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: aluminum 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.

A furniture shop sells 2 000 bookcases of the same model per year. Each order to the supplier costs $\$10$ including transport and administration, and holding one bookcase in the warehouse costs $\$1$ per year. Wilson's Economic Order Quantity (EOQ) model gives the optimal order quantity: $Q = \sqrt{\frac{2 \times D \times K}{g}}$, 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 $\$80$ each; then it purchases 200 coils at $\$140$ 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 $\$9$ per unit or manufacture itself by incurring annual fixed costs of $\$42,000$ and a variable cost per unit of $\$3$. 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.

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{ pesos}/unit.

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

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

• Industrial screws: 50 000 units/year at 0.10\ \text{ pesos}/unit.

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

• Work gloves: 4 000 pairs/year at 1.50\ \text{ pesos}/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{ pesos} per day and contractual delay penalties of 120 000\ \text{ pesos}.

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{ pesos}/bag. The administrative and transport cost of placing each order is 25\ \text{ pesos}, and the annual holding cost of each bag is estimated at 2\ \text{ pesos}. 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{ pesos} 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?