- 20 Marks
PM – May 2021 – L2 – Q5 – Decision-Making Techniques
Calculate the optimal order quantity to maximize expected profits considering ordering constraints and probability distribution of demand.
Question
A national boutique chain sells a wide range of high-quality customized fashion goods. One particular outfit is bought at ₦8,000 and sold at ₦13,000. Mean holding costs per season per outfit are ₦500, and it costs ₦80,000 to order and receive goods in stock. The manufacturers require orders in advance, and once a batch is made, it is impossible to place a repeat order. Additionally, delivery cannot be staggered over the fashion season.
When a customer buys an outfit that requires adjustments, alterations are made, and the customer collects it later. Generally, if an outfit is out of stock at one boutique, it can be obtained from another branch within hours. However, if the chain as a whole runs out of stock, it loses both the outfit’s profit and an estimated ₦2,000 profit from additional items customers typically buy. If excess stock remains at season’s end, it is disposed of at ₦5,000 per outfit.
The sales pattern for a comparable outfit indicates the following probability distribution for total chain sales:
| Outfits Sold | Probability |
|---|---|
| 1,100 | 0.30 |
| 1,200 | 0.40 |
| 1,300 | 0.20 |
| 1,400 | 0.10 |
The management accountant must determine the optimal order quantity for the upcoming season to maximize expected profit, factoring in overstocking and understocking costs.
Required:
a) Determine the number of outfits to order to maximize expected profits.
(17 Marks)
b) Compare and contrast the model developed with the classical Economic Order Quantity (EOQ) model.
(3 Marks)
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