Chapter 6, Problem 5P

The Swanky Hotel provides room service for its guests. The process for room service begins with a room service manager who takes orders by phone at an average of 2 minutes per order. The manager then sends the order to the kitchen, where it takes a cook an average of 16 minutes to prepare the food for each order. There are four cooks in the kitchen. If the customer orders a beverage, the room service manager sends the order to the bar at the same time the order is sent to the kitchen. It takes 3 minutes for a bartender to fill the order, and so percent of the orders require a beverage. When the kitchen and bar orders are both ready, a waiter takes them to the room and bills the guest. There are six waiters to provide the service, and each order takes 20 minutes for the waiter to complete.

1. a. What is the capacity of the process, and what is the bottleneck?
2. b. What is the throughput time of a typical order?
3. c. Assume that on Friday evenings an average of 10 room-service orders per hour are placed. How many orders are in the system on average on Friday nights?

Summary Introduction

To determine: The capacity of the process.

Introduction:

Flow rate is the number of flow units through a business procedure per unit time. Flow rate refers to the number of customers who will be served per hour or the parts produced per minute.

Explanation of Solution

Given information:

Hotel S provides room service for its guests. The process starts at the room, where the guest would place the order through phone. It takes 2 minutes to receive the order by phone, which is taken by the room service manager. The order will be sent to the kitchen and it takes 16 minutes to prepare the food. There are four cooks in the kitchen.

If the guest orders a beverage along with the food, the order details will be sent to the bar at the same time as it is sent to the kitchen. 80 percent of the order comes with beverages. It takes 3 minutes to fill the order in the bar. There are six waiters and it takes 20 minutes to complete the order.

Determine the capacity:

The capacity of the service manager is 30 orders per hour (2 minutes per order).

Determine the capacity of the chefs:

The capacity of Person J’s assistant is 7 minutes per customers (it includes 2 minutes of receiving the order, 2 minutes of packing, and 3 minutes of billing).

$\begin{array}{c}\text{Orders per hour}=\text{Number of chef}\times \left(\frac{\text{Minutes per hour}}{\text{Minutes taken per customer by chefs}}\right)\\ =4\times \left(\frac{60\text{}\text{ minutes per hour}}{16\text{ minutes per customer}}\right)\\ =15\text{ orders per hour}\end{array}$

Hence, the chefs can handle 15 orders per hour and the bartender can handle 20 orders per hour (as he takes 3 minutes to fill).

Determine the capacity of waiter:

$\begin{array}{c}\text{Orders per hour}=\text{Number of waiter}\times \left(\frac{\text{Minutes per hour}}{\text{Minutes taken per customer by waiters}}\right)\\ =6\times \left(\frac{60\text{}\text{ minutes per hour}}{20\text{ minutes per customer}}\right)\\ =18\text{ orders per hour}\end{array}$

Hence, the waiters can handle 18 orders per hour.

Note: As the capacity of bartender (20 orders per hour) is more than the capacity of the kitchen (15 orders per hour), bar is not a constraint. Hence, kitchen is the bottleneck.

Summary Introduction

To determine: The average throughput time.

Introduction:

Flow rate is the number of flow units through a business procedure per unit time. Flow rate refers to the number of customers who will be served per hour or the parts produced per minute.

Explanation of Solution

Given information:

Hotel S provides room service for its guests. The process starts at the room, where the guest would place the order through phone. It takes 2 minutes to receive the order by phone, which is taken by the room service manager. The order will be sent to the kitchen and it takes 16 minutes to prepare the food. There are four cooks in the kitchen.

If the guest orders a beverage along with the food, the order details will be sent to the bar at the same time as it is sent to the kitchen. 80 percent of the order comes with beverages. It takes 3 minutes to fill the order in the bar. There are six waiters and it takes 20 minutes to complete the order.

Determine the average throughput time:

Average throughput time is the average of the time taken to receive and deliver the order. The bar time of 3 minutes is not considered, as it is done parallelly.

$\begin{array}{c}\text{Average throughput time}=\text{Time taken to receive and deliver the order}\\ =2+16+20\\ =38\text{ minutes}\end{array}$

Hence, the average throughput time is 38 minutes.

Summary Introduction

To determine: The number of orders in the system.

Introduction:

Flow rate is the number of flow units through a business procedure per unit time. Flow rate refers to the number of customers who will be served per hour or the parts produced per minute.

Explanation of Solution

Given information:

Hotel S provides room service for its guests. The process starts at the room, where the guest would place the order through phone. It takes 2 minutes to receive the order by phone, which is taken by the room service manager. The order will be sent to the kitchen and it takes 16 minutes to prepare the food. There are four cooks in the kitchen.

If the guest orders a beverage along with the food, the order details will be sent to the bar at the same time as it is sent to the kitchen. 80 percent of the order comes with beverages. It takes 3 minutes to fill the order in the bar. There are six waiters and it takes 20 minutes to complete the order. There is an average of 10 room-service placed on Friday evenings.

Formula to determine the average number of orders in the system:

$\text{I}=\text{T}\times \text{R}$

Here

I refers to the number of orders in the systems.

T refers to the average throughout time.

R refers to the average flow rate in the process.

Determine the average number of orders in the system:

It calculated by multiplying the average throughput time with the average flow rate in the process.

$\begin{array}{c}\text{I}=\text{T}\times \text{R}\\ =\left(\frac{38}{60}\right)\times 10\\ =0.6333\times 10\\ =6.33\text{ orders}\end{array}$

Hence, the average number of orders in the system is 6.33 orders.

Summary Introduction

To determine: The average cost of an order and the minimum cost per order.

Introduction:

Flow rate is the number of flow units through a business procedure per unit time. Flow rate refers to the number of customers who will be served per hour or the parts produced per minute.

Explanation of Solution

Given information:

Hotel S provides room service for its guests. The process starts at the room, where the guest would place the order through phone. It takes 2 minutes to receive the order by phone, which is taken by the room service manager. The order will be sent to the kitchen and it takes 16 minutes to prepare the food. There are four cooks in the kitchen.

If the guest orders a beverage along with the food, the order details will be sent to the bar at the same time as it is sent to the kitchen. 80 percent of the order comes with beverages. It takes 3 minutes to fill the order in the bar. There are six waiters and it takes 20 minutes to complete the order.

Additional information:

Waiters are paid $9 per hour and the chefs are paid $15 per hour. The room service manager is paid $18 per hour and the bartender is paid $10 per hour. The cost of beverages and food averages $6 per order and assume that 60 percent overhead is added to the direct labor.

Determine the total labor costs:

Labor cost can be calculated by multiplying the number of labors and the amount paid to labors per hour. If the overhead is added, the total cost is 227.20 (142+(142×0.6).

Hence, the labor cost per order including overhead is $22.70 per orders when the number of order is 10 orders per hour.

Hence, the average cost per order is $28.70 (sum of labor cost per order and the food and beverage cost).

Determine the minimum cost per order:

It is calculated by adding the value attained by dividing the total labor cost including overhead by the capacity of the chefs to the food beverage cost.

$\begin{array}{c}\text{Minimum cost per order}=\text{Food and beverage cost}+\frac{\text{Total labor cost inclulding overhead}}{\text{Capacity of the chefs}}\\ =\$6+\frac{227.2}{15}\\ =\$6+\$15.15\\ =\$21.15\end{array}$

Hence, the minimum cost per order is $21.15.

Summary Introduction

To determine: The assumptions that are made in the calculations which are not reasonable.

Introduction:

Flow rate is the number of flow units through a business procedure per unit time. Flow rate refers to the number of customers who will be served per hour or the parts produced per minute.

Explanation of Solution

Given information:

Hotel S provides room service for its guests. The process starts at the room, where the guest would place the order through phone. It takes 2 minutes to receive the order by phone, which is taken by the room service manager. The order will be sent to the kitchen and it takes 16 minutes to prepare the food. There are four cooks in the kitchen.

If the guest orders a beverage along with the food, the order details will be sent to the bar at the same time as it is sent to the kitchen. 80 percent of the order comes with beverages. It takes 3 minutes to fill the order in the bar. There are six waiters and it takes 20 minutes to complete the order.

Determine the assumptions that are made in the calculations which are not reasonable:

The assumption that is made in the calculations which is not reasonable is the notion of using the resources fully. In addition, there were no worker breaks, no missing ingredients, and no kitchen downtime. It is also assumed that there is no variation in the flow rates.