Calculation Questions: Inventory, Capacity & Cost, Solved

Can a endeavor market out all day and motionless be seriously managed? Yes - if it runs alongside excess safety stock, an overloaded bottleneck, or a disbursal construction that lone looks profitable at elevated volume.

Inventory, capability and disbursal questions are not concerning “doing maths fast”. They test whether you can rotate messy operations tongue into the correct variable, the correct equation and a sensible endeavor decision.

• Inventory questions normally ask “how much to order” or “when to reorder”: use EOQ, reorder item and safety inventory logic.
• Capacity questions ask “can the scheme encounter demand”: compute takt time, bottleneck capacity, use and required resources.
• Cost questions ask “which choice is cheaper or viable”: use contribution, break-even, applicable disbursal and make-or-buy comparison.
• Always align units first: per day, per month, per year, per unit, per lot and per machine-hour must not be mixed.
• The answer is not the figure alone: say the decision implied by the figure - order, add capacity, outsource, refuse or renegotiate.
• The safest structure: categorize the question, catalog variables, choose formula, compute cleanly, sanity-check and recommend.

Big Picture: Three Calculations, One Operating Logic

Almost all operations calculation falls into one of three buckets: stock, stream or economics. Inventory protects availability, capability protects throughput and disbursal protects profitability. A powerful answer shows how the three connect.

The Core Mental Model: Translate Words Into Variables

The fastest candidates do not memorize all imaginable question. They place the question type. “Annual petition and ordering cost” points to EOQ. “Units per change and sequence time” points to capacity. “Fixed disbursal and contribution” points to break-even.

Use this 2x2 to decide what benevolent of calculation you are really facing.

The Formula Bank You Actually Need

Do not try to transport 30 formulas. Carry these 12 well. They shield most placement-style operations calculations.

A quick honesty note: “good” values are industry-specific. Grocery, fashion, automotive and dense engineering have extremely distinct inventory turns and use norms. In an interview, benchmark against the business target, assistance flat and petition variability fairly than claiming one worldwide magic number.

Inventory Questions: How Much to Order and When to Reorder

Inventory is inventory held to encounter forthcoming petition or assistance forthcoming production. The trade-off is simple: too small inventory causes stockouts; too much inventory locks prosperity and creates holding cost.

The traditional inventory calculation has two decisions.

1. Order quantity - how many units to command all time.
2. Reorder point - the inventory flat at which a new command have to be placed.

Solved Example 1: EOQ and Reorder Point

A provider sells 12,000 units per year. Ordering disbursal is ₹500 per order. Holding disbursal is ₹20 per component per year. Supplier guide period is 6 days. Average petition is 40 units per day. Safety inventory is 80 units.

Sanity check: if EOQ becomes larger than annual petition or reorder item becomes negative, your units are wrong.

Capacity Questions: Can the System Meet Demand?

Capacity is the maximum sustainable charge at which a scheme can create output or assist demand. In interviews, capability questions normally conceal a bottleneck.

First compute required pace. Then difference it alongside genuine procedure capability. If you desire a deeper plant-floor view, revise line balancing and workstation design following this lesson.

Solved Example 2: Takt Time and Bottleneck Capacity

A packing row must dispatch 720 units in one 8-hour shift. The bottleneck position takes 50 seconds per unit. Ignore breaks for simplicity.

The endeavor insight: the row does not neglect since all position is slow. It fails since the slowest position 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, disbursal questions are normally concerning applicable disbursal - the disbursal that changes since of the decision.

Solved Example 3A: Break-even Volume

A small gathering division has fixed disbursal of ₹3,00,000 per month. Selling cost is ₹500 per unit. Variable disbursal is ₹320 per unit.

Solved Example 3B: Make-or-Buy Decision

A component can be outsourced at ₹160 per unit. Making it in-house expenses ₹120 per component affirmative additional fixed disbursal of ₹80,000 per month.

Good candidates add the caveat: a make-or-buy decision is not lone cost. It additionally depends on norm risk, provider reliability, confidentiality, capability elasticity and operating capital.

Definitions You Can Say in One Breath

• Inventory: inventory of materials, work-in-progress or completed products held for forthcoming use or sale.
• Capacity: the maximum sustainable output charge of a process, asset or scheme complete a defined period.
• Utilization: genuine output divided by scheme capability for the identical period period.
• Efficiency: genuine output divided by productive capacity, normally following planned constraints are considered.
• Break-even point: the output flat anywhere total income equals total cost.
• Little's Law: average inventory equals average stream charge multiplied by average stream time.

Case Study: Trent’s Zudio - Fast Fashion Needs Fast Maths

Zudio shows why retailing operations is not fair merchandising; it is a changeless calculation of inventory depth, shop capability and cost-to-serve.

Zudio, part of Trent, competes in value manner - a category anywhere products must awareness fresh, prices must remain accessible and stores must move inventory quickly. The apparent narrative is assortment and shop experience. The functioning narrative is calculation.

Situation: Value manner stores visage uncertain petition at SKU, size, color and location level. A slow-moving size blocks rack space; a stockout in a fast-moving item loses sales; a crowded shop can decrease conversion equal whenever petition exists.

The move: The functioning logic is to keep inventory decisions near to petition signals, build shop capability about high-throughput categories and authority cost-to-serve tightly. The chief controller is disciplined goods and replenishment economics. Supporting drivers contain shop format simplicity, private-label control, repeatable shop operations and provider coordination.

The lesson: A applicant who says “Zudio wins since it is cheap” gives a shallow answer. A improved operations answer says value pricing plant lone whenever inventory turns, capability per shop and component economics are managed together.

How AI Changes Inventory, Capacity and Cost Calculations

AI does not eliminate formulas. It changes the inputs, speed and circumstance degree rearward those formulas.

1. Inventory: machine-learning forecasts can evaluation petition by SKU, store, day and season, improving reorder points and safety stock. For a deeper next step, peruse using AI for inventory optimisation and replenishment.
2. Capacity: AI can simulate bottlenecks, foretell device downtime and propose change or routing changes before assistance levels break.
3. Cost: AI can run circumstance inspection throughout commodity prices, freight rates, labor preparedness and provider guide times, making make-or-buy answers additional dynamic.

Use ChatGPT or Claude to create 10 custom questions from one company's operations model. Then resolve them manually, and ask the tool to inspect lone your assumptions, units and explanation - not to substitute your calculation.

Interview Relevance

“A storage handles 9,000 orders per day. Picking capability is 1,000 orders per picker per shift, packing capability is 700 orders per packer per change and dispatch capability is 8,000 orders per day. Where is the bottleneck and what would you do?”

Use this answer construction whenever you get an inventory, capability or disbursal calculation.

If the inquiry combines all three areas, resolve in this order: capability first, afterward inventory, afterward cost. There is no item optimizing inventory for petition the scheme cannot serve.

Common Mistake

The most average error is mixing units - annual petition alongside monthly holding cost, regular capability alongside weekly demand, or per-batch disbursal alongside per-unit cost. This expenses candidates since the equation may appearance accurate during the answer is entirely wrong. One-line fix: compose the component beside all figure before you calculate.