M451 Supply Chain Management- Tutorial 3
AssignmentTutorOnline
Dr Banafsheh Khosravi
Discrete and Continuous News Vendor models
- A furniture shop sells wardrobes. The cost of purchasing a wardrobe is 1800 and the sale price is 2500. If a wardrobe cannot be sold after Christmas holiday, its sale price drops to 1700. Calculate the wardrobe shortage and overage cost. If the demand distribution is given as below.
- What are the shortage and overage costs?
- What is probability of demand to be equal to 130?
- What is probability of demand to be less than or equal to 140?
- What is probability of demand to be greater than 140?
- What is probability of demand to be greater than or equal to 140?
- What is the average demand?
- A student has obtained the concession for picnic lunch boxes at a local football club. The demand for lunch boxes follows a probability distribution given on the table below.
| Demand D | P (D = d) |
| 10 | 0.10 |
| 20 | 0.10 |
| 30 | 0.30 |
| 40 | 0.30 |
| 50 | 0.10 |
| 60 | 0.10 |
The lunch boxes cost £3 each and are sold at £5. Any lunch boxes left over can be disposed for £0.5 each.
Determine the order quantity to maximise profit. Calculate the maximum profit.
- A company needs to order a daily amount of a fresh food product. The estimated demand follows a normal distribution with a mean of 150 items and a standard deviation of 40 items. The cost of not supplying one unit of demand is estimated at £0.35 and any unsold items must be discarded, resulting in an average cost of £0.50 per unsold item.
How many items should be ordered each day to minimise costs?
- A company needs to determine how many pianos to manufacture for the next three months planning period. The demand for pianos is believed to follow a normal distribution with a mean of 250 pianos and a standard deviation of 90 pianos. Any piano that is made but unsold incurs extra holding costs of £300. The estimated cost of not supplying a piano when there is demand for one is estimated at £450.
i) How many pianos should be manufactured to minimise costs?
ii) What is the probability of having 20 more pianos left over at the end of the planning period under the solution found in part (i)?
