One Operating Logic
Almost every operations calculation falls into one of three buckets: stock, flow or economics. Inventory protects availability, capacity protects throughput and cost protects profitability. A strong answer shows how the three connect.
The Core Mental Model: Translate Words Into Variables
The fastest candidates do not memorize every possible question. They spot the question type. “Annual demand and ordering cost” points to EOQ. “Units per shift and cycle time” points to capacity. “Fixed cost and contribution” points to break-even.
Use this 2x2 to decide what kind of calculation you are really facing.
The Formula Bank You Actually Need
Do not try to carry 30 formulas. Carry these 12 well. They cover most placement-style operations calculations.
A quick honesty note: “good” values are industry-specific. Grocery, fashion, automotive and heavy engineering have very different inventory turns and utilization norms. In an interview, benchmark against the company target, service level and demand variability rather than claiming one universal magic number.
Inventory Questions: How Much to Order and When to Reorder
Inventory is stock held to meet future demand or support future production. The trade-off is simple: too little stock causes stockouts; too much stock locks cash and creates holding cost.
The classic inventory calculation has two decisions.
- Order quantity - how many units to order each time.
- Reorder point - the inventory level at which a new order should be placed.
Solved Example 1: EOQ and Reorder Point
A distributor sells 12,000 units per year. Ordering cost is ₹500 per order. Holding cost is ₹20 per unit per year. Supplier lead time is 6 days. Average demand is 40 units per day. Safety stock is 80 units.
Sanity check: if EOQ becomes larger than annual demand or reorder point becomes negative, your units are wrong.
Capacity Questions: Can the System Meet Demand?
Capacity is the maximum sustainable rate at which a system can produce output or serve demand. In interviews, capacity questions usually hide a bottleneck.
First calculate required pace. Then compare it with actual process capability. If you want a deeper plant-floor view, revise line balancing and workstation design after this lesson.
Solved Example 2: Takt Time and Bottleneck Capacity
A packing line must dispatch 720 units in one 8-hour shift. The bottleneck station takes 50 seconds per unit. Ignore breaks for simplicity.
The business insight: the line does not fail because every station is slow. It fails because the slowest station sets the output ceiling.
Cost Questions: Which Option Actually Makes Money?
Cost is the monetary value of resources consumed to produce, move or serve. In operations interviews, cost questions are usually about relevant cost - the cost that changes because of the decision.
Solved Example 3A: Break-even Volume
A small assembly cell has fixed cost of ₹3,00,000 per month. Selling price is ₹500 per unit. Variable cost is ₹320 per unit.
Solved Example 3B: Make-or-Buy Decision
A component can be outsourced at ₹160 per unit. Making it in-house costs ₹120 per unit plus additional fixed cost of ₹80,000 per month.
Good candidates add the caveat: a make-or-buy decision is not only cost. It also depends on quality risk, supplier reliability, confidentiality, capacity flexibility and working capital.
Definitions You Can Say in One Breath
- Inventory: stock of materials, work-in-progress or finished goods held for future use or sale.
- Capacity: the maximum sustainable output rate of a process, asset or system over a defined period.
- Utilization: actual output divided by design capacity for the same time period.
- Efficiency: actual output divided by effective capacity, usually after planned constraints are considered.
- Break-even point: the output level where total revenue equals total cost.
- Little's Law: average inventory equals average flow rate multiplied by average flow time.
Case Study: Trent’s Zudio - Fast Fashion Needs Fast Maths
Zudio shows why retail operations is not just merchandising; it is a constant calculation of inventory depth, store capacity and cost-to-serve.
Zudio, part of Trent, competes in value fashion - a category where products must feel fresh, prices must stay accessible and stores must move stock quickly. The visible story is assortment and store experience. The operating story is calculation.
Situation: Value fashion stores face uncertain demand at SKU, size, colour and location level. A slow-moving size blocks shelf space; a stockout in a fast-moving item loses sales; a crowded store can reduce conversion even when demand exists.
The move: The operating logic is to keep inventory decisions close to demand signals, build store capacity around high-throughput categories and control cost-to-serve tightly. The primary driver is disciplined merchandise and replenishment economics. Supporting drivers include store format simplicity, private-label control, repeatable store operations and supplier coordination.
The lesson: A candidate who says “Zudio wins because it is cheap” gives a shallow answer. A better operations answer says value pricing works only when inventory turns, capacity per store and unit economics are managed together.
How AI Changes Inventory, Capacity and Cost Calculations
AI does not remove formulas. It changes the inputs, speed and scenario depth behind those formulas.
- Inventory: machine-learning forecasts can estimate demand by SKU, store, day and season, improving reorder points and safety stock. For a deeper next step, read using AI for inventory optimisation and replenishment.
- Capacity: AI can simulate bottlenecks, predict machine downtime and recommend shift or routing changes before service levels break.
- Cost: AI can run scenario analysis across commodity prices, freight rates, labour availability and supplier lead times, making make-or-buy answers more dynamic.
Use ChatGPT or Claude to generate 10 practice questions from one company's operations model. Then solve them manually, and ask the tool to check only your assumptions, units and interpretation - not to replace your calculation.
Interview Relevance
“A warehouse handles 9,000 orders per day. Picking capacity is 1,000 orders per picker per shift, packing capacity is 700 orders per packer per shift and dispatch capacity is 8,000 orders per day. Where is the bottleneck and what would you do?”
Use this answer structure whenever you get an inventory, capacity or cost calculation.
If the question combines all three areas, solve in this order: capacity first, then inventory, then cost. There is no point optimizing inventory for demand the system cannot serve.
Common Mistake
The most common error is mixing units - annual demand with monthly holding cost, daily capacity with weekly demand, or per-batch cost with per-unit cost. This costs candidates because the formula may look correct while the answer is completely wrong. One-line fix: write the unit beside every number before you calculate.