Tutorial 7 Exercises
Question 1
Prefab, a furniture manufacturer, uses 20,000 square feet of plywood per month. Their trucking company charges Prefab $400 per shipment, independent of the quantity purchased. The manufacturer offers an all-unit quantity discount:
| Order Quantity | Price per sq ft |
|---|---|
| Less than 20,000 | $1.00 |
| 20,000–40,000 | $0.98 |
| More than 40,000 | $0.96 |
Prefab incurs a holding cost of 20% per unit per year.
- What is the optimal lot size for Prefab?
- What is the annual cost of such a policy?
- What is the cycle inventory of plywood at Prefab?
- How does it compare with the cycle inventory if the manufacturer does not offer a quantity discount but sells all plywood at $0.96 per square foot?
Working Table
| Price Tier | Quantity Range | Price | \(h\) | \(q_i\) | \(Q\) | \(Q\) Adjust | \(TC\) |
|---|---|---|---|---|---|---|---|
| 1 | < 20,000 | $1.00 | |||||
| 2 | 20,000–40,000 | $0.98 | |||||
| 3 | > 40,000 | $0.96 |
Question 2
Reconsider Question 1. The manufacturer now offers a marginal unit quantity discount:
- First 20,000 sq ft: $1.00
- Next 20,000 sq ft: $0.98
- Quantity over 40,000 sq ft: $0.96
- What is the optimal lot size for Prefab given this pricing structure?
- How much cycle inventory of plywood will Prefab carry?
Working Table
| Price Tier | Quantity Range | Price | \(h\) | \(q_i\) | \(R_i\) | \(Q\) | \(Q\) Adjust | \(TC\) |
|---|---|---|---|---|---|---|---|---|
| 1 | First 20,000 | $1.00 | ||||||
| 2 | 20,000–40,000 | $0.98 | ||||||
| 3 | Over 40,000 | $0.96 |
Question 3
Amazon Online (AO) is a retailer of prescription OTC drugs online. Vitamins represent a significant percentage of its sales.
- Demand: 10,000 bottles/month
- Fixed ordering, transportation, and receiving cost: $100 per order
- Holding cost: 20%
- All-unit discount schedule:
| Order Quantity | Unit Price |
|---|---|
| 0–5,000 | $3.00 |
| 5,000–10,000 | $2.96 |
| 10,000 or more | $2.92 |
Evaluate the number of bottles that AO should order in each lot under:
- Average (All-Unit) Quantity Discount
| \(i\) | Order Quantity | \(q\) | \(C\) | \(i\)th Lot Size | Feasible? | \(Q\) Adjust | \(TC\) |
|---|---|---|---|---|---|---|---|
| 0 | 0–5,000 | 0 | $3.00 | ||||
| 1 | 5,000–10,000 | 5,000 | $2.96 | ||||
| 2 | 10,000 or more | 10,000 | $2.92 |
- Marginal Unit Quantity Discount
| \(i\) | Order Quantity | \(q\) | \(C\) | \(V\) | \(Q_i\) | Feasible? | \(TC\) |
|---|---|---|---|---|---|---|---|
| 0 | 0–5,000 | 0 | $3.00 | ||||
| 1 | 5,000–10,000 | 5,000 | $2.96 | ||||
| 2 | 10,000 or more | 10,000 | $2.92 |
Question 4
Crunchy, a cereal manufacturer, has dedicated a plant for one major retail chain.
- Retail sales: 20,000 boxes/month
- Production keeps pace with demand
- Cost per box: $3
- Wholesale price: $5
- Holding cost: 20% for both parties
- Retailer ordering cost: $200/order
- Crunchy transportation and loading cost: $1,000/order
- Given that it is trying to minimise its ordering and holding cost:
- What lot size will the retailer ask for?
- What is the retailer’s annual ordering and holding cost?
- What is Crunchy’s annual ordering and holding cost?
- What is the total inventory cost across both parties?
- What lot size minimises total inventory costs (ordering, delivery, and holding) across both parties?
- How much cost reduction relative to part (a) results from this policy?
Question 5
Sun.com sells three models of solar panels:
| Model | Annual Demand |
|---|---|
| Polar Panel | 12,000 |
| PV Polar Panel | 1,200 |
| Off-Grid Polar Panel | 120 |
Additional data:
- Unit cost: $500
- Transportation cost per delivery: $4,000
- Additional receiving/storage cost per model on the same truck: $1,000
- Holding cost: 20%
Tasks:
- Evaluate the optimal lot size for each model.
- Evaluate the annual cost of such a policy.
- How many packs should Sun.com produce in each batch?
Three models are ordered and delivered independently.
All three models are aggregated and ordered together.
Question 6
FB HiFi sells three computer models:
| Product | Annual Demand | Unit Cost |
|---|---|---|
| LAPTOP | 5,000 | $800 |
| DESKTOP | 500 | $500 |
| TABLET | 500 | $100 |
Additional data:
- Transportation cost per delivery: $2,000
- Receiving/storage cost per model on the same truck: $500
- Holding cost: 20%
Evaluate optimal lot sizes, order frequency, and annual inventory-related cost for:
Lots for each product are ordered and delivered independently.
All three models are included each time an order is placed.
Some products are ordered jointly.