Question

Agan Interior Design provides home and office decorating assistance to its customers. In normal operation, an average of 2.3 customers arrive each hour. One design consultant is available to answer customer questions and make product recommendations. The consultant averages 12 minutes with each customer. Agan's management would like to evaluate two alternatives:

1. Use one consultant with an average service time of 9 minutes per customer.
2. Expand to two consultants, each of whom has an average service time of 12 minutes per customer. If the consultants are paid $15 per hour and the customer waiting time is valued at $24 per hour, should Agan expand to the two-consultant system? Explain.

Answer 1

Agan Interior Design should not expand to the two-consultant system.

Step-by-step explanation:

Agan Interior Design is considering two alternatives to improve customer service: using one consultant with a shorter average service time or expanding to two consultants with the same average service time. To evaluate these options, we need to consider the cost and value of customer waiting time.

Firstly, let's calculate the average number of customers served per hour for each alternative. For the current setup, with one consultant spending 12 minutes per customer, the consultant serves (60 minutes/12minutes per customer} = 5) customers per hour. In the first alternative, with a shorter service time of 9 minutes per customer, the consultant serves (60 minutes/9 , minutes per customer approx 6.67) customers per hour. For the second alternative, with two consultants spending 12 minutes per customer, each consultant serves (60 minutes /12 minutes per customer} = 5) customers per hour. As the number of customers served is higher in the first alternative, it is more efficient.

Next, we need to consider the cost of service. In the current setup, one consultant is paid for the entire hour, resulting in a cost of \(1 \times $15 = $15\) per hour. In the first alternative, the cost remains the same as there is still only one consultant. In the second alternative, with two consultants, the cost is (2 \times $15 = $30\) per hour.

Now, let's consider the value of customer waiting time. With the current setup, the waiting time per customer is (60 minutes / 2.3 , customers} = 26.09) minutes. In the second alternative, with two consultants, the waiting time per customer remains the same, as the number of consultants does not affect the arrival rate of customers.

Considering both the cost and the waiting time, the first alternative is more cost-effective for Agan Interior Design. Therefore, expanding to the two-consultant system is not recommended.