Exercises: Procurement and inventory management

Explain what inventory (or stock) is and what purpose it serves for a business. Then classify these inventory items for a bicycle manufacturer as raw materials, work in progress, or finished goods: aluminium sheets, half-assembled bicycles on the assembly line, packaged bicycles ready for dispatch, and spare tyres for technical service.

Holding inventory generates three types of costs: holding/storage costs, ordering costs, and stockout costs. Assign each situation to its cost type: paying warehouse rent, transport and paperwork for each supplier order, a customer switching to a competitor because of a stockout, and warehouse insurance and security. Explain why lowering stock levels reduces certain costs but increases the risk of another.

The figure shows how the stock level of an item evolves in a distributor's warehouse: when an order arrives, the level jumps up and then decreases at a constant rate due to sales. Each order is for 400 units, and the business always maintains a minimum reserve of 100 units (the green line). a) Calculate the maximum stock level reached by the warehouse, marked with "?". b) Explain the purpose of this reserve and the risk the business faces if the supplier is delayed and there is no reserve.

Explain what a business's procurement function consists of (buying and storing what is needed to produce or sell) and what two basic questions it must answer: how much to order and when to order it. Apply it to a school canteen that buys soft drinks every week.

Explain what safety stock is and what the reorder point is, and relate them: why the order must be placed before reaching the safety stock if the supplier takes a few days to deliver. Illustrate it with a stationery shop that sells about 20 backpacks a week and whose supplier takes two weeks to deliver.

Explain what a stockout is and what consequences it has for an online shop (lost sale, customer who does not come back, bad review) and for a factory (production line stopped, workers unable to work). Give an everyday example in which you, as a customer, have suffered a stockout and say what you did.

A car dealership has cars worth $2.000.000\ \text{€}$ on display. Explain what it means that this stock is "tied-up money": what costs it generates even though the cars are standing still (storage, insurance, deterioration, interest on money that is not available) and why it is in the company's interest for the stock to rotate quickly.

State what type of inventory (raw materials, work in progress, finished goods, spare parts or merchandise) each business mainly handles and give a specific example of each: a bakery, a shipyard that takes two years to build a ship, a clothing shop and an official washing machine repair service.

A furniture shop sells 2 000 bookcases of the same model per year. Each order to the supplier costs $10\ \text{€}$ including transport and administration, and holding one bookcase in the warehouse costs $1\ \text{€}$ per year. Wilson's Economic Order Quantity (EOQ) model gives the optimal order quantity: $Q = \sqrt{\frac{2 \cdot D \cdot K}{g}}$, where $D$ is the annual demand, $K$ is the ordering cost, and $g$ is the holding cost per unit per year. a) Calculate the optimal order quantity. b) Calculate how many orders will be placed per year and approximately every how many days an order will be received.

An electrical supplies warehouse records these inventory movements for a cable model: opening stock of 100 coils at $4\ \text{€}$ each; then it purchases 200 coils at $7\ \text{€}$ each; finally, it sells 150 coils. a) Calculate the value of ending inventory using the weighted average cost method (AVCO / PMP). b) Calculate it using the FIFO method (first in, first out). c) Explain why the two results differ and which method gives a higher warehouse valuation when purchase prices are rising.

A business requires a component each year that it can buy from a supplier at $9\ \text{€}$ per unit or manufacture itself by incurring annual fixed costs of $42.000\ \text{€}$ and a variable cost per unit of $3\ \text{€}$. a) Formulate the annual cost of each option in terms of the quantity $q$. b) Calculate the annual volume above which it becomes worthwhile to make rather than buy (indifference point). c) If it anticipates needing 10 000 components per year, decide what action to take and justify your decision.

A toy shop sells 1 800 board games a year of the same title. Each order to the distributor costs it $8\ \text{€}$ and keeping one game in storage costs $2\ \text{€}$ a year (recall Wilson's EOQ model: $Q = \sqrt{\frac{2 \cdot D \cdot K}{g}}$). a) Calculate the optimal order quantity. b) Calculate how many orders it will place per year and approximately every how many days it will receive one. c) The distributor proposes delivering in fixed batches of 400 games: reason, comparing the ordering and storage costs, why moving away from the optimal order quantity can make management more expensive.

A stationery shop's warehouse records these movements of a calculator model in March: 50 units come in at $10\ \text{€}$ per unit; 30 are sold; 40 units come in at $16\ \text{€}$; 35 are sold. a) Build the warehouse record using the weighted average cost method (AVCO / PMP), with the columns for entries, issues and stock (quantity, price and value). b) Calculate the value of the ending inventory.

A computer shop's warehouse records these movements of an external hard drive: opening stock of 60 units at $40\ \text{€}$ per unit; 40 are sold; 60 units are bought at $50\ \text{€}$; 60 are sold. a) Build the warehouse record using the FIFO method (entries, issues and stock, with quantity, price and value). b) Calculate the value of the ending inventory using FIFO. c) Calculate that same value using the weighted average cost method and explain what the difference is due to.

A pharmacy sells about 15 boxes a day of a sunscreen in high demand in summer, and the laboratory takes 4 days to deliver each order. The pharmacy wants to keep a safety stock of 30 boxes. a) Calculate the reorder point: the stock level at which it must place the order so as not to run out of product. b) Explain what would happen if the laboratory started taking 8 days and the pharmacy did not recalculate the reorder point.

A bicycle shop wants to apply the ABC method, which classifies items according to their annual usage value (units sold multiplied by their price), to decide where to put the most care into stock control. These are four of its items: electric bicycles (40 units at $1.500\ \text{€}$), helmets (300 units at $50\ \text{€}$), locks (500 units at $20\ \text{€}$) and inner tubes (2 000 units at $5\ \text{€}$). a) Calculate the annual value of each item and the total value. b) Calculate what percentage of the total value each one represents. c) Propose a reasoned A/B/C classification and explain which item you would watch most closely.

The new purchasing manager of an industrial hardware store reviews six product families to optimize the capital tied up in the warehouse:

• Professional drills: 120 units/year at 250\ \text{€}/unit.

• Standard drill bits: 3 000 units/year at 2\ \text{€}/unit.

• Grinders: 150 units/year at 120\ \text{€}/unit.

• Industrial screws: 50 000 units/year at 0,10\ \text{€}/unit.

• Electric saws: 80 units/year at 180\ \text{€}/unit.

• Work gloves: 4 000 pairs/year at 1,50\ \text{€}/pair.

To reduce operating costs, he proposes: “Let's do weekly physical counts and strict batch-by-batch negotiation for screws and drill bits, since together they total 53 000 units and occupy most of the warehouse. In contrast, for drills and grinders, it is enough to place a massive semi-annual order so we don't have to worry about them and can save on ordering costs.”

1. a) Develop the ABC classification for these items by calculating the annual consumption value, the percentages of total investment, and the cumulative percentages.
2. b) Refute the manager's proposal with technical and quantitative arguments: demonstrate what mistake he makes by confusing physical volume with economic relevance, and explain the financial risk his decision entails.
3. c) Design a differentiated logistics management proposal for Type A families compared to Type C families, detailing and justifying: inventory frequency, safety stock policy, and contractual relationship with suppliers.

A heat pump manufacturer located in Zaragoza operates under the Just in Time (JIT) system, receiving microchips from Taiwan and compressors from Germany directly onto the assembly line with daily deliveries. Following a maritime transport strike and border crossing blockades, the plant had to shut down production for 15 days, incurring fixed downtime costs of 20 000\ \text{€} per day and contractual delay penalties of 120 000\ \text{€}.

The financial management proposes abandoning JIT entirely and switching to a traditional mass procurement model, renting an additional warehouse to accumulate a safety stock equivalent to four months for all components.

1. a) Evaluate the financial management's proposal: justify why switching to mass storage can trade one set of problems for others just as serious, identifying at least three costs or risks arising from that accumulation (financial, obsolescence, and operational).
2. b) Analyze the existing contradictions between the company's current supply chain (geographic origin of the components) and the indispensable conditions required for JIT to function without collapsing.
3. c) Design a hybrid and resilient logistics strategy for this company: determine which components should be managed under JIT principles through proximity agreements (nearshoring) and which ones through safety stocks or vendor-managed inventory (VMI), justifying the decision criteria.

An animal feed distributor sells 2.500 bags per year of its flagship product at a purchase price of 18\ \text{€}/bag. The administrative and transport cost of placing each order is 25\ \text{€}, and the annual holding cost of each bag is estimated at 2\ \text{€}. The company operates 250 working days per year and the manufacturer's average delivery lead time is 6 days.

The manufacturer offers a commercial discount of 3\ % on the unit price if orders are for at least 500 bags. However, the distributor's warehouse only has capacity for 350 bags; if it accepts orders of 500 bags, it must subcontract space in an adjacent warehouse at a rate of an additional 1,20\ \text{€} per bag stored per year on the totality of the average stock.

1. a) Determine the initial optimal order quantity according to the Wilson model and calculate the reorder point needed if the distributor establishes a safety stock of 20 bags.
2. b) Calculate and compare the total annual inventory cost (acquisition cost + ordering cost + holding cost) under the standard optimal policy versus accepting the offer of 500 bags with subcontracted space.
3. c) Provide a justified assessment of whether it is advantageous for the distributor to accept the volume discount. What qualitative risk variables (product expiration, available liquidity) would you warn management about before making the final decision?

A beverage distributor sells 10.000 cases per year of a soft drink. Its logistics department applies a rigid policy of always ordering batches of 1.000 cases because it «makes the monthly balancing with the trucks easier». Each order generates an ordering cost of 50\ \text{€} and holding a case stored for one year costs 4\ \text{€} (financing costs, waste/spoilage, and refrigeration).

1. a) Demonstrate analytically that the 1.000-case batch does not minimize costs: calculate the optimal order quantity according to the Wilson model and quantify the total annual extra cost (ordering cost plus holding cost) incurred by the company for maintaining its fixed policy compared to the mathematical optimum.
2. b) Explain the opposing behavior of the ordering cost and holding cost curves, and justify why at Wilson's optimal batch size both annual costs must coincide exactly.
3. c) Assume that an increase in interest rates and electricity prices raises the annual holding cost to 6\\ \\text{€}/case, while the implementation of a digital ordering system reduces the ordering cost to 25\\ \\text{€} per order. Predict quantitatively how the batch size and the number of orders per year should be readjusted, and deduce what general procurement rule the company should adopt in this new economic environment.

An oil distributor begins the financial year with zero inventory and carries out the following operations in a quarter marked by strong inflationary pressures:

• January: purchases 1.000 liters at 3\ \text{€}/l.

• February: purchases 1.000 liters at 5\ \text{€}/l.

• March: sells 1.200 liters at 8\ \text{€}/l.

The majority shareholder insists on valuing inventories using the FIFO method in order to «show the highest possible profit to the bank and distribute dividends», while the financial director demands applying the WAP to «protect the solvency and liquidity of the company».

1. a) Determine the value of ending inventory and the cost of goods sold at the end of the quarter applying both the Weighted Average Price (WAP) method and the FIFO method.
2. b) Prepare the condensed income statement (sales revenue, cost of goods sold, profit before tax, and net profit with a corporate income tax rate of 25\\ %) under each method.
3. c) Critically assess both positions: justify why the FIFO method creates a «financial illusion» or fictitious profit during periods of inflation, quantify the direct tax impact of choosing FIFO over WAP, and reason which method leaves the company better prepared to face the replacement of the stock sold at the current market price (5\\ \\text{€}/l).

An automotive plant located in Zaragoza assembles dashboards. It uses two main inputs:

• Electronic microcontrollers: imported from Malaysia, with a maritime shipping time of 8 weeks, a minimum import batch, and a cost of 90\ \text{€}/unit.

• Injected plastic moldings: supplied by a manufacturer located in the same industrial park 5 km away, with three daily deliveries using synchronized carts and a cost of 8\ \text{€}/unit.

Operations management has ordered the strict application of the Just in Time «zero inventory» principle to both components equally starting next month, eliminating all buffer warehouses.

1. a) Evaluate the technical and operational feasibility of management's order. Justify which fundamental JIT requirements are met in one case and blatantly violated in the other.
2. b) Analyze the financial and operational consequences that the factory would suffer if the container ship from Malaysia experienced a 10-day delay due to weather or customs incidents under the «zero inventory» policy.
3. c) Design a comprehensive procurement proposal for both components: reasonably assign an inventory management model to each (pure JIT, traditional Wilson with safety stock, or advanced vendor warehousing agreements) and propose measures to mitigate dependency on distant suppliers.

A retail chain sells 12.500 jugs per year of engine lubricant. Its regular supplier invoices them at 20\ \text{€} per unit; each order costs 40\ \text{€} in administrative and transport expenses, and the annual holding cost per jug is 1\ \text{€}. The delivery lead time is 2 days, so the company only needs to maintain a safety stock of 50 jugs.

A new wholesale supplier offers a price of 19,70\ \text{€}/jug (a saving of 0,30\ \text{€} per unit). However, being farther away, its shipping and handling costs are 90\ \text{€} per order, its delivery lead time is 12 days (which forces the safety stock to be increased to 250 jugs to avoid stockouts), and it requires a minimum purchase batch of 2.000 jugs per order.

1. a) Calculate the theoretical optimal order quantity for each supplier applying the Wilson model and analyze whether the second supplier's minimum batch restriction constrains the quantity that should be ordered in practice.
2. b) Calculate and compare the total annual cost of both options (annual acquisition cost + annual ordering cost + annual holding cost, considering both cycle stock and the safety stock needed in each case).
3. c) Issue an executive report with your properly justified final decision: rule on whether the discount offsets the increase in logistics costs and warn of two strategic or quality risks that must be assessed before changing suppliers.

An electrical supplies distributor records the following transactions for its flagship product during the first quarter:

• Beginning inventory: 10 units at 60\ \text{€}/unit.

• January 15: purchase of 20 units at 66\ \text{€}/unit.

• February 2: sale of 18 units at 95\ \text{€}/unit.

• February 20: purchase of 12 units at 76\ \text{€}/unit.

• March 10: sale of 20 units at 105\ \text{€}/unit.

When performing the physical stock count at the end of the quarter, the warehouse manager finds that only 3 usable units remain, as 1 unit suffered accidental, irreparable damage that had not been recorded in the accounts.

1. a) Prepare the stock card applying the WAP and FIFO methods up to the last sale, determine the theoretical inventory value, and quantify the economic loss from the damaged unit according to each method.
2. b) Calculate the gross commercial margin obtained in the quarter under each method (sales revenue minus cost of goods sold) and explain how the choice of method impacts current assets on the balance sheet.
3. c) Knowing that the company forecasts annual sales of 160 units and that the annual holding cost represents 15\\ % of the average inventory value: if through improved management inventory turnover increases from 4 to 8 times per year, calculate the new average stock (in units and in euros, using the last WAP) and quantify the annual financial savings achieved in holding costs.

Unit challenge. Imagine that you are launching a microenterprise of healthy energy bars for your school. Design your production proposal by completing these phases:

1. Creativity: Generate 5 innovative product ideas (divergence) and select the final one using a convergence matrix with three weighted criteria.

2. Cost structure: Look up yesterday's electricity price ($€/\text{kWh}$) on the Red Eléctrica de España (REE) website and check the price of ingredients in an online supermarket. Classify costs into fixed ($CF$) and variable ($CV$), and calculate the total cost ($CT$) and average cost ($CMe$) for a batch of $100$ units.

3. Procurement and inventories: For the main perishable ingredient, assume a demand of $400$ bars per month and establish, with justification, the safety stock and the reorder point to avoid stockouts without creating spoilage.

Submit a one-page executive report with your cost tables and operational decisions.

Evaluation criteria:

• Methodological rigour in the divergence and convergence phases.

• Correctness in the classification and numerical calculation of $CF$, $CV$, and $CMe$ from real sources.

• Technical-economic consistency when setting the safety stock and reorder point.