An event manager reserves rooms at a nearby hotel for an annual meeting. The meeting is arranged at a prime location in the city, where hotels are generally expensive and fully booked, so he doesn’t want to risk waiting until the last moment. He has invited managers from other locations.

- If he reserves rooms now, he'll spend Rs. 1500 per room at an offer price.
- From his past experience with previous meetings, he expects an average attendance of 40, with a standard deviation of 8.
- If he cancels any booked room, a refund will be made after deducting Rs. 750.
- If he decides to book after receiving last-minute confirmations, he’ll find some rooms around the wedding hall at Rs. 2000 per room.

What should be the number of rooms he should book now?

the number of rooms the event manager should book now is the average expected demand plus the safety stock: 40 + 14 = 54 rooms. determine the number of rooms the event manager should book now, we need to consider the expected demand, cancellation costs, and the cost of booking at the last moment.

Given that the average expected demand is 40 rooms with a standard deviation of 8, we can calculate the safety stock using the desired service level and the lead time demand variability.

Considering the cancellation cost of Rs. 750 per room, we can calculate the effective holding cost as follows: Effective Holding Cost = Holding Cost - Cancellation Cost = Rs. 1500 - Rs. 750 = Rs. 750.

To calculate the safety stock, we can use the formula: Safety Stock = Z * σ, where Z is the Z-score corresponding to the desired service level and σ is the standard deviation.

Assuming a service level of 95% (corresponding to a Z-score of 1.645), the safety stock is 1.645 * 8 = 13.16 (rounding up to 14 rooms).

Therefore, the number of rooms the event manager should book now is the average expected demand plus the safety stock: 40 + 14 = 54 rooms.

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